C
C.Benham
Sat, May 25, 2019 2:31 PM
There are several Condorcet algorithms that decide the winner by
weighing "defeat strengths" and they
are all equivalent to MinMax when there are no more than 3 candidates.
The ones I have in mind that are equal or very nearly equal in merit are
River, Schulze, Ranked Pairs, Smith//MinMax.
In public political elections they are very very unlikely to give
different winners. River and Smith//MinMax seem to me
to be the easiest to understand and explain and use. The other two are
perhaps a bit more elegant and have their
enthusiastic supporters.
This is to make the case that measuring pairwise defeat strength by the
number of votes on the losing side with above-bottom
equal-ranking contributing a whole vote to each side (and otherwise as
with normal Winning Votes) is much better than either
Winning Votes or Margins.
The case for Losing Votes(erw) against Margins is that it (in common
with WV) it meets the Plurality criterion and the Non-Drastic
Defense criterion.
The case for Losing Votes(erw) against Winning Votes is that it meets
the Chicken Dilemma criterion and that is much less likely
to fail to elect a positionally dominant uncovered candidate. (I don't
see how it can fail to elect such a candidate in the 3-candidate case.)
For those who think that Margins might be acceptable:
46: A
44: B>C
10: C
A>B 46-44 (margin=2), B>C 44-10 (margin=34), C>A 54-46 (margin=8).
Using Losing Votes (erw) as the measure of defeat strength, the weakest
defeat is the one with the most votes on the losing side.
That is the C>A defeat so MinMax drops that and A wins. Conversely the
strongest defeat is the one with the fewest votes on the
losing side. That is the B>C defeat so River and Ranked Pairs lock
that. The second strongest is the A>B defeat so those methods
also lock that. All but one candidate has been thereby disqualified so B
wins, or we ignore the third pairwise defeat because that
makes a cycle, so give a final order A>B>C and A wins.
To meet both of the Plurality criterion and the Chicken Dilemma
criterion A must win.
Winning Votes elects C, violating Chicken Dilemma (which it has to do to
meet the previously fashionable Minimal Defense criterion).
Margins elects B. This fails the Plurality criterion because A has more
exclusive first-place votes than B has any sort of above-bottom
votes. It is also an egregious and outrageous failure of Later-no-Help
(assuming that if all the ballots just vote for one candidate we
elect the plurality winner).
To anyone who is remotely positionally or strategically minded or has
any common sense and isn't blind to everything except the
Margins pairwise matrix, B is clearly the weakest candidate and a
completely unacceptable winner.
35: A
10: A=B
30: B>C
25: C
A>B 45-40 (erw, "normally" 35-30, margin=5), B>C 40-25 (margin=15),
C>A 55-45 (margin=10).
Voted at least equal-top (or Top Ratings) scores: A45, B40, C25.
Voted above bottom (or Approval) scores: A45, B40, C55
An old Kevin Venzke example. B is neither the most top-rated candidate
or the most approved candidate and is
pairwise-beaten and positionally dominated by A (the most top-rated).
Winning Votes and Margins both elect the clearly weakest candidate, B.
Losing Votes(erw) elects A.
For those who prefer to have a method comply with Minimal Defense (which
says that if on more than half the ballots
C is voted above A and A no higher than equal-bottom then A can't win)
rather than Chicken Dilemma another method
I prefer to WV is Smith//Approval which here elects C.
25: A>B
26: B>C
23: C>A
26: C
C>A 75-25 (margin=50), A>B 48-26 (margin=22), B>C 51-49 (margin=2).
Voted at least equal-top (or Top Ratings) scores: C49, B26, A25.
Voted above bottom (or Approval) scores: C75, B51, A48.
C is an overwhelmingly positionally dominant uncovered candidate.
Margins and Losing Votes elect C.
WV and IRV elect B.
Now say we change 4 of the 26 C ballots to A>C, thereby making C a bit
weaker.
25: A>B
26: B>C
23: C>A
22: C
04: A>C
C>A 71-29 (margin=42), A>B 52-26 (margin=26), B>C 51-49 (margin=2).
Voted at least equal-top (or Top Ratings) scores: C45, B26, A29.
Voted above bottom (or Approval) scores: C75, B51, A52.
The weakening of C has caused WV and IRV to change from B to C, now
agreeing with LV and Margins.
Assuming the change was from sincere to insincere, those very lucky
and/or very well informed 4 voters
have pulled off a Push-over strategy.
This is a failure of Mono-raise-delete (more obvious if we reverse the
order of the two situations), which
is one of Woodall's mononicity criteria that he says is incompatible
with Condorcet.
Nonetheless in this case C is still the positionally dominant uncovered
candidate and Losing Votes (erw)
and Margins both still elect C.
Steve Eppley's old example to illustrate (I think his) Non-Drastic
Defense criterion, which says that if
on more than half the ballots B is voted no lower than equal-top and
above A then A can't win.
46: A>C (sincere may be A>B)
10: B>A
10: B>C
34: C=B (the "defenders", sincere may be C>B)
B>A 54-46 (m=8), A>C 56-44 (m=12), C>B (80-54 erw, "normally" 46-20, m=26).
Voted at least equal-top (or Top Ratings) scores: B54, A46, C34.
Voted above bottom (or Approval) scores: B54, A56, C90.
B is the only candidate top-rated on more than half the ballots. More
than half the voters voted B
above A and B not lower than equal-top. Margins and Losing Votes
without my recommended
"above-bottom equal-ranking whole" bit elect A, violating the
Non-Drastic Defense criterion.
Losing Votes (erw) and WV elect B.
If anyone has some counter-examples where they think that Winning Votes
does better than
Losing Votes (erw), I'd be interested in seeing them.
Chris Benham
This email has been checked for viruses by AVG.
https://www.avg.com
There are several Condorcet algorithms that decide the winner by
weighing "defeat strengths" and they
are all equivalent to MinMax when there are no more than 3 candidates.
The ones I have in mind that are equal or very nearly equal in merit are
River, Schulze, Ranked Pairs, Smith//MinMax.
In public political elections they are very very unlikely to give
different winners. River and Smith//MinMax seem to me
to be the easiest to understand and explain and use. The other two are
perhaps a bit more elegant and have their
enthusiastic supporters.
This is to make the case that measuring pairwise defeat strength by the
number of votes on the losing side with above-bottom
equal-ranking contributing a whole vote to each side (and otherwise as
with normal Winning Votes) is much better than either
Winning Votes or Margins.
The case for Losing Votes(erw) against Margins is that it (in common
with WV) it meets the Plurality criterion and the Non-Drastic
Defense criterion.
The case for Losing Votes(erw) against Winning Votes is that it meets
the Chicken Dilemma criterion and that is much less likely
to fail to elect a positionally dominant uncovered candidate. (I don't
see how it can fail to elect such a candidate in the 3-candidate case.)
For those who think that Margins might be acceptable:
46: A
44: B>C
10: C
A>B 46-44 (margin=2), B>C 44-10 (margin=34), C>A 54-46 (margin=8).
Using Losing Votes (erw) as the measure of defeat strength, the weakest
defeat is the one with the most votes on the losing side.
That is the C>A defeat so MinMax drops that and A wins. Conversely the
strongest defeat is the one with the fewest votes on the
losing side. That is the B>C defeat so River and Ranked Pairs lock
that. The second strongest is the A>B defeat so those methods
also lock that. All but one candidate has been thereby disqualified so B
wins, or we ignore the third pairwise defeat because that
makes a cycle, so give a final order A>B>C and A wins.
To meet both of the Plurality criterion and the Chicken Dilemma
criterion A must win.
Winning Votes elects C, violating Chicken Dilemma (which it has to do to
meet the previously fashionable Minimal Defense criterion).
Margins elects B. This fails the Plurality criterion because A has more
exclusive first-place votes than B has any sort of above-bottom
votes. It is also an egregious and outrageous failure of Later-no-Help
(assuming that if all the ballots just vote for one candidate we
elect the plurality winner).
To anyone who is remotely positionally or strategically minded or has
any common sense and isn't blind to everything except the
Margins pairwise matrix, B is clearly the weakest candidate and a
completely unacceptable winner.
35: A
10: A=B
30: B>C
25: C
A>B 45-40 (erw, "normally" 35-30, margin=5), B>C 40-25 (margin=15),
C>A 55-45 (margin=10).
Voted at least equal-top (or Top Ratings) scores: A45, B40, C25.
Voted above bottom (or Approval) scores: A45, B40, C55
An old Kevin Venzke example. B is neither the most top-rated candidate
or the most approved candidate and is
pairwise-beaten and positionally dominated by A (the most top-rated).
Winning Votes and Margins both elect the clearly weakest candidate, B.
Losing Votes(erw) elects A.
For those who prefer to have a method comply with Minimal Defense (which
says that if on more than half the ballots
C is voted above A and A no higher than equal-bottom then A can't win)
rather than Chicken Dilemma another method
I prefer to WV is Smith//Approval which here elects C.
25: A>B
26: B>C
23: C>A
26: C
C>A 75-25 (margin=50), A>B 48-26 (margin=22), B>C 51-49 (margin=2).
Voted at least equal-top (or Top Ratings) scores: C49, B26, A25.
Voted above bottom (or Approval) scores: C75, B51, A48.
C is an overwhelmingly positionally dominant uncovered candidate.
Margins and Losing Votes elect C.
WV and IRV elect B.
Now say we change 4 of the 26 C ballots to A>C, thereby making C a bit
weaker.
25: A>B
26: B>C
23: C>A
22: C
04: A>C
C>A 71-29 (margin=42), A>B 52-26 (margin=26), B>C 51-49 (margin=2).
Voted at least equal-top (or Top Ratings) scores: C45, B26, A29.
Voted above bottom (or Approval) scores: C75, B51, A52.
The weakening of C has caused WV and IRV to change from B to C, now
agreeing with LV and Margins.
Assuming the change was from sincere to insincere, those very lucky
and/or very well informed 4 voters
have pulled off a Push-over strategy.
This is a failure of Mono-raise-delete (more obvious if we reverse the
order of the two situations), which
is one of Woodall's mononicity criteria that he says is incompatible
with Condorcet.
Nonetheless in this case C is still the positionally dominant uncovered
candidate and Losing Votes (erw)
and Margins both still elect C.
Steve Eppley's old example to illustrate (I think his) Non-Drastic
Defense criterion, which says that if
on more than half the ballots B is voted no lower than equal-top and
above A then A can't win.
46: A>C (sincere may be A>B)
10: B>A
10: B>C
34: C=B (the "defenders", sincere may be C>B)
B>A 54-46 (m=8), A>C 56-44 (m=12), C>B (80-54 erw, "normally" 46-20, m=26).
Voted at least equal-top (or Top Ratings) scores: B54, A46, C34.
Voted above bottom (or Approval) scores: B54, A56, C90.
B is the only candidate top-rated on more than half the ballots. More
than half the voters voted B
above A and B not lower than equal-top. Margins and Losing Votes
without my recommended
"above-bottom equal-ranking whole" bit elect A, violating the
Non-Drastic Defense criterion.
Losing Votes (erw) and WV elect B.
If anyone has some counter-examples where they think that Winning Votes
does better than
Losing Votes (erw), I'd be interested in seeing them.
Chris Benham
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TP
Toby Pereira
Sun, May 26, 2019 3:34 PM
I think it's a mistake to assume some sort of approval of a ranked candidate. If it's not explicitly part of a method then you should not infer it. As far as I'm concerned:
46: A44: B>C10: C
Is the same as:
46: A>B=C44: B>C>A10: C>A=B
Presented with these ballots, does this change who you think the winner should be?
This isn't a defence of margins by me or an argument against anything else in your post, but I think the plurality criterion, by talking about unranked candidates, is based on false premises.
Toby
On Sat, 25 May 2019 at 15:31, C.Benhamcbenham@adam.com.au wrote: There are several Condorcet algorithms that decide the winner by
weighing "defeat strengths" and they
are all equivalent to MinMax when there are no more than 3 candidates.
The ones I have in mind that are equal or very nearly equal in merit are
River, Schulze, Ranked Pairs, Smith//MinMax.
In public political elections they are very very unlikely to give
different winners. River and Smith//MinMax seem to me
to be the easiest to understand and explain and use. The other two are
perhaps a bit more elegant and have their
enthusiastic supporters.
This is to make the case that measuring pairwise defeat strength by the
number of votes on the losing side with above-bottom
equal-ranking contributing a whole vote to each side (and otherwise as
with normal Winning Votes) is much better than either
Winning Votes or Margins.
The case for Losing Votes(erw) against Margins is that it (in common
with WV) it meets the Plurality criterion and the Non-Drastic
Defense criterion.
The case for Losing Votes(erw) against Winning Votes is that it meets
the Chicken Dilemma criterion and that is much less likely
to fail to elect a positionally dominant uncovered candidate. (I don't
see how it can fail to elect such a candidate in the 3-candidate case.)
For those who think that Margins might be acceptable:
46: A
44: B>C
10: C
A>B 46-44 (margin=2), B>C 44-10 (margin=34), C>A 54-46 (margin=8).
Using Losing Votes (erw) as the measure of defeat strength, the weakest
defeat is the one with the most votes on the losing side.
That is the C>A defeat so MinMax drops that and A wins. Conversely the
strongest defeat is the one with the fewest votes on the
losing side. That is the B>C defeat so River and Ranked Pairs lock
that. The second strongest is the A>B defeat so those methods
also lock that. All but one candidate has been thereby disqualified so B
wins, or we ignore the third pairwise defeat because that
makes a cycle, so give a final order A>B>C and A wins.
To meet both of the Plurality criterion and the Chicken Dilemma
criterion A must win.
Winning Votes elects C, violating Chicken Dilemma (which it has to do to
meet the previously fashionable Minimal Defense criterion).
Margins elects B. This fails the Plurality criterion because A has more
exclusive first-place votes than B has any sort of above-bottom
votes. It is also an egregious and outrageous failure of Later-no-Help
(assuming that if all the ballots just vote for one candidate we
elect the plurality winner).
To anyone who is remotely positionally or strategically minded or has
any common sense and isn't blind to everything except the
Margins pairwise matrix, B is clearly the weakest candidate and a
completely unacceptable winner.
35: A
10: A=B
30: B>C
25: C
A>B 45-40 (erw, "normally" 35-30, margin=5), B>C 40-25 (margin=15),
C>A 55-45 (margin=10).
Voted at least equal-top (or Top Ratings) scores: A45, B40, C25.
Voted above bottom (or Approval) scores: A45, B40, C55
An old Kevin Venzke example. B is neither the most top-rated candidate
or the most approved candidate and is
pairwise-beaten and positionally dominated by A (the most top-rated).
Winning Votes and Margins both elect the clearly weakest candidate, B.
Losing Votes(erw) elects A.
For those who prefer to have a method comply with Minimal Defense (which
says that if on more than half the ballots
C is voted above A and A no higher than equal-bottom then A can't win)
rather than Chicken Dilemma another method
I prefer to WV is Smith//Approval which here elects C.
25: A>B
26: B>C
23: C>A
26: C
C>A 75-25 (margin=50), A>B 48-26 (margin=22), B>C 51-49 (margin=2).
Voted at least equal-top (or Top Ratings) scores: C49, B26, A25.
Voted above bottom (or Approval) scores: C75, B51, A48.
C is an overwhelmingly positionally dominant uncovered candidate.
Margins and Losing Votes elect C.
WV and IRV elect B.
Now say we change 4 of the 26 C ballots to A>C, thereby making C a bit
weaker.
25: A>B
26: B>C
23: C>A
22: C
04: A>C
C>A 71-29 (margin=42), A>B 52-26 (margin=26), B>C 51-49 (margin=2).
Voted at least equal-top (or Top Ratings) scores: C45, B26, A29.
Voted above bottom (or Approval) scores: C75, B51, A52.
The weakening of C has caused WV and IRV to change from B to C, now
agreeing with LV and Margins.
Assuming the change was from sincere to insincere, those very lucky
and/or very well informed 4 voters
have pulled off a Push-over strategy.
This is a failure of Mono-raise-delete (more obvious if we reverse the
order of the two situations), which
is one of Woodall's mononicity criteria that he says is incompatible
with Condorcet.
Nonetheless in this case C is still the positionally dominant uncovered
candidate and Losing Votes (erw)
and Margins both still elect C.
Steve Eppley's old example to illustrate (I think his) Non-Drastic
Defense criterion, which says that if
on more than half the ballots B is voted no lower than equal-top and
above A then A can't win.
46: A>C (sincere may be A>B)
10: B>A
10: B>C
34: C=B (the "defenders", sincere may be C>B)
B>A 54-46 (m=8), A>C 56-44 (m=12), C>B (80-54 erw, "normally" 46-20, m=26).
Voted at least equal-top (or Top Ratings) scores: B54, A46, C34.
Voted above bottom (or Approval) scores: B54, A56, C90.
B is the only candidate top-rated on more than half the ballots. More
than half the voters voted B
above A and B not lower than equal-top. Margins and Losing Votes
without my recommended
"above-bottom equal-ranking whole" bit elect A, violating the
Non-Drastic Defense criterion.
Losing Votes (erw) and WV elect B.
If anyone has some counter-examples where they think that Winning Votes
does better than
Losing Votes (erw), I'd be interested in seeing them.
Chris Benham
This email has been checked for viruses by AVG.
https://www.avg.com
Election-Methods mailing list - see https://electorama.com/em for list info
I think it's a mistake to assume some sort of approval of a ranked candidate. If it's not explicitly part of a method then you should not infer it. As far as I'm concerned:
46: A44: B>C10: C
Is the same as:
46: A>B=C44: B>C>A10: C>A=B
Presented with these ballots, does this change who you think the winner should be?
This isn't a defence of margins by me or an argument against anything else in your post, but I think the plurality criterion, by talking about unranked candidates, is based on false premises.
Toby
On Sat, 25 May 2019 at 15:31, C.Benham<cbenham@adam.com.au> wrote: There are several Condorcet algorithms that decide the winner by
weighing "defeat strengths" and they
are all equivalent to MinMax when there are no more than 3 candidates.
The ones I have in mind that are equal or very nearly equal in merit are
River, Schulze, Ranked Pairs, Smith//MinMax.
In public political elections they are very very unlikely to give
different winners. River and Smith//MinMax seem to me
to be the easiest to understand and explain and use. The other two are
perhaps a bit more elegant and have their
enthusiastic supporters.
This is to make the case that measuring pairwise defeat strength by the
number of votes on the losing side with above-bottom
equal-ranking contributing a whole vote to each side (and otherwise as
with normal Winning Votes) is much better than either
Winning Votes or Margins.
The case for Losing Votes(erw) against Margins is that it (in common
with WV) it meets the Plurality criterion and the Non-Drastic
Defense criterion.
The case for Losing Votes(erw) against Winning Votes is that it meets
the Chicken Dilemma criterion and that is much less likely
to fail to elect a positionally dominant uncovered candidate. (I don't
see how it can fail to elect such a candidate in the 3-candidate case.)
For those who think that Margins might be acceptable:
46: A
44: B>C
10: C
A>B 46-44 (margin=2), B>C 44-10 (margin=34), C>A 54-46 (margin=8).
Using Losing Votes (erw) as the measure of defeat strength, the weakest
defeat is the one with the most votes on the losing side.
That is the C>A defeat so MinMax drops that and A wins. Conversely the
strongest defeat is the one with the fewest votes on the
losing side. That is the B>C defeat so River and Ranked Pairs lock
that. The second strongest is the A>B defeat so those methods
also lock that. All but one candidate has been thereby disqualified so B
wins, or we ignore the third pairwise defeat because that
makes a cycle, so give a final order A>B>C and A wins.
To meet both of the Plurality criterion and the Chicken Dilemma
criterion A must win.
Winning Votes elects C, violating Chicken Dilemma (which it has to do to
meet the previously fashionable Minimal Defense criterion).
Margins elects B. This fails the Plurality criterion because A has more
exclusive first-place votes than B has any sort of above-bottom
votes. It is also an egregious and outrageous failure of Later-no-Help
(assuming that if all the ballots just vote for one candidate we
elect the plurality winner).
To anyone who is remotely positionally or strategically minded or has
any common sense and isn't blind to everything except the
Margins pairwise matrix, B is clearly the weakest candidate and a
completely unacceptable winner.
35: A
10: A=B
30: B>C
25: C
A>B 45-40 (erw, "normally" 35-30, margin=5), B>C 40-25 (margin=15),
C>A 55-45 (margin=10).
Voted at least equal-top (or Top Ratings) scores: A45, B40, C25.
Voted above bottom (or Approval) scores: A45, B40, C55
An old Kevin Venzke example. B is neither the most top-rated candidate
or the most approved candidate and is
pairwise-beaten and positionally dominated by A (the most top-rated).
Winning Votes and Margins both elect the clearly weakest candidate, B.
Losing Votes(erw) elects A.
For those who prefer to have a method comply with Minimal Defense (which
says that if on more than half the ballots
C is voted above A and A no higher than equal-bottom then A can't win)
rather than Chicken Dilemma another method
I prefer to WV is Smith//Approval which here elects C.
25: A>B
26: B>C
23: C>A
26: C
C>A 75-25 (margin=50), A>B 48-26 (margin=22), B>C 51-49 (margin=2).
Voted at least equal-top (or Top Ratings) scores: C49, B26, A25.
Voted above bottom (or Approval) scores: C75, B51, A48.
C is an overwhelmingly positionally dominant uncovered candidate.
Margins and Losing Votes elect C.
WV and IRV elect B.
Now say we change 4 of the 26 C ballots to A>C, thereby making C a bit
weaker.
25: A>B
26: B>C
23: C>A
22: C
04: A>C
C>A 71-29 (margin=42), A>B 52-26 (margin=26), B>C 51-49 (margin=2).
Voted at least equal-top (or Top Ratings) scores: C45, B26, A29.
Voted above bottom (or Approval) scores: C75, B51, A52.
The weakening of C has caused WV and IRV to change from B to C, now
agreeing with LV and Margins.
Assuming the change was from sincere to insincere, those very lucky
and/or very well informed 4 voters
have pulled off a Push-over strategy.
This is a failure of Mono-raise-delete (more obvious if we reverse the
order of the two situations), which
is one of Woodall's mononicity criteria that he says is incompatible
with Condorcet.
Nonetheless in this case C is still the positionally dominant uncovered
candidate and Losing Votes (erw)
and Margins both still elect C.
Steve Eppley's old example to illustrate (I think his) Non-Drastic
Defense criterion, which says that if
on more than half the ballots B is voted no lower than equal-top and
above A then A can't win.
46: A>C (sincere may be A>B)
10: B>A
10: B>C
34: C=B (the "defenders", sincere may be C>B)
B>A 54-46 (m=8), A>C 56-44 (m=12), C>B (80-54 erw, "normally" 46-20, m=26).
Voted at least equal-top (or Top Ratings) scores: B54, A46, C34.
Voted above bottom (or Approval) scores: B54, A56, C90.
B is the only candidate top-rated on more than half the ballots. More
than half the voters voted B
above A and B not lower than equal-top. Margins and Losing Votes
without my recommended
"above-bottom equal-ranking whole" bit elect A, violating the
Non-Drastic Defense criterion.
Losing Votes (erw) and WV elect B.
If anyone has some counter-examples where they think that Winning Votes
does better than
Losing Votes (erw), I'd be interested in seeing them.
Chris Benham
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CB
Chris Benham
Sun, May 26, 2019 5:08 PM
Toby,
You would like this old online ranked-ballot voting calculator:
https://www.cse.wustl.edu/~legrand/rbvote/calc.html
What do you think are the "false premises" that the Plurality criterion
is based on??? It was coined with the assumption
that voters could only strictly rank from the top however many
candidates they wish, and those not truncated had in
some sense been "voted for". It says that if A has more first-place
votes than B has any sort of votes then B can't win.
No explicit mention of "unranked candidates".
(Adapting it to ballots that allow equal-ranking at the top, "first
preferences" refers to first-preference score on the
ballots symmetrically completed, at least at the top, ballots).
To sensibly claim that it is a "mistake" for an algorithm to do (or
apparently "assume") something, I think you need to
point to something wrong with an actual result of it doing so.
My answer to your question is no.
Chris Benham
On 27/05/2019 1:04 am, Toby Pereira wrote:
I think it's a mistake to assume some sort of approval of a ranked
candidate. If it's not explicitly part of a method then you should not
infer it. As far as I'm concerned:
46: A
44: B>C
10: C
Is the same as:
46: A>B=C
44: B>C>A
10: C>A=B
Presented with these ballots, does this change who you think the
winner should be?
This isn't a defence of margins by me or an argument against anything
else in your post, but I think the plurality criterion, by talking
about unranked candidates, is based on false premises.
Toby
On Sat, 25 May 2019 at 15:31, C.Benham
<cbenham@adam.com.au> wrote:
There are several Condorcet algorithms that decide the winner by
weighing "defeat strengths" and they
are all equivalent to MinMax?? when there are no more than 3
candidates.
The ones I have in mind that are equal or very nearly equal in
merit are
River, Schulze, Ranked Pairs, Smith//MinMax.
In public political elections they are very very unlikely to give
different winners. River and Smith//MinMax seem to me
to be the easiest to understand and explain and use. The other two
are
perhaps a bit more elegant and have their
enthusiastic supporters.
This is to make the case that measuring pairwise defeat strength
by the
number of votes on the losing side with above-bottom
equal-ranking contributing a whole vote to each side (and
otherwise as
with normal Winning Votes) is much better than either
Winning Votes or Margins.
The case for Losing Votes(erw)?? against Margins is that it (in common
with WV) it meets the Plurality criterion and the Non-Drastic
Defense criterion.
The case for Losing Votes(erw) against Winning Votes is that it meets
the Chicken Dilemma criterion and that is much less likely
to fail to elect a positionally dominant uncovered candidate. (I
don't
see how it can fail to elect such a candidate in the 3-candidate
case.)
For those who think that Margins might be acceptable:
46: A
44: B>C
10: C
A>B 46-44 (margin=2),???? B>C 44-10 (margin=34),???? C>A 54-46 (margin=8).
Using Losing Votes (erw) as the measure of defeat strength, the
weakest
defeat is the one with the most votes on the losing side.
That is the C>A defeat so MinMax drops that and A wins. Conversely
the
strongest defeat is the one with the fewest votes on the
losing side.?? That is the B>C defeat so River and Ranked Pairs lock
that. The second strongest is the A>B defeat so those methods
also lock that. All but one candidate has been thereby
disqualified so B
wins, or we ignore the third pairwise defeat because that
makes a cycle, so give a final order A>B>C and A wins.
To meet both of?? the Plurality criterion and the Chicken Dilemma
criterion A must win.
Winning Votes elects C, violating Chicken Dilemma (which it has to
do to
meet the previously fashionable Minimal Defense criterion).
Margins elects B.?? This fails the Plurality criterion because A
has more
exclusive first-place votes than B has any sort of above-bottom
votes.?? It is also an egregious and outrageous failure of
Later-no-Help
(assuming that if all the ballots just vote for one candidate we
elect the plurality winner).
To anyone who is remotely positionally or strategically minded or has
any common sense and isn't blind to everything except the
Margins pairwise matrix, B is clearly the weakest candidate and a
completely unacceptable winner.
35: A
10: A=B
30: B>C
25: C
A>B 45-40 (erw, "normally" 35-30, margin=5),?? ?? B>C 40-25
(margin=15),
?? C>A 55-45 (margin=10).
Voted at least equal-top (or Top Ratings) scores:?? A45, ?? B40, C25.
Voted above bottom (or Approval) scores: ?? ???? A45, ?? B40, C55
An old Kevin Venzke example.?? B is neither the most top-rated
candidate
or the most approved candidate and is
pairwise-beaten and positionally dominated by A (the most top-rated).
Winning Votes and Margins both elect the clearly weakest
candidate, B.
Losing Votes(erw) elects A.
For those who prefer to have a method comply with Minimal Defense
(which
says that if on more than half the ballots
C is voted above A and A no higher than equal-bottom then A can't
win)
rather than Chicken Dilemma another method
I prefer to WV is Smith//Approval which here elects C.
25: A>B
26: B>C
23: C>A
26: C
C>A 75-25 (margin=50),???????? A>B 48-26 (margin=22),???? B>C 51-49
(margin=2).
Voted at least equal-top (or Top Ratings) scores:?? C49, ?? B26, A25.
Voted above bottom (or Approval) scores: ?? ?? ?? C75,???? B51, A48.
C is an overwhelmingly positionally dominant uncovered candidate.
Margins and Losing Votes elect C.
WV and IRV elect B.
Now say we change 4 of the 26 C ballots to A>C, thereby making C a
bit
weaker.
25: A>B
26: B>C
23: C>A
22: C
04: A>C
C>A 71-29 (margin=42),???????? A>B 52-26 (margin=26),???? B>C 51-49
(margin=2).
Voted at least equal-top (or Top Ratings) scores:?? C45, ?? B26, A29.
Voted above bottom (or Approval) scores: ?? ?? ?? C75,???? B51, A52.
The weakening of C has caused WV and IRV to change from B to C, now
agreeing with LV and Margins.
Assuming the change was from sincere to insincere, those very lucky
and/or very well informed 4 voters
have pulled off a Push-over strategy.
This is a failure of Mono-raise-delete (more obvious if we reverse
the
order of the two situations), which
is one of Woodall's mononicity criteria that he says is incompatible
with Condorcet.
Nonetheless in this case C is still the positionally dominant
uncovered
candidate and Losing Votes (erw)
and Margins both still elect C.
Steve Eppley's old example to illustrate (I think his) Non-Drastic
Defense criterion, which says that if
on more than half the ballots B is voted no lower than equal-top and
above A then A can't win.
46: A>C (sincere may be A>B)
10: B>A
10: B>C
34: C=B (the "defenders", sincere may be C>B)
B>A 54-46 (m=8),?? A>C 56-44 (m=12), C>B (80-54 erw, "normally"
46-20, m=26).
Voted at least equal-top (or Top Ratings) scores:?? B54, ?? A46, C34.
Voted above bottom (or Approval) scores: ?? ?? ?? B54,???? A56, C90.
B is the only candidate top-rated on more than half the ballots. More
than half the voters voted B
above A and B not lower than equal-top. Margins and Losing Votes
without my recommended
"above-bottom equal-ranking whole" bit elect A, violating the
Non-Drastic Defense criterion.
Losing Votes (erw) and WV elect B.
If anyone has?? some counter-examples where they think that Winning
Votes
does better than
Losing Votes (erw), I'd be interested in seeing them.
Chris Benham
---
This email has been checked for viruses by AVG.
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Election-Methods mailing list - see https://electorama.com/em for
list info
Toby,
You would like this old online ranked-ballot voting calculator:
https://www.cse.wustl.edu/~legrand/rbvote/calc.html
What do you think are the "false premises" that the Plurality criterion
is based on??? It was coined with the assumption
that voters could only strictly rank from the top however many
candidates they wish, and those not truncated had in
some sense been "voted for". It says that if A has more first-place
votes than B has any sort of votes then B can't win.
No explicit mention of "unranked candidates".
(Adapting it to ballots that allow equal-ranking at the top, "first
preferences" refers to first-preference score on the
ballots symmetrically completed, at least at the top, ballots).
To sensibly claim that it is a "mistake" for an algorithm to do (or
apparently "assume") something, I think you need to
point to something wrong with an actual result of it doing so.
My answer to your question is no.
Chris Benham
On 27/05/2019 1:04 am, Toby Pereira wrote:
> I think it's a mistake to assume some sort of approval of a ranked
> candidate. If it's not explicitly part of a method then you should not
> infer it. As far as I'm concerned:
>
> 46: A
> 44: B>C
> 10: C
>
> Is the same as:
>
> 46: A>B=C
> 44: B>C>A
> 10: C>A=B
>
> Presented with these ballots, does this change who you think the
> winner should be?
>
> This isn't a defence of margins by me or an argument against anything
> else in your post, but I think the plurality criterion, by talking
> about unranked candidates, is based on false premises.
>
> Toby
>
> On Sat, 25 May 2019 at 15:31, C.Benham
> <cbenham@adam.com.au> wrote:
> There are several Condorcet algorithms that decide the winner by
> weighing "defeat strengths" and they
> are all equivalent to MinMax?? when there are no more than 3
> candidates.
>
> The ones I have in mind that are equal or very nearly equal in
> merit are
> River, Schulze, Ranked Pairs, Smith//MinMax.
> In public political elections they are very very unlikely to give
> different winners. River and Smith//MinMax seem to me
> to be the easiest to understand and explain and use. The other two
> are
> perhaps a bit more elegant and have their
> enthusiastic supporters.
>
> This is to make the case that measuring pairwise defeat strength
> by the
> number of votes on the losing side with above-bottom
> equal-ranking contributing a whole vote to each side (and
> otherwise as
> with normal Winning Votes) is much better than either
> Winning Votes or Margins.
>
> The case for Losing Votes(erw)?? against Margins is that it (in common
> with WV) it meets the Plurality criterion and the Non-Drastic
> Defense criterion.
>
> The case for Losing Votes(erw) against Winning Votes is that it meets
> the Chicken Dilemma criterion and that is much less likely
> to fail to elect a positionally dominant uncovered candidate. (I
> don't
> see how it can fail to elect such a candidate in the 3-candidate
> case.)
>
> For those who think that Margins might be acceptable:
>
> 46: A
> 44: B>C
> 10: C
>
> A>B 46-44 (margin=2),???? B>C 44-10 (margin=34),???? C>A 54-46 (margin=8).
>
> Using Losing Votes (erw) as the measure of defeat strength, the
> weakest
> defeat is the one with the most votes on the losing side.
> That is the C>A defeat so MinMax drops that and A wins. Conversely
> the
> strongest defeat is the one with the fewest votes on the
> losing side.?? That is the B>C defeat so River and Ranked Pairs lock
> that. The second strongest is the A>B defeat so those methods
> also lock that. All but one candidate has been thereby
> disqualified so B
> wins, or we ignore the third pairwise defeat because that
> makes a cycle, so give a final order A>B>C and A wins.
>
> To meet both of?? the Plurality criterion and the Chicken Dilemma
> criterion A must win.
>
> Winning Votes elects C, violating Chicken Dilemma (which it has to
> do to
> meet the previously fashionable Minimal Defense criterion).
>
> Margins elects B.?? This fails the Plurality criterion because A
> has more
> exclusive first-place votes than B has any sort of above-bottom
> votes.?? It is also an egregious and outrageous failure of
> Later-no-Help
> (assuming that if all the ballots just vote for one candidate we
> elect the plurality winner).
>
> To anyone who is remotely positionally or strategically minded or has
> any common sense and isn't blind to everything except the
> Margins pairwise matrix, B is clearly the weakest candidate and a
> completely unacceptable winner.
>
> 35: A
> 10: A=B
> 30: B>C
> 25: C
>
> A>B 45-40 (erw, "normally" 35-30, margin=5),?? ?? B>C 40-25
> (margin=15),
> ?? C>A 55-45 (margin=10).
>
> Voted at least equal-top (or Top Ratings) scores:?? A45, ?? B40, C25.
> Voted above bottom (or Approval) scores: ?? ???? A45, ?? B40, C55
>
> An old Kevin Venzke example.?? B is neither the most top-rated
> candidate
> or the most approved candidate and is
> pairwise-beaten and positionally dominated by A (the most top-rated).
>
> Winning Votes and Margins both elect the clearly weakest
> candidate, B.
> Losing Votes(erw) elects A.
>
> For those who prefer to have a method comply with Minimal Defense
> (which
> says that if on more than half the ballots
> C is voted above A and A no higher than equal-bottom then A can't
> win)
> rather than Chicken Dilemma another method
> I prefer to WV is Smith//Approval which here elects C.
>
> 25: A>B
> 26: B>C
> 23: C>A
> 26: C
>
> C>A 75-25 (margin=50),???????? A>B 48-26 (margin=22),???? B>C 51-49
> (margin=2).
>
> Voted at least equal-top (or Top Ratings) scores:?? C49, ?? B26, A25.
> Voted above bottom (or Approval) scores: ?? ?? ?? C75,???? B51, A48.
>
> C is an overwhelmingly positionally dominant uncovered candidate.
> Margins and Losing Votes elect C.
> WV and IRV elect B.
>
> Now say we change 4 of the 26 C ballots to A>C, thereby making C a
> bit
> weaker.
>
> 25: A>B
> 26: B>C
> 23: C>A
> 22: C
> 04: A>C
>
> C>A 71-29 (margin=42),???????? A>B 52-26 (margin=26),???? B>C 51-49
> (margin=2).
>
> Voted at least equal-top (or Top Ratings) scores:?? C45, ?? B26, A29.
> Voted above bottom (or Approval) scores: ?? ?? ?? C75,???? B51, A52.
>
>
> The weakening of C has caused WV and IRV to change from B to C, now
> agreeing with LV and Margins.
> Assuming the change was from sincere to insincere, those very lucky
> and/or very well informed 4 voters
> have pulled off a Push-over strategy.
>
> This is a failure of Mono-raise-delete (more obvious if we reverse
> the
> order of the two situations), which
> is one of Woodall's mononicity criteria that he says is incompatible
> with Condorcet.
>
> Nonetheless in this case C is still the positionally dominant
> uncovered
> candidate and Losing Votes (erw)
> and Margins both still elect C.
>
> Steve Eppley's old example to illustrate (I think his) Non-Drastic
> Defense criterion, which says that if
> on more than half the ballots B is voted no lower than equal-top and
> above A then A can't win.
>
> 46: A>C (sincere may be A>B)
> 10: B>A
> 10: B>C
> 34: C=B (the "defenders", sincere may be C>B)
>
> B>A 54-46 (m=8),?? A>C 56-44 (m=12), C>B (80-54 erw, "normally"
> 46-20, m=26).
>
> Voted at least equal-top (or Top Ratings) scores:?? B54, ?? A46, C34.
> Voted above bottom (or Approval) scores: ?? ?? ?? B54,???? A56, C90.
>
> B is the only candidate top-rated on more than half the ballots. More
> than half the voters voted B
> above A and B not lower than equal-top. Margins and Losing Votes
> without my recommended
> "above-bottom equal-ranking whole" bit elect A, violating the
> Non-Drastic Defense criterion.
>
> Losing Votes (erw) and WV elect B.
>
> If anyone has?? some counter-examples where they think that Winning
> Votes
> does better than
> Losing Votes (erw), I'd be interested in seeing them.
>
> Chris Benham
>
>
>
>
>
>
>
>
> ---
> This email has been checked for viruses by AVG.
> https://www.avg.com
>
> ----
> Election-Methods mailing list - see https://electorama.com/em for
> list info
>
TP
Toby Pereira
Sun, May 26, 2019 6:08 PM
By unranked candidates, I meant the ones that had not had any sort of "vote" - the ones not explicitly listed by the voter. If there are three candidates in an election, A, B, and C, I might like A but absolutely hate the others. My vote might simply be:
A
On the other hand, while I might still absolutely hate B and C, I might still hate C more. So my vote might be:
A>B
But just because I have ranked B on my ballot, this should not be taken as any sort of endorsement of B or a vote "for" B.
My vote could also be:
A>B>C
Does adding C on the end mean that I have in some sense voted for C? I don't think there would actually be any methods where adding C on the end would have any effect on how the winner is calculated, but the plurality criterion would presumably in theory find it acceptable to do so.
But this is more a philosophical objection to the assumptions implicit in the plurality criterion than an an objection to the results that a method obeying the criterion would produce in practice. But anyway, I put my thoughts about the plurality criterion a while ago (as did Juho) here: http://election-methods.5485.n7.nabble.com/EM-Fwd-Ordering-defeats-in-Minimax-td34236.html#a34247
But anyway, thank you for the link to the calculator.
Toby
From: Chris Benham <cbenhamau@yahoo.com.au>
To: "tdp201b@yahoo.co.uk" tdp201b@yahoo.co.uk; "cbenham@adam.com.au" cbenham@adam.com.au; "election-methods@lists.electorama.com" election-methods@lists.electorama.com
Sent: Sunday, 26 May 2019, 18:08
Subject: Re: [EM] Losing Votes (equal-ranking whole)
Toby,
You would like this old online ranked-ballot voting calculator:
https://www.cse.wustl.edu/~legrand/rbvote/calc.html
What do you think are the "false premises" that the Plurality criterion is based on??? It was coined with the assumption
that voters could only strictly rank from the top however many candidates they wish, and those not truncated had in
some sense been "voted for". It says that if A has more first-place votes than B has any sort of votes then B can't win.
No explicit mention of "unranked candidates".
(Adapting it to ballots that allow equal-ranking at the top,?? "first preferences" refers to first-preference score on the
ballots symmetrically completed, at least at the top, ballots).
To sensibly claim that it is a "mistake" for an algorithm to do (or apparently "assume") something, I think you need to
point to something wrong with an actual result of it doing so.
My answer to your question is no.
Chris Benham
On 27/05/2019 1:04 am, Toby Pereira wrote:
I think it's a mistake to assume some sort of approval of a ranked candidate. If it's not explicitly part of a method then you should not infer it. As far as I'm concerned:
46: A 44: B>C 10: C
Is the same as:
46: A>B=C 44: B>C>A 10: C>A=B
Presented with these ballots, does this change who you think the winner should be?
This isn't a defence of margins by me or an argument against anything else in your post, but I think the plurality criterion, by talking about unranked candidates, is based on false premises.
Toby
On Sat, 25 May 2019 at 15:31, C.Benham cbenham@adam.com.au wrote: There are several Condorcet algorithms that decide the winner by
weighing "defeat strengths" and they
are all equivalent to MinMax?? when there are no more than 3 candidates.
The ones I have in mind that are equal or very nearly equal in merit are
River, Schulze, Ranked Pairs, Smith//MinMax.
In public political elections they are very very unlikely to give
different winners. River and Smith//MinMax seem to me
to be the easiest to understand and explain and use. The other two are
perhaps a bit more elegant and have their
enthusiastic supporters.
This is to make the case that measuring pairwise defeat strength by the
number of votes on the losing side with above-bottom
equal-ranking contributing a whole vote to each side (and otherwise as
with normal Winning Votes) is much better than either
Winning Votes or Margins.
The case for Losing Votes(erw)?? against Margins is that it (in common
with WV) it meets the Plurality criterion and the Non-Drastic
Defense criterion.
The case for Losing Votes(erw) against Winning Votes is that it meets
the Chicken Dilemma criterion and that is much less likely
to fail to elect a positionally dominant uncovered candidate. (I don't
see how it can fail to elect such a candidate in the 3-candidate case.)
For those who think that Margins might be acceptable:
46: A
44: B>C
10: C
A>B 46-44 (margin=2),???? B>C 44-10 (margin=34),???? C>A 54-46 (margin=8).
Using Losing Votes (erw) as the measure of defeat strength, the weakest
defeat is the one with the most votes on the losing side.
That is the C>A defeat so MinMax drops that and A wins. Conversely the
strongest defeat is the one with the fewest votes on the
losing side.?? That is the B>C defeat so River and Ranked Pairs lock
that. The second strongest is the A>B defeat so those methods
also lock that. All but one candidate has been thereby disqualified so B
wins, or we ignore the third pairwise defeat because that
makes a cycle, so give a final order A>B>C and A wins.
To meet both of?? the Plurality criterion and the Chicken Dilemma
criterion A must win.
Winning Votes elects C, violating Chicken Dilemma (which it has to do to
meet the previously fashionable Minimal Defense criterion).
Margins elects B.?? This fails the Plurality criterion because A has more
exclusive first-place votes than B has any sort of above-bottom
votes.?? It is also an egregious and outrageous failure of Later-no-Help
(assuming that if all the ballots just vote for one candidate we
elect the plurality winner).
To anyone who is remotely positionally or strategically minded or has
any common sense and isn't blind to everything except the
Margins pairwise matrix, B is clearly the weakest candidate and a
completely unacceptable winner.
35: A
10: A=B
30: B>C
25: C
A>B 45-40 (erw, "normally" 35-30, margin=5),?? ?? B>C 40-25 (margin=15), ??
?? C>A 55-45 (margin=10).
Voted at least equal-top (or Top Ratings) scores:?? A45, ?? B40, C25.
Voted above bottom (or Approval) scores: ?? ?? ?? ?? ???? A45, ?? B40, C55
An old Kevin Venzke example.?? B is neither the most top-rated candidate
or the most approved candidate and is
pairwise-beaten and positionally dominated by A (the most top-rated).
Winning Votes and Margins both elect the clearly weakest candidate, B.??
Losing Votes(erw) elects A.
For those who prefer to have a method comply with Minimal Defense (which
says that if on more than half the ballots
C is voted above A and A no higher than equal-bottom then A can't win)
rather than Chicken Dilemma another method
I prefer to WV is Smith//Approval which here elects C.
25: A>B
26: B>C
23: C>A
26: C
C>A 75-25 (margin=50),???????? A>B 48-26 (margin=22),???? B>C 51-49 (margin=2).
Voted at least equal-top (or Top Ratings) scores:?? C49, ?? B26, A25.
Voted above bottom (or Approval) scores: ?? ?? ?? ?? ?? ?? C75,???? B51, A48.
C is an overwhelmingly positionally dominant uncovered candidate.
Margins and Losing Votes elect C.
WV and IRV elect B.
Now say we change 4 of the 26 C ballots to A>C, thereby making C a bit
weaker.
25: A>B
26: B>C
23: C>A
22: C
04: A>C
C>A 71-29 (margin=42),???????? A>B 52-26 (margin=26),???? B>C 51-49 (margin=2).
Voted at least equal-top (or Top Ratings) scores:?? C45, ?? B26, A29.
Voted above bottom (or Approval) scores: ?? ?? ?? ?? ?? ?? C75,???? B51, A52.
The weakening of C has caused WV and IRV to change from B to C, now
agreeing with LV and Margins.
Assuming the change was from sincere to insincere, those very lucky
and/or very well informed 4 voters
have pulled off a Push-over strategy.
This is a failure of Mono-raise-delete (more obvious if we reverse the
order of the two situations), which
is one of Woodall's mononicity criteria that he says is incompatible
with Condorcet.
Nonetheless in this case C is still the positionally dominant uncovered
candidate and Losing Votes (erw)
and Margins both still elect C.
Steve Eppley's old example to illustrate (I think his) Non-Drastic
Defense criterion, which says that if
on more than half the ballots B is voted no lower than equal-top and
above A then A can't win.
46: A>C (sincere may be A>B)
10: B>A
10: B>C
34: C=B (the "defenders", sincere may be C>B)
B>A 54-46 (m=8),?? A>C 56-44 (m=12), C>B (80-54 erw, "normally" 46-20, m=26).
Voted at least equal-top (or Top Ratings) scores:?? B54, ?? A46, C34.
Voted above bottom (or Approval) scores: ?? ?? ?? ?? ?? ?? B54,???? A56, C90.
B is the only candidate top-rated on more than half the ballots. More
than half the voters voted B
above A and B not lower than equal-top.?? Margins and Losing Votes
without my recommended
"above-bottom equal-ranking whole" bit elect A, violating the
Non-Drastic Defense criterion.
Losing Votes (erw) and WV elect B.
If anyone has?? some counter-examples where they think that Winning Votes
does better than
Losing Votes (erw), I'd be interested in seeing them.
Chris Benham
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By unranked candidates, I meant the ones that had not had any sort of "vote" - the ones not explicitly listed by the voter. If there are three candidates in an election, A, B, and C, I might like A but absolutely hate the others. My vote might simply be:
A
On the other hand, while I might still absolutely hate B and C, I might still hate C more. So my vote might be:
A>B
But just because I have ranked B on my ballot, this should not be taken as any sort of endorsement of B or a vote "for" B.
My vote could also be:
A>B>C
Does adding C on the end mean that I have in some sense voted for C? I don't think there would actually be any methods where adding C on the end would have any effect on how the winner is calculated, but the plurality criterion would presumably in theory find it acceptable to do so.
But this is more a philosophical objection to the assumptions implicit in the plurality criterion than an an objection to the results that a method obeying the criterion would produce in practice. But anyway, I put my thoughts about the plurality criterion a while ago (as did Juho) here: http://election-methods.5485.n7.nabble.com/EM-Fwd-Ordering-defeats-in-Minimax-td34236.html#a34247
But anyway, thank you for the link to the calculator.
Toby
From: Chris Benham <cbenhamau@yahoo.com.au>
To: "tdp201b@yahoo.co.uk" <tdp201b@yahoo.co.uk>; "cbenham@adam.com.au" <cbenham@adam.com.au>; "election-methods@lists.electorama.com" <election-methods@lists.electorama.com>
Sent: Sunday, 26 May 2019, 18:08
Subject: Re: [EM] Losing Votes (equal-ranking whole)
Toby,
You would like this old online ranked-ballot voting calculator:
https://www.cse.wustl.edu/~legrand/rbvote/calc.html
What do you think are the "false premises" that the Plurality criterion is based on??? It was coined with the assumption
that voters could only strictly rank from the top however many candidates they wish, and those not truncated had in
some sense been "voted for". It says that if A has more first-place votes than B has any sort of votes then B can't win.
No explicit mention of "unranked candidates".
(Adapting it to ballots that allow equal-ranking at the top,?? "first preferences" refers to first-preference score on the
ballots symmetrically completed, at least at the top, ballots).
To sensibly claim that it is a "mistake" for an algorithm to do (or apparently "assume") something, I think you need to
point to something wrong with an actual result of it doing so.
My answer to your question is no.
Chris Benham
On 27/05/2019 1:04 am, Toby Pereira wrote:
I think it's a mistake to assume some sort of approval of a ranked candidate. If it's not explicitly part of a method then you should not infer it. As far as I'm concerned:
46: A 44: B>C 10: C
Is the same as:
46: A>B=C 44: B>C>A 10: C>A=B
Presented with these ballots, does this change who you think the winner should be?
This isn't a defence of margins by me or an argument against anything else in your post, but I think the plurality criterion, by talking about unranked candidates, is based on false premises.
Toby
On Sat, 25 May 2019 at 15:31, C.Benham <cbenham@adam.com.au> wrote: There are several Condorcet algorithms that decide the winner by
weighing "defeat strengths" and they
are all equivalent to MinMax?? when there are no more than 3 candidates.
The ones I have in mind that are equal or very nearly equal in merit are
River, Schulze, Ranked Pairs, Smith//MinMax.
In public political elections they are very very unlikely to give
different winners. River and Smith//MinMax seem to me
to be the easiest to understand and explain and use. The other two are
perhaps a bit more elegant and have their
enthusiastic supporters.
This is to make the case that measuring pairwise defeat strength by the
number of votes on the losing side with above-bottom
equal-ranking contributing a whole vote to each side (and otherwise as
with normal Winning Votes) is much better than either
Winning Votes or Margins.
The case for Losing Votes(erw)?? against Margins is that it (in common
with WV) it meets the Plurality criterion and the Non-Drastic
Defense criterion.
The case for Losing Votes(erw) against Winning Votes is that it meets
the Chicken Dilemma criterion and that is much less likely
to fail to elect a positionally dominant uncovered candidate. (I don't
see how it can fail to elect such a candidate in the 3-candidate case.)
For those who think that Margins might be acceptable:
46: A
44: B>C
10: C
A>B 46-44 (margin=2),???? B>C 44-10 (margin=34),???? C>A 54-46 (margin=8).
Using Losing Votes (erw) as the measure of defeat strength, the weakest
defeat is the one with the most votes on the losing side.
That is the C>A defeat so MinMax drops that and A wins. Conversely the
strongest defeat is the one with the fewest votes on the
losing side.?? That is the B>C defeat so River and Ranked Pairs lock
that. The second strongest is the A>B defeat so those methods
also lock that. All but one candidate has been thereby disqualified so B
wins, or we ignore the third pairwise defeat because that
makes a cycle, so give a final order A>B>C and A wins.
To meet both of?? the Plurality criterion and the Chicken Dilemma
criterion A must win.
Winning Votes elects C, violating Chicken Dilemma (which it has to do to
meet the previously fashionable Minimal Defense criterion).
Margins elects B.?? This fails the Plurality criterion because A has more
exclusive first-place votes than B has any sort of above-bottom
votes.?? It is also an egregious and outrageous failure of Later-no-Help
(assuming that if all the ballots just vote for one candidate we
elect the plurality winner).
To anyone who is remotely positionally or strategically minded or has
any common sense and isn't blind to everything except the
Margins pairwise matrix, B is clearly the weakest candidate and a
completely unacceptable winner.
35: A
10: A=B
30: B>C
25: C
A>B 45-40 (erw, "normally" 35-30, margin=5),?? ?? B>C 40-25 (margin=15), ??
?? C>A 55-45 (margin=10).
Voted at least equal-top (or Top Ratings) scores:?? A45, ?? B40, C25.
Voted above bottom (or Approval) scores: ?? ?? ?? ?? ???? A45, ?? B40, C55
An old Kevin Venzke example.?? B is neither the most top-rated candidate
or the most approved candidate and is
pairwise-beaten and positionally dominated by A (the most top-rated).
Winning Votes and Margins both elect the clearly weakest candidate, B.??
Losing Votes(erw) elects A.
For those who prefer to have a method comply with Minimal Defense (which
says that if on more than half the ballots
C is voted above A and A no higher than equal-bottom then A can't win)
rather than Chicken Dilemma another method
I prefer to WV is Smith//Approval which here elects C.
25: A>B
26: B>C
23: C>A
26: C
C>A 75-25 (margin=50),???????? A>B 48-26 (margin=22),???? B>C 51-49 (margin=2).
Voted at least equal-top (or Top Ratings) scores:?? C49, ?? B26, A25.
Voted above bottom (or Approval) scores: ?? ?? ?? ?? ?? ?? C75,???? B51, A48.
C is an overwhelmingly positionally dominant uncovered candidate.
Margins and Losing Votes elect C.
WV and IRV elect B.
Now say we change 4 of the 26 C ballots to A>C, thereby making C a bit
weaker.
25: A>B
26: B>C
23: C>A
22: C
04: A>C
C>A 71-29 (margin=42),???????? A>B 52-26 (margin=26),???? B>C 51-49 (margin=2).
Voted at least equal-top (or Top Ratings) scores:?? C45, ?? B26, A29.
Voted above bottom (or Approval) scores: ?? ?? ?? ?? ?? ?? C75,???? B51, A52.
The weakening of C has caused WV and IRV to change from B to C, now
agreeing with LV and Margins.
Assuming the change was from sincere to insincere, those very lucky
and/or very well informed 4 voters
have pulled off a Push-over strategy.
This is a failure of Mono-raise-delete (more obvious if we reverse the
order of the two situations), which
is one of Woodall's mononicity criteria that he says is incompatible
with Condorcet.
Nonetheless in this case C is still the positionally dominant uncovered
candidate and Losing Votes (erw)
and Margins both still elect C.
Steve Eppley's old example to illustrate (I think his) Non-Drastic
Defense criterion, which says that if
on more than half the ballots B is voted no lower than equal-top and
above A then A can't win.
46: A>C (sincere may be A>B)
10: B>A
10: B>C
34: C=B (the "defenders", sincere may be C>B)
B>A 54-46 (m=8),?? A>C 56-44 (m=12), C>B (80-54 erw, "normally" 46-20, m=26).
Voted at least equal-top (or Top Ratings) scores:?? B54, ?? A46, C34.
Voted above bottom (or Approval) scores: ?? ?? ?? ?? ?? ?? B54,???? A56, C90.
B is the only candidate top-rated on more than half the ballots. More
than half the voters voted B
above A and B not lower than equal-top.?? Margins and Losing Votes
without my recommended
"above-bottom equal-ranking whole" bit elect A, violating the
Non-Drastic Defense criterion.
Losing Votes (erw) and WV elect B.
If anyone has?? some counter-examples where they think that Winning Votes
does better than
Losing Votes (erw), I'd be interested in seeing them.
Chris Benham
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C
C.Benham
Sun, May 26, 2019 7:19 PM
Toby,
If you try to give that calculator a truncated ballot it will just turn
it into the sort of ballot you like.
How do you think equally-ranked ballots should be counted in a pairwise
comparison? A half-vote to
each or zero to both?
So you can't actually point to any election example where the Plurality
criterion bars from winning the candidate
that you think should have won?
46: A
44: B>C
10: C
Returning to this, are you happy with B winning? And if not, why not?
Chris Benham
On 27/05/2019 3:38 am, Toby Pereira wrote:
By unranked candidates, I meant the ones that had not had any sort of
"vote" - the ones not explicitly listed by the voter. If there are
three candidates in an election, A, B, and C, I might like A but
absolutely hate the others. My vote might simply be:
A
On the other hand, while I might still absolutely hate B and C, I
might still hate C more. So my vote might be:
A>B
But just because I have ranked B on my ballot, this should not be
taken as any sort of endorsement of B or a vote "for" B.
My vote could also be:
A>B>C
Does adding C on the end mean that I have in some sense voted for C? I
don't think there would actually be any methods where adding C on the
end would have any effect on how the winner is calculated, but the
plurality criterion would presumably in theory find it acceptable to
do so.
But this is more a philosophical objection to the assumptions implicit
in the plurality criterion than an an objection to the results that a
method obeying the criterion would produce in practice. But anyway, I
put my thoughts about the plurality criterion a while ago (as did
Juho) here:
http://election-methods.5485.n7.nabble.com/EM-Fwd-Ordering-defeats-in-Minimax-td34236.html#a34247
But anyway, thank you for the link to the calculator.
Toby
From: Chris Benham cbenhamau@yahoo.com.au
To: "tdp201b@yahoo.co.uk" tdp201b@yahoo.co.uk;
"cbenham@adam.com.au" cbenham@adam.com.au;
"election-methods@lists.electorama.com"
election-methods@lists.electorama.com
Sent: Sunday, 26 May 2019, 18:08
Subject: Re: [EM] Losing Votes (equal-ranking whole)
Toby,
You would like this old online ranked-ballot voting calculator:
https://www.cse.wustl.edu/~legrand/rbvote/calc.html
What do you think are the "false premises" that the Plurality
criterion is based on??? It was coined with the assumption
that voters could only strictly rank from the top however many
candidates they wish, and those not truncated had in
some sense been "voted for". It says that if A has more first-place
votes than B has any sort of votes then B can't win.
No explicit mention of "unranked candidates".
(Adapting it to ballots that allow equal-ranking at the top,?? "first
preferences" refers to first-preference score on the
ballots symmetrically completed, at least at the top, ballots).
To sensibly claim that it is a "mistake" for an algorithm to do (or
apparently "assume") something, I think you need to
point to something wrong with an actual result of it doing so.
My answer to your question is no.
Chris Benham
On 27/05/2019 1:04 am, Toby Pereira wrote:
I think it's a mistake to assume some sort of approval of a ranked
candidate. If it's not explicitly part of a method then you should not
infer it. As far as I'm concerned:
46: A
44: B>C
10: C
Is the same as:
46: A>B=C
44: B>C>A
10: C>A=B
Presented with these ballots, does this change who you think the
winner should be?
This isn't a defence of margins by me or an argument against anything
else in your post, but I think the plurality criterion, by talking
about unranked candidates, is based on false premises.
Toby
On Sat, 25 May 2019 at 15:31, C.Benham
<cbenham@adam.com.au> <mailto:cbenham@adam.com.au> wrote:
There are several Condorcet algorithms that decide the winner by
weighing "defeat strengths" and they
are all equivalent to MinMax?? when there are no more than 3
candidates.
The ones I have in mind that are equal or very nearly equal in
merit are
River, Schulze, Ranked Pairs, Smith//MinMax.
In public political elections they are very very unlikely to give
different winners. River and Smith//MinMax seem to me
to be the easiest to understand and explain and use. The other two
are
perhaps a bit more elegant and have their
enthusiastic supporters.
This is to make the case that measuring pairwise defeat strength
by the
number of votes on the losing side with above-bottom
equal-ranking contributing a whole vote to each side (and
otherwise as
with normal Winning Votes) is much better than either
Winning Votes or Margins.
The case for Losing Votes(erw)?? against Margins is that it (in
common
with WV) it meets the Plurality criterion and the Non-Drastic
Defense criterion.
The case for Losing Votes(erw) against Winning Votes is that it meets
the Chicken Dilemma criterion and that is much less likely
to fail to elect a positionally dominant uncovered candidate. (I
don't
see how it can fail to elect such a candidate in the 3-candidate
case.)
For those who think that Margins might be acceptable:
46: A
44: B>C
10: C
A>B 46-44 (margin=2),???? B>C 44-10 (margin=34),???? C>A 54-46
(margin=8).
Using Losing Votes (erw) as the measure of defeat strength, the
weakest
defeat is the one with the most votes on the losing side.
That is the C>A defeat so MinMax drops that and A wins. Conversely
the
strongest defeat is the one with the fewest votes on the
losing side.?? That is the B>C defeat so River and Ranked Pairs lock
that. The second strongest is the A>B defeat so those methods
also lock that. All but one candidate has been thereby
disqualified so B
wins, or we ignore the third pairwise defeat because that
makes a cycle, so give a final order A>B>C and A wins.
To meet both of?? the Plurality criterion and the Chicken Dilemma
criterion A must win.
Winning Votes elects C, violating Chicken Dilemma (which it has to
do to
meet the previously fashionable Minimal Defense criterion).
Margins elects B.?? This fails the Plurality criterion because A
has more
exclusive first-place votes than B has any sort of above-bottom
votes.?? It is also an egregious and outrageous failure of
Later-no-Help
(assuming that if all the ballots just vote for one candidate we
elect the plurality winner).
To anyone who is remotely positionally or strategically minded or has
any common sense and isn't blind to everything except the
Margins pairwise matrix, B is clearly the weakest candidate and a
completely unacceptable winner.
35: A
10: A=B
30: B>C
25: C
A>B 45-40 (erw, "normally" 35-30, margin=5),?? ?? B>C 40-25
(margin=15), ??
?? C>A 55-45 (margin=10).
Voted at least equal-top (or Top Ratings) scores:?? A45, ?? B40, C25.
Voted above bottom (or Approval) scores: ?? ?? ?? ?? ???? A45, ??
B40, C55
An old Kevin Venzke example.?? B is neither the most top-rated
candidate
or the most approved candidate and is
pairwise-beaten and positionally dominated by A (the most top-rated).
Winning Votes and Margins both elect the clearly weakest
candidate, B.??
Losing Votes(erw) elects A.
For those who prefer to have a method comply with Minimal Defense
(which
says that if on more than half the ballots
C is voted above A and A no higher than equal-bottom then A can't
win)
rather than Chicken Dilemma another method
I prefer to WV is Smith//Approval which here elects C.
25: A>B
26: B>C
23: C>A
26: C
C>A 75-25 (margin=50),???????? A>B 48-26 (margin=22),???? B>C
51-49 (margin=2).
Voted at least equal-top (or Top Ratings) scores:?? C49, ?? B26, A25.
Voted above bottom (or Approval) scores: ?? ?? ?? ?? ?? ??
C75,???? B51, A48.
C is an overwhelmingly positionally dominant uncovered candidate.
Margins and Losing Votes elect C.
WV and IRV elect B.
Now say we change 4 of the 26 C ballots to A>C, thereby making C a
bit
weaker.
25: A>B
26: B>C
23: C>A
22: C
04: A>C
C>A 71-29 (margin=42),???????? A>B 52-26 (margin=26),???? B>C
51-49 (margin=2).
Voted at least equal-top (or Top Ratings) scores:?? C45, ?? B26, A29.
Voted above bottom (or Approval) scores: ?? ?? ?? ?? ?? ??
C75,???? B51, A52.
The weakening of C has caused WV and IRV to change from B to C, now
agreeing with LV and Margins.
Assuming the change was from sincere to insincere, those very lucky
and/or very well informed 4 voters
have pulled off a Push-over strategy.
This is a failure of Mono-raise-delete (more obvious if we reverse
the
order of the two situations), which
is one of Woodall's mononicity criteria that he says is incompatible
with Condorcet.
Nonetheless in this case C is still the positionally dominant
uncovered
candidate and Losing Votes (erw)
and Margins both still elect C.
Steve Eppley's old example to illustrate (I think his) Non-Drastic
Defense criterion, which says that if
on more than half the ballots B is voted no lower than equal-top and
above A then A can't win.
46: A>C (sincere may be A>B)
10: B>A
10: B>C
34: C=B (the "defenders", sincere may be C>B)
B>A 54-46 (m=8),?? A>C 56-44 (m=12), C>B (80-54 erw, "normally"
46-20, m=26).
Voted at least equal-top (or Top Ratings) scores:?? B54, ?? A46, C34.
Voted above bottom (or Approval) scores: ?? ?? ?? ?? ?? ??
B54,???? A56, C90.
B is the only candidate top-rated on more than half the ballots. More
than half the voters voted B
above A and B not lower than equal-top.?? Margins and Losing Votes
without my recommended
"above-bottom equal-ranking whole" bit elect A, violating the
Non-Drastic Defense criterion.
Losing Votes (erw) and WV elect B.
If anyone has?? some counter-examples where they think that
Winning Votes
does better than
Losing Votes (erw), I'd be interested in seeing them.
Chris Benham
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Toby,
If you try to give that calculator a truncated ballot it will just turn
it into the sort of ballot you like.
How do you think equally-ranked ballots should be counted in a pairwise
comparison? A half-vote to
each or zero to both?
So you can't actually point to any election example where the Plurality
criterion bars from winning the candidate
that you think should have won?
46: A
44: B>C
10: C
Returning to this, are you happy with B winning? And if not, why not?
Chris Benham
On 27/05/2019 3:38 am, Toby Pereira wrote:
> By unranked candidates, I meant the ones that had not had any sort of
> "vote" - the ones not explicitly listed by the voter. If there are
> three candidates in an election, A, B, and C, I might like A but
> absolutely hate the others. My vote might simply be:
>
> A
>
> On the other hand, while I might still absolutely hate B and C, I
> might still hate C more. So my vote might be:
>
> A>B
>
> But just because I have ranked B on my ballot, this should not be
> taken as any sort of endorsement of B or a vote "for" B.
>
> My vote could also be:
>
> A>B>C
>
> Does adding C on the end mean that I have in some sense voted for C? I
> don't think there would actually be any methods where adding C on the
> end would have any effect on how the winner is calculated, but the
> plurality criterion would presumably in theory find it acceptable to
> do so.
>
> But this is more a philosophical objection to the assumptions implicit
> in the plurality criterion than an an objection to the results that a
> method obeying the criterion would produce in practice. But anyway, I
> put my thoughts about the plurality criterion a while ago (as did
> Juho) here:
> http://election-methods.5485.n7.nabble.com/EM-Fwd-Ordering-defeats-in-Minimax-td34236.html#a34247
>
> But anyway, thank you for the link to the calculator.
>
> Toby
>
>
>
>
> ------------------------------------------------------------------------
> *From:* Chris Benham <cbenhamau@yahoo.com.au>
> *To:* "tdp201b@yahoo.co.uk" <tdp201b@yahoo.co.uk>;
> "cbenham@adam.com.au" <cbenham@adam.com.au>;
> "election-methods@lists.electorama.com"
> <election-methods@lists.electorama.com>
> *Sent:* Sunday, 26 May 2019, 18:08
> *Subject:* Re: [EM] Losing Votes (equal-ranking whole)
>
> Toby,
>
> You would like this old online ranked-ballot voting calculator:
>
> https://www.cse.wustl.edu/~legrand/rbvote/calc.html
>
> What do you think are the "false premises" that the Plurality
> criterion is based on??? It was coined with the assumption
> that voters could only strictly rank from the top however many
> candidates they wish, and those not truncated had in
> some sense been "voted for". It says that if A has more first-place
> votes than B has any sort of votes then B can't win.
> No explicit mention of "unranked candidates".
>
> (Adapting it to ballots that allow equal-ranking at the top,?? "first
> preferences" refers to first-preference score on the
> ballots symmetrically completed, at least at the top, ballots).
> To sensibly claim that it is a "mistake" for an algorithm to do (or
> apparently "assume") something, I think you need to
> point to something wrong with an actual result of it doing so.
>
> My answer to your question is no.
> Chris Benham
>
>
> On 27/05/2019 1:04 am, Toby Pereira wrote:
> I think it's a mistake to assume some sort of approval of a ranked
> candidate. If it's not explicitly part of a method then you should not
> infer it. As far as I'm concerned:
>
> 46: A
> 44: B>C
> 10: C
>
> Is the same as:
>
> 46: A>B=C
> 44: B>C>A
> 10: C>A=B
>
> Presented with these ballots, does this change who you think the
> winner should be?
>
> This isn't a defence of margins by me or an argument against anything
> else in your post, but I think the plurality criterion, by talking
> about unranked candidates, is based on false premises.
>
> Toby
>
> On Sat, 25 May 2019 at 15:31, C.Benham
> <cbenham@adam.com.au> <mailto:cbenham@adam.com.au> wrote:
> There are several Condorcet algorithms that decide the winner by
> weighing "defeat strengths" and they
> are all equivalent to MinMax?? when there are no more than 3
> candidates.
>
> The ones I have in mind that are equal or very nearly equal in
> merit are
> River, Schulze, Ranked Pairs, Smith//MinMax.
> In public political elections they are very very unlikely to give
> different winners. River and Smith//MinMax seem to me
> to be the easiest to understand and explain and use. The other two
> are
> perhaps a bit more elegant and have their
> enthusiastic supporters.
>
> This is to make the case that measuring pairwise defeat strength
> by the
> number of votes on the losing side with above-bottom
> equal-ranking contributing a whole vote to each side (and
> otherwise as
> with normal Winning Votes) is much better than either
> Winning Votes or Margins.
>
> The case for Losing Votes(erw)?? against Margins is that it (in
> common
> with WV) it meets the Plurality criterion and the Non-Drastic
> Defense criterion.
>
> The case for Losing Votes(erw) against Winning Votes is that it meets
> the Chicken Dilemma criterion and that is much less likely
> to fail to elect a positionally dominant uncovered candidate. (I
> don't
> see how it can fail to elect such a candidate in the 3-candidate
> case.)
>
> For those who think that Margins might be acceptable:
>
> 46: A
> 44: B>C
> 10: C
>
> A>B 46-44 (margin=2),???? B>C 44-10 (margin=34),???? C>A 54-46
> (margin=8).
>
> Using Losing Votes (erw) as the measure of defeat strength, the
> weakest
> defeat is the one with the most votes on the losing side.
> That is the C>A defeat so MinMax drops that and A wins. Conversely
> the
> strongest defeat is the one with the fewest votes on the
> losing side.?? That is the B>C defeat so River and Ranked Pairs lock
> that. The second strongest is the A>B defeat so those methods
> also lock that. All but one candidate has been thereby
> disqualified so B
> wins, or we ignore the third pairwise defeat because that
> makes a cycle, so give a final order A>B>C and A wins.
>
> To meet both of?? the Plurality criterion and the Chicken Dilemma
> criterion A must win.
>
> Winning Votes elects C, violating Chicken Dilemma (which it has to
> do to
> meet the previously fashionable Minimal Defense criterion).
>
> Margins elects B.?? This fails the Plurality criterion because A
> has more
> exclusive first-place votes than B has any sort of above-bottom
> votes.?? It is also an egregious and outrageous failure of
> Later-no-Help
> (assuming that if all the ballots just vote for one candidate we
> elect the plurality winner).
>
> To anyone who is remotely positionally or strategically minded or has
> any common sense and isn't blind to everything except the
> Margins pairwise matrix, B is clearly the weakest candidate and a
> completely unacceptable winner.
>
> 35: A
> 10: A=B
> 30: B>C
> 25: C
>
> A>B 45-40 (erw, "normally" 35-30, margin=5),?? ?? B>C 40-25
> (margin=15), ??
> ?? C>A 55-45 (margin=10).
>
> Voted at least equal-top (or Top Ratings) scores:?? A45, ?? B40, C25.
> Voted above bottom (or Approval) scores: ?? ?? ?? ?? ???? A45, ??
> B40, C55
>
> An old Kevin Venzke example.?? B is neither the most top-rated
> candidate
> or the most approved candidate and is
> pairwise-beaten and positionally dominated by A (the most top-rated).
>
> Winning Votes and Margins both elect the clearly weakest
> candidate, B.??
> Losing Votes(erw) elects A.
>
> For those who prefer to have a method comply with Minimal Defense
> (which
> says that if on more than half the ballots
> C is voted above A and A no higher than equal-bottom then A can't
> win)
> rather than Chicken Dilemma another method
> I prefer to WV is Smith//Approval which here elects C.
>
> 25: A>B
> 26: B>C
> 23: C>A
> 26: C
>
> C>A 75-25 (margin=50),???????? A>B 48-26 (margin=22),???? B>C
> 51-49 (margin=2).
>
> Voted at least equal-top (or Top Ratings) scores:?? C49, ?? B26, A25.
> Voted above bottom (or Approval) scores: ?? ?? ?? ?? ?? ??
> C75,???? B51, A48.
>
> C is an overwhelmingly positionally dominant uncovered candidate.
> Margins and Losing Votes elect C.
> WV and IRV elect B.
>
> Now say we change 4 of the 26 C ballots to A>C, thereby making C a
> bit
> weaker.
>
> 25: A>B
> 26: B>C
> 23: C>A
> 22: C
> 04: A>C
>
> C>A 71-29 (margin=42),???????? A>B 52-26 (margin=26),???? B>C
> 51-49 (margin=2).
>
> Voted at least equal-top (or Top Ratings) scores:?? C45, ?? B26, A29.
> Voted above bottom (or Approval) scores: ?? ?? ?? ?? ?? ??
> C75,???? B51, A52.
>
>
> The weakening of C has caused WV and IRV to change from B to C, now
> agreeing with LV and Margins.
> Assuming the change was from sincere to insincere, those very lucky
> and/or very well informed 4 voters
> have pulled off a Push-over strategy.
>
> This is a failure of Mono-raise-delete (more obvious if we reverse
> the
> order of the two situations), which
> is one of Woodall's mononicity criteria that he says is incompatible
> with Condorcet.
>
> Nonetheless in this case C is still the positionally dominant
> uncovered
> candidate and Losing Votes (erw)
> and Margins both still elect C.
>
> Steve Eppley's old example to illustrate (I think his) Non-Drastic
> Defense criterion, which says that if
> on more than half the ballots B is voted no lower than equal-top and
> above A then A can't win.
>
> 46: A>C (sincere may be A>B)
> 10: B>A
> 10: B>C
> 34: C=B (the "defenders", sincere may be C>B)
>
> B>A 54-46 (m=8),?? A>C 56-44 (m=12), C>B (80-54 erw, "normally"
> 46-20, m=26).
>
> Voted at least equal-top (or Top Ratings) scores:?? B54, ?? A46, C34.
> Voted above bottom (or Approval) scores: ?? ?? ?? ?? ?? ??
> B54,???? A56, C90.
>
> B is the only candidate top-rated on more than half the ballots. More
> than half the voters voted B
> above A and B not lower than equal-top.?? Margins and Losing Votes
> without my recommended
> "above-bottom equal-ranking whole" bit elect A, violating the
> Non-Drastic Defense criterion.
>
> Losing Votes (erw) and WV elect B.
>
> If anyone has?? some counter-examples where they think that
> Winning Votes
> does better than
> Losing Votes (erw), I'd be interested in seeing them.
>
> Chris Benham
>
>
>
>
>
>
>
>
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>
>
TP
Toby Pereira
Wed, May 29, 2019 1:07 PM
I don't have a definite answer to the question of equally ranked ballots, and to me I suppose it's still an open question exactly what the best way forwards is, even if you make a good argument against margins.
I don't have an example where the plurality criterion bars from winning the candidate that I think should have won. Looking at the definition on the Wikipedia: "If the number of ballots ranking A as the first preference is greater than the number of ballots on which another candidate B is given any preference, then A's probability of winning must be no less than B's.", it's more that I would disagree with the terminology "given any preference."
If the definition was "If the number of ballots ranking A as the first preference is greater than the number of ballots on which another candidate B is ranked anything other than last or joint last (either explicitly or through implication on a truncated ballot), then A's probability of winning must be no less than B's." then I'd be less critical of it. I think the way it's worded implies an approval cut-off even if in practice it makes no difference.
Toby
From: C.Benham <cbenham@adam.com.au>
To: Toby Pereira tdp201b@yahoo.co.uk; "cbenham@adam.com.au" cbenham@adam.com.au; "election-methods@lists.electorama.com" election-methods@lists.electorama.com
Sent: Sunday, 26 May 2019, 20:19
Subject: Re: [EM] Losing Votes (equal-ranking whole)
Toby,
If you try to give that calculator a truncated ballot it will just turn it into the sort of ballot you like.
How do you think equally-ranked ballots should be counted in a pairwise comparison? A half-vote to
each or zero to both?
So you can't actually point to any election example where the Plurality criterion bars from winning the candidate
that you think should have won?
46: A 44: B>C 10: C Returning to this, are you happy with B winning? And if not, why not?
Chris Benham
On 27/05/2019 3:38 am, Toby Pereira wrote:
By unranked candidates, I meant the ones that had not had any sort of "vote" - the ones not explicitly listed by the voter. If there are three candidates in an election, A, B, and C, I might like A but absolutely hate the others. My vote might simply be:
A
On the other hand, while I might still absolutely hate B and C, I might still hate C more. So my vote might be:
A>B
But just because I have ranked B on my ballot, this should not be taken as any sort of endorsement of B or a vote "for" B.
My vote could also be:
A>B>C
Does adding C on the end mean that I have in some sense voted for C? I don't think there would actually be any methods where adding C on the end would have any effect on how the winner is calculated, but the plurality criterion would presumably in theory find it acceptable to do so.
But this is more a philosophical objection to the assumptions implicit in the plurality criterion than an an objection to the results that a method obeying the criterion would produce in practice. But anyway, I put my thoughts about the plurality criterion a while ago (as did Juho) here: http://election-methods.5485.n7.nabble.com/EM-Fwd-Ordering-defeats-in-Minimax-td34236.html#a34247
But anyway, thank you for the link to the calculator.
Toby
From: Chris Benham <cbenhamau@yahoo.com.au>
To: "tdp201b@yahoo.co.uk" tdp201b@yahoo.co.uk; "cbenham@adam.com.au" cbenham@adam.com.au; "election-methods@lists.electorama.com" election-methods@lists.electorama.com
Sent: Sunday, 26 May 2019, 18:08
Subject: Re: [EM] Losing Votes (equal-ranking whole)
Toby,
You would like this old online ranked-ballot voting calculator:
https://www.cse.wustl.edu/~legrand/rbvote/calc.html
What do you think are the "false premises" that the Plurality criterion is based on??? It was coined with the assumption
that voters could only strictly rank from the top however many candidates they wish, and those not truncated had in
some sense been "voted for". It says that if A has more first-place votes than B has any sort of votes then B can't win.
No explicit mention of "unranked candidates".
(Adapting it to ballots that allow equal-ranking at the top,?? "first preferences" refers to first-preference score on the
ballots symmetrically completed, at least at the top, ballots).
To sensibly claim that it is a "mistake" for an algorithm to do (or apparently "assume") something, I think you need to
point to something wrong with an actual result of it doing so.
My answer to your question is no.
Chris Benham
On 27/05/2019 1:04 am, Toby Pereira wrote:
I think it's a mistake to assume some sort of approval of a ranked candidate. If it's not explicitly part of a method then you should not infer it. As far as I'm concerned:
46: A 44: B>C 10: C
Is the same as:
46: A>B=C 44: B>C>A 10: C>A=B
Presented with these ballots, does this change who you think the winner should be?
This isn't a defence of margins by me or an argument against anything else in your post, but I think the plurality criterion, by talking about unranked candidates, is based on false premises.
Toby
On Sat, 25 May 2019 at 15:31, C.Benham cbenham@adam.com.au wrote: There are several Condorcet algorithms that decide the winner by
weighing "defeat strengths" and they
are all equivalent to MinMax?? when there are no more than 3 candidates.
The ones I have in mind that are equal or very nearly equal in merit are
River, Schulze, Ranked Pairs, Smith//MinMax.
In public political elections they are very very unlikely to give
different winners. River and Smith//MinMax seem to me
to be the easiest to understand and explain and use. The other two are
perhaps a bit more elegant and have their
enthusiastic supporters.
This is to make the case that measuring pairwise defeat strength by the
number of votes on the losing side with above-bottom
equal-ranking contributing a whole vote to each side (and otherwise as
with normal Winning Votes) is much better than either
Winning Votes or Margins.
The case for Losing Votes(erw)?? against Margins is that it (in common
with WV) it meets the Plurality criterion and the Non-Drastic
Defense criterion.
The case for Losing Votes(erw) against Winning Votes is that it meets
the Chicken Dilemma criterion and that is much less likely
to fail to elect a positionally dominant uncovered candidate. (I don't
see how it can fail to elect such a candidate in the 3-candidate case.)
For those who think that Margins might be acceptable:
46: A
44: B>C
10: C
A>B 46-44 (margin=2),???? B>C 44-10 (margin=34),???? C>A 54-46 (margin=8).
Using Losing Votes (erw) as the measure of defeat strength, the weakest
defeat is the one with the most votes on the losing side.
That is the C>A defeat so MinMax drops that and A wins. Conversely the
strongest defeat is the one with the fewest votes on the
losing side.?? That is the B>C defeat so River and Ranked Pairs lock
that. The second strongest is the A>B defeat so those methods
also lock that. All but one candidate has been thereby disqualified so B
wins, or we ignore the third pairwise defeat because that
makes a cycle, so give a final order A>B>C and A wins.
To meet both of?? the Plurality criterion and the Chicken Dilemma
criterion A must win.
Winning Votes elects C, violating Chicken Dilemma (which it has to do to
meet the previously fashionable Minimal Defense criterion).
Margins elects B.?? This fails the Plurality criterion because A has more
exclusive first-place votes than B has any sort of above-bottom
votes.?? It is also an egregious and outrageous failure of Later-no-Help
(assuming that if all the ballots just vote for one candidate we
elect the plurality winner).
To anyone who is remotely positionally or strategically minded or has
any common sense and isn't blind to everything except the
Margins pairwise matrix, B is clearly the weakest candidate and a
completely unacceptable winner.
35: A
10: A=B
30: B>C
25: C
A>B 45-40 (erw, "normally" 35-30, margin=5),?? ?? B>C 40-25 (margin=15), ??
?? C>A 55-45 (margin=10).
Voted at least equal-top (or Top Ratings) scores:?? A45, ?? B40, C25.
Voted above bottom (or Approval) scores: ?? ?? ?? ?? ???? A45, ?? B40, C55
An old Kevin Venzke example.?? B is neither the most top-rated candidate
or the most approved candidate and is
pairwise-beaten and positionally dominated by A (the most top-rated).
Winning Votes and Margins both elect the clearly weakest candidate, B.??
Losing Votes(erw) elects A.
For those who prefer to have a method comply with Minimal Defense (which
says that if on more than half the ballots
C is voted above A and A no higher than equal-bottom then A can't win)
rather than Chicken Dilemma another method
I prefer to WV is Smith//Approval which here elects C.
25: A>B
26: B>C
23: C>A
26: C
C>A 75-25 (margin=50),???????? A>B 48-26 (margin=22),???? B>C 51-49 (margin=2).
Voted at least equal-top (or Top Ratings) scores:?? C49, ?? B26, A25.
Voted above bottom (or Approval) scores: ?? ?? ?? ?? ?? ?? C75,???? B51, A48.
C is an overwhelmingly positionally dominant uncovered candidate.
Margins and Losing Votes elect C.
WV and IRV elect B.
Now say we change 4 of the 26 C ballots to A>C, thereby making C a bit
weaker.
25: A>B
26: B>C
23: C>A
22: C
04: A>C
C>A 71-29 (margin=42),???????? A>B 52-26 (margin=26),???? B>C 51-49 (margin=2).
Voted at least equal-top (or Top Ratings) scores:?? C45, ?? B26, A29.
Voted above bottom (or Approval) scores: ?? ?? ?? ?? ?? ?? C75,???? B51, A52.
The weakening of C has caused WV and IRV to change from B to C, now
agreeing with LV and Margins.
Assuming the change was from sincere to insincere, those very lucky
and/or very well informed 4 voters
have pulled off a Push-over strategy.
This is a failure of Mono-raise-delete (more obvious if we reverse the
order of the two situations), which
is one of Woodall's mononicity criteria that he says is incompatible
with Condorcet.
Nonetheless in this case C is still the positionally dominant uncovered
candidate and Losing Votes (erw)
and Margins both still elect C.
Steve Eppley's old example to illustrate (I think his) Non-Drastic
Defense criterion, which says that if
on more than half the ballots B is voted no lower than equal-top and
above A then A can't win.
46: A>C (sincere may be A>B)
10: B>A
10: B>C
34: C=B (the "defenders", sincere may be C>B)
B>A 54-46 (m=8),?? A>C 56-44 (m=12), C>B (80-54 erw, "normally" 46-20, m=26).
Voted at least equal-top (or Top Ratings) scores:?? B54, ?? A46, C34.
Voted above bottom (or Approval) scores: ?? ?? ?? ?? ?? ?? B54,???? A56, C90.
B is the only candidate top-rated on more than half the ballots. More
than half the voters voted B
above A and B not lower than equal-top.?? Margins and Losing Votes
without my recommended
"above-bottom equal-ranking whole" bit elect A, violating the
Non-Drastic Defense criterion.
Losing Votes (erw) and WV elect B.
If anyone has?? some counter-examples where they think that Winning Votes
does better than
Losing Votes (erw), I'd be interested in seeing them.
Chris Benham
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I don't have a definite answer to the question of equally ranked ballots, and to me I suppose it's still an open question exactly what the best way forwards is, even if you make a good argument against margins.
I don't have an example where the plurality criterion bars from winning the candidate that I think should have won. Looking at the definition on the Wikipedia: "If the number of ballots ranking A as the first preference is greater than the number of ballots on which another candidate B is given any preference, then A's probability of winning must be no less than B's.", it's more that I would disagree with the terminology "given any preference."
If the definition was "If the number of ballots ranking A as the first preference is greater than the number of ballots on which another candidate B is ranked anything other than last or joint last (either explicitly or through implication on a truncated ballot), then A's probability of winning must be no less than B's." then I'd be less critical of it. I think the way it's worded implies an approval cut-off even if in practice it makes no difference.
Toby
From: C.Benham <cbenham@adam.com.au>
To: Toby Pereira <tdp201b@yahoo.co.uk>; "cbenham@adam.com.au" <cbenham@adam.com.au>; "election-methods@lists.electorama.com" <election-methods@lists.electorama.com>
Sent: Sunday, 26 May 2019, 20:19
Subject: Re: [EM] Losing Votes (equal-ranking whole)
Toby,
If you try to give that calculator a truncated ballot it will just turn it into the sort of ballot you like.
How do you think equally-ranked ballots should be counted in a pairwise comparison? A half-vote to
each or zero to both?
So you can't actually point to any election example where the Plurality criterion bars from winning the candidate
that you think should have won?
46: A 44: B>C 10: C Returning to this, are you happy with B winning? And if not, why not?
Chris Benham
On 27/05/2019 3:38 am, Toby Pereira wrote:
By unranked candidates, I meant the ones that had not had any sort of "vote" - the ones not explicitly listed by the voter. If there are three candidates in an election, A, B, and C, I might like A but absolutely hate the others. My vote might simply be:
A
On the other hand, while I might still absolutely hate B and C, I might still hate C more. So my vote might be:
A>B
But just because I have ranked B on my ballot, this should not be taken as any sort of endorsement of B or a vote "for" B.
My vote could also be:
A>B>C
Does adding C on the end mean that I have in some sense voted for C? I don't think there would actually be any methods where adding C on the end would have any effect on how the winner is calculated, but the plurality criterion would presumably in theory find it acceptable to do so.
But this is more a philosophical objection to the assumptions implicit in the plurality criterion than an an objection to the results that a method obeying the criterion would produce in practice. But anyway, I put my thoughts about the plurality criterion a while ago (as did Juho) here: http://election-methods.5485.n7.nabble.com/EM-Fwd-Ordering-defeats-in-Minimax-td34236.html#a34247
But anyway, thank you for the link to the calculator.
Toby
From: Chris Benham <cbenhamau@yahoo.com.au>
To: "tdp201b@yahoo.co.uk" <tdp201b@yahoo.co.uk>; "cbenham@adam.com.au" <cbenham@adam.com.au>; "election-methods@lists.electorama.com" <election-methods@lists.electorama.com>
Sent: Sunday, 26 May 2019, 18:08
Subject: Re: [EM] Losing Votes (equal-ranking whole)
Toby,
You would like this old online ranked-ballot voting calculator:
https://www.cse.wustl.edu/~legrand/rbvote/calc.html
What do you think are the "false premises" that the Plurality criterion is based on??? It was coined with the assumption
that voters could only strictly rank from the top however many candidates they wish, and those not truncated had in
some sense been "voted for". It says that if A has more first-place votes than B has any sort of votes then B can't win.
No explicit mention of "unranked candidates".
(Adapting it to ballots that allow equal-ranking at the top,?? "first preferences" refers to first-preference score on the
ballots symmetrically completed, at least at the top, ballots).
To sensibly claim that it is a "mistake" for an algorithm to do (or apparently "assume") something, I think you need to
point to something wrong with an actual result of it doing so.
My answer to your question is no.
Chris Benham
On 27/05/2019 1:04 am, Toby Pereira wrote:
I think it's a mistake to assume some sort of approval of a ranked candidate. If it's not explicitly part of a method then you should not infer it. As far as I'm concerned:
46: A 44: B>C 10: C
Is the same as:
46: A>B=C 44: B>C>A 10: C>A=B
Presented with these ballots, does this change who you think the winner should be?
This isn't a defence of margins by me or an argument against anything else in your post, but I think the plurality criterion, by talking about unranked candidates, is based on false premises.
Toby
On Sat, 25 May 2019 at 15:31, C.Benham <cbenham@adam.com.au> wrote: There are several Condorcet algorithms that decide the winner by
weighing "defeat strengths" and they
are all equivalent to MinMax?? when there are no more than 3 candidates.
The ones I have in mind that are equal or very nearly equal in merit are
River, Schulze, Ranked Pairs, Smith//MinMax.
In public political elections they are very very unlikely to give
different winners. River and Smith//MinMax seem to me
to be the easiest to understand and explain and use. The other two are
perhaps a bit more elegant and have their
enthusiastic supporters.
This is to make the case that measuring pairwise defeat strength by the
number of votes on the losing side with above-bottom
equal-ranking contributing a whole vote to each side (and otherwise as
with normal Winning Votes) is much better than either
Winning Votes or Margins.
The case for Losing Votes(erw)?? against Margins is that it (in common
with WV) it meets the Plurality criterion and the Non-Drastic
Defense criterion.
The case for Losing Votes(erw) against Winning Votes is that it meets
the Chicken Dilemma criterion and that is much less likely
to fail to elect a positionally dominant uncovered candidate. (I don't
see how it can fail to elect such a candidate in the 3-candidate case.)
For those who think that Margins might be acceptable:
46: A
44: B>C
10: C
A>B 46-44 (margin=2),???? B>C 44-10 (margin=34),???? C>A 54-46 (margin=8).
Using Losing Votes (erw) as the measure of defeat strength, the weakest
defeat is the one with the most votes on the losing side.
That is the C>A defeat so MinMax drops that and A wins. Conversely the
strongest defeat is the one with the fewest votes on the
losing side.?? That is the B>C defeat so River and Ranked Pairs lock
that. The second strongest is the A>B defeat so those methods
also lock that. All but one candidate has been thereby disqualified so B
wins, or we ignore the third pairwise defeat because that
makes a cycle, so give a final order A>B>C and A wins.
To meet both of?? the Plurality criterion and the Chicken Dilemma
criterion A must win.
Winning Votes elects C, violating Chicken Dilemma (which it has to do to
meet the previously fashionable Minimal Defense criterion).
Margins elects B.?? This fails the Plurality criterion because A has more
exclusive first-place votes than B has any sort of above-bottom
votes.?? It is also an egregious and outrageous failure of Later-no-Help
(assuming that if all the ballots just vote for one candidate we
elect the plurality winner).
To anyone who is remotely positionally or strategically minded or has
any common sense and isn't blind to everything except the
Margins pairwise matrix, B is clearly the weakest candidate and a
completely unacceptable winner.
35: A
10: A=B
30: B>C
25: C
A>B 45-40 (erw, "normally" 35-30, margin=5),?? ?? B>C 40-25 (margin=15), ??
?? C>A 55-45 (margin=10).
Voted at least equal-top (or Top Ratings) scores:?? A45, ?? B40, C25.
Voted above bottom (or Approval) scores: ?? ?? ?? ?? ???? A45, ?? B40, C55
An old Kevin Venzke example.?? B is neither the most top-rated candidate
or the most approved candidate and is
pairwise-beaten and positionally dominated by A (the most top-rated).
Winning Votes and Margins both elect the clearly weakest candidate, B.??
Losing Votes(erw) elects A.
For those who prefer to have a method comply with Minimal Defense (which
says that if on more than half the ballots
C is voted above A and A no higher than equal-bottom then A can't win)
rather than Chicken Dilemma another method
I prefer to WV is Smith//Approval which here elects C.
25: A>B
26: B>C
23: C>A
26: C
C>A 75-25 (margin=50),???????? A>B 48-26 (margin=22),???? B>C 51-49 (margin=2).
Voted at least equal-top (or Top Ratings) scores:?? C49, ?? B26, A25.
Voted above bottom (or Approval) scores: ?? ?? ?? ?? ?? ?? C75,???? B51, A48.
C is an overwhelmingly positionally dominant uncovered candidate.
Margins and Losing Votes elect C.
WV and IRV elect B.
Now say we change 4 of the 26 C ballots to A>C, thereby making C a bit
weaker.
25: A>B
26: B>C
23: C>A
22: C
04: A>C
C>A 71-29 (margin=42),???????? A>B 52-26 (margin=26),???? B>C 51-49 (margin=2).
Voted at least equal-top (or Top Ratings) scores:?? C45, ?? B26, A29.
Voted above bottom (or Approval) scores: ?? ?? ?? ?? ?? ?? C75,???? B51, A52.
The weakening of C has caused WV and IRV to change from B to C, now
agreeing with LV and Margins.
Assuming the change was from sincere to insincere, those very lucky
and/or very well informed 4 voters
have pulled off a Push-over strategy.
This is a failure of Mono-raise-delete (more obvious if we reverse the
order of the two situations), which
is one of Woodall's mononicity criteria that he says is incompatible
with Condorcet.
Nonetheless in this case C is still the positionally dominant uncovered
candidate and Losing Votes (erw)
and Margins both still elect C.
Steve Eppley's old example to illustrate (I think his) Non-Drastic
Defense criterion, which says that if
on more than half the ballots B is voted no lower than equal-top and
above A then A can't win.
46: A>C (sincere may be A>B)
10: B>A
10: B>C
34: C=B (the "defenders", sincere may be C>B)
B>A 54-46 (m=8),?? A>C 56-44 (m=12), C>B (80-54 erw, "normally" 46-20, m=26).
Voted at least equal-top (or Top Ratings) scores:?? B54, ?? A46, C34.
Voted above bottom (or Approval) scores: ?? ?? ?? ?? ?? ?? B54,???? A56, C90.
B is the only candidate top-rated on more than half the ballots. More
than half the voters voted B
above A and B not lower than equal-top.?? Margins and Losing Votes
without my recommended
"above-bottom equal-ranking whole" bit elect A, violating the
Non-Drastic Defense criterion.
Losing Votes (erw) and WV elect B.
If anyone has?? some counter-examples where they think that Winning Votes
does better than
Losing Votes (erw), I'd be interested in seeing them.
Chris Benham
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C
C.Benham
Sat, Jun 1, 2019 9:28 AM
Toby,
I didn't coin the Plurality criterion, and I do somewhat prefer your
suggested alternative wording. To take account of equal-top ranking being
allowed, I would specify the fractional interpretation of "number of
ballots ranking A as the first preference". The original coiner of the
criterion
was operating on the assumption that no equal-ranking would be allowed
(except at the bottom implied by truncation which would be allowed)
and perhaps also that no-one would needlessly mark a candidate strictly
bottom when they could just truncate.
I think in part the criterion is tailor-made for voters accustomed to
and content with plurality voting, and after some new election on ballots
that allow voters to rank the candidates is used, they want to know why
B won while their favourite candidate A was voted (alone) in first place
on more ballots than B was voted above bottom. And I like the criterion
because I agree that there can't be a good enough answer.
A standard (and possible criterion) I like says that if A both
positionally dominates and pairwise beats B then B can't win. That
implies Plurality.
35: A
10: A=B
30: B>C
25: C
Here no ballots vote A or B below equal-top. A has more top (or first)
place votes than B so positionally dominates and pairwise beats B.
Do you think B is an acceptable winner?
Chris Benham
On 29/05/2019 10:37 pm, Toby Pereira wrote:
I don't have a definite answer to the question of equally ranked
ballots, and to me I suppose it's still an open question exactly what
the best way forwards is, even if you make a good argument against
margins.
I don't have an example where the plurality criterion bars from
winning the candidate that I think should have won. Looking at the
definition on the Wikipedia: "If the number of ballots ranking A as
the first preference is greater than the number of ballots on which
another candidate B is given any preference, then A's probability of
winning must be no less than B's.", it's more that I would disagree
with the terminology "given any preference."
If the definition was "If the number of ballots ranking A as the first
preference is greater than the number of ballots on which another
candidate B is ranked anything other than last or joint last (either
explicitly or through implication on a truncated ballot), then A's
probability of winning must be no less than B's." then I'd be less
critical of it. I think the way it's worded implies an approval
cut-off even if in practice it makes no difference.
Toby
From: C.Benham cbenham@adam.com.au
To: Toby Pereira tdp201b@yahoo.co.uk; "cbenham@adam.com.au"
cbenham@adam.com.au; "election-methods@lists.electorama.com"
election-methods@lists.electorama.com
Sent: Sunday, 26 May 2019, 20:19
Subject: Re: [EM] Losing Votes (equal-ranking whole)
Toby,
If you try to give that calculator a truncated ballot it will just
turn it into the sort of ballot you like.
How do you think equally-ranked ballots should be counted in a
pairwise comparison? A half-vote to
each or zero to both?
So you can't actually point to any election example where the
Plurality criterion bars from winning the candidate
that you think should have won?
46: A
44: B>C
10: C
Returning to this, are you happy with B winning? And if not, why not?
Chris Benham
On 27/05/2019 3:38 am, Toby Pereira wrote:
By unranked candidates, I meant the ones that had not had any sort of
"vote" - the ones not explicitly listed by the voter. If there are
three candidates in an election, A, B, and C, I might like A but
absolutely hate the others. My vote might simply be:
A
On the other hand, while I might still absolutely hate B and C, I
might still hate C more. So my vote might be:
A>B
But just because I have ranked B on my ballot, this should not be
taken as any sort of endorsement of B or a vote "for" B.
My vote could also be:
A>B>C
Does adding C on the end mean that I have in some sense voted for C? I
don't think there would actually be any methods where adding C on the
end would have any effect on how the winner is calculated, but the
plurality criterion would presumably in theory find it acceptable to
do so.
But this is more a philosophical objection to the assumptions implicit
in the plurality criterion than an an objection to the results that a
method obeying the criterion would produce in practice. But anyway, I
put my thoughts about the plurality criterion a while ago (as did
Juho) here:
http://election-methods.5485.n7.nabble.com/EM-Fwd-Ordering-defeats-in-Minimax-td34236.html#a34247
But anyway, thank you for the link to the calculator.
Toby
From: Chris Benham cbenhamau@yahoo.com.au
mailto:cbenhamau@yahoo.com.au
To: "tdp201b@yahoo.co.uk" mailto:tdp201b@yahoo.co.uk
tdp201b@yahoo.co.uk mailto:tdp201b@yahoo.co.uk;
"cbenham@adam.com.au" mailto:cbenham@adam.com.au
cbenham@adam.com.au mailto:cbenham@adam.com.au;
"election-methods@lists.electorama.com"
mailto:election-methods@lists.electorama.com
election-methods@lists.electorama.com
mailto:election-methods@lists.electorama.com
Sent: Sunday, 26 May 2019, 18:08
Subject: Re: [EM] Losing Votes (equal-ranking whole)
Toby,
You would like this old online ranked-ballot voting calculator:
https://www.cse.wustl.edu/~legrand/rbvote/calc.html
What do you think are the "false premises" that the Plurality
criterion is based on??? It was coined with the assumption
that voters could only strictly rank from the top however many
candidates they wish, and those not truncated had in
some sense been "voted for". It says that if A has more first-place
votes than B has any sort of votes then B can't win.
No explicit mention of "unranked candidates".
(Adapting it to ballots that allow equal-ranking at the top,?? "first
preferences" refers to first-preference score on the
ballots symmetrically completed, at least at the top, ballots).
To sensibly claim that it is a "mistake" for an algorithm to do (or
apparently "assume") something, I think you need to
point to something wrong with an actual result of it doing so.
My answer to your question is no.
Chris Benham
On 27/05/2019 1:04 am, Toby Pereira wrote:
I think it's a mistake to assume some sort of approval of a ranked
candidate. If it's not explicitly part of a method then you should not
infer it. As far as I'm concerned:
46: A
44: B>C
10: C
Is the same as:
46: A>B=C
44: B>C>A
10: C>A=B
Presented with these ballots, does this change who you think the
winner should be?
This isn't a defence of margins by me or an argument against anything
else in your post, but I think the plurality criterion, by talking
about unranked candidates, is based on false premises.
Toby
On Sat, 25 May 2019 at 15:31, C.Benham
<cbenham@adam.com.au> <mailto:cbenham@adam.com.au> wrote:
There are several Condorcet algorithms that decide the winner by
weighing "defeat strengths" and they
are all equivalent to MinMax when there are no more than 3 candidates.
The ones I have in mind that are equal or very nearly equal in
merit are
River, Schulze, Ranked Pairs, Smith//MinMax.
In public political elections they are very very unlikely to give
different winners. River and Smith//MinMax seem to me
to be the easiest to understand and explain and use. The other two
are
perhaps a bit more elegant and have their
enthusiastic supporters.
This is to make the case that measuring pairwise defeat strength
by the
number of votes on the losing side with above-bottom
equal-ranking contributing a whole vote to each side (and
otherwise as
with normal Winning Votes) is much better than either
Winning Votes or Margins.
The case for Losing Votes(erw) against Margins is that it (in common
with WV) it meets the Plurality criterion and the Non-Drastic
Defense criterion.
The case for Losing Votes(erw) against Winning Votes is that it meets
the Chicken Dilemma criterion and that is much less likely
to fail to elect a positionally dominant uncovered candidate. (I
don't
see how it can fail to elect such a candidate in the 3-candidate
case.)
For those who think that Margins might be acceptable:
46: A
44: B>C
10: C
A>B 46-44 (margin=2), B>C 44-10 (margin=34), C>A 54-46 (margin=8).
Using Losing Votes (erw) as the measure of defeat strength, the
weakest
defeat is the one with the most votes on the losing side.
That is the C>A defeat so MinMax drops that and A wins. Conversely
the
strongest defeat is the one with the fewest votes on the
losing side. That is the B>C defeat so River and Ranked Pairs lock
that. The second strongest is the A>B defeat so those methods
also lock that. All but one candidate has been thereby
disqualified so B
wins, or we ignore the third pairwise defeat because that
makes a cycle, so give a final order A>B>C and A wins.
To meet both of the Plurality criterion and the Chicken Dilemma
criterion A must win.
Winning Votes elects C, violating Chicken Dilemma (which it has to
do to
meet the previously fashionable Minimal Defense criterion).
Margins elects B. This fails the Plurality criterion because A has
more
exclusive first-place votes than B has any sort of above-bottom
votes. It is also an egregious and outrageous failure of
Later-no-Help
(assuming that if all the ballots just vote for one candidate we
elect the plurality winner).
To anyone who is remotely positionally or strategically minded or has
any common sense and isn't blind to everything except the
Margins pairwise matrix, B is clearly the weakest candidate and a
completely unacceptable winner.
35: A
10: A=B
30: B>C
25: C
A>B 45-40 (erw, "normally" 35-30, margin=5), B>C 40-25 (margin=15),
C>A 55-45 (margin=10).
Voted at least equal-top (or Top Ratings) scores: A45, B40, C25.
Voted above bottom (or Approval) scores: A45, B40, C55
An old Kevin Venzke example. B is neither the most top-rated
candidate
or the most approved candidate and is
pairwise-beaten and positionally dominated by A (the most top-rated).
Winning Votes and Margins both elect the clearly weakest candidate, B.
Losing Votes(erw) elects A.
For those who prefer to have a method comply with Minimal Defense
(which
says that if on more than half the ballots
C is voted above A and A no higher than equal-bottom then A can't
win)
rather than Chicken Dilemma another method
I prefer to WV is Smith//Approval which here elects C.
25: A>B
26: B>C
23: C>A
26: C
C>A 75-25 (margin=50), A>B 48-26 (margin=22), B>C 51-49 (margin=2).
Voted at least equal-top (or Top Ratings) scores: C49, B26, A25.
Voted above bottom (or Approval) scores: C75, B51, A48.
C is an overwhelmingly positionally dominant uncovered candidate.
Margins and Losing Votes elect C.
WV and IRV elect B.
Now say we change 4 of the 26 C ballots to A>C, thereby making C a
bit
weaker.
25: A>B
26: B>C
23: C>A
22: C
04: A>C
C>A 71-29 (margin=42), A>B 52-26 (margin=26), B>C 51-49 (margin=2).
Voted at least equal-top (or Top Ratings) scores: C45, B26, A29.
Voted above bottom (or Approval) scores: C75, B51, A52.
The weakening of C has caused WV and IRV to change from B to C, now
agreeing with LV and Margins.
Assuming the change was from sincere to insincere, those very lucky
and/or very well informed 4 voters
have pulled off a Push-over strategy.
This is a failure of Mono-raise-delete (more obvious if we reverse
the
order of the two situations), which
is one of Woodall's mononicity criteria that he says is incompatible
with Condorcet.
Nonetheless in this case C is still the positionally dominant
uncovered
candidate and Losing Votes (erw)
and Margins both still elect C.
Steve Eppley's old example to illustrate (I think his) Non-Drastic
Defense criterion, which says that if
on more than half the ballots B is voted no lower than equal-top and
above A then A can't win.
46: A>C (sincere may be A>B)
10: B>A
10: B>C
34: C=B (the "defenders", sincere may be C>B)
B>A 54-46 (m=8), A>C 56-44 (m=12), C>B (80-54 erw, "normally"
46-20, m=26).
Voted at least equal-top (or Top Ratings) scores: B54, A46, C34.
Voted above bottom (or Approval) scores: B54, A56, C90.
B is the only candidate top-rated on more than half the ballots. More
than half the voters voted B
above A and B not lower than equal-top. Margins and Losing Votes
without my recommended
"above-bottom equal-ranking whole" bit elect A, violating the
Non-Drastic Defense criterion.
Losing Votes (erw) and WV elect B.
If anyone has some counter-examples where they think that Winning
Votes
does better than
Losing Votes (erw), I'd be interested in seeing them.
Chris Benham
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Toby,
I didn't coin the Plurality criterion, and I do somewhat prefer your
suggested alternative wording. To take account of equal-top ranking being
allowed, I would specify the fractional interpretation of "number of
ballots ranking A as the first preference". The original coiner of the
criterion
was operating on the assumption that no equal-ranking would be allowed
(except at the bottom implied by truncation which would be allowed)
and perhaps also that no-one would needlessly mark a candidate strictly
bottom when they could just truncate.
I think in part the criterion is tailor-made for voters accustomed to
and content with plurality voting, and after some new election on ballots
that allow voters to rank the candidates is used, they want to know why
B won while their favourite candidate A was voted (alone) in first place
on more ballots than B was voted above bottom. And I like the criterion
because I agree that there can't be a good enough answer.
A standard (and possible criterion) I like says that if A both
positionally dominates and pairwise beats B then B can't win. That
implies Plurality.
35: A
10: A=B
30: B>C
25: C
Here no ballots vote A or B below equal-top. A has more top (or first)
place votes than B so positionally dominates and pairwise beats B.
Do you think B is an acceptable winner?
Chris Benham
On 29/05/2019 10:37 pm, Toby Pereira wrote:
> I don't have a definite answer to the question of equally ranked
> ballots, and to me I suppose it's still an open question exactly what
> the best way forwards is, even if you make a good argument against
> margins.
>
> I don't have an example where the plurality criterion bars from
> winning the candidate that I think should have won. Looking at the
> definition on the Wikipedia: "If the number of ballots ranking A as
> the first preference is greater than the number of ballots on which
> another candidate B is given any preference, then A's probability of
> winning must be no less than B's.", it's more that I would disagree
> with the terminology "given any preference."
>
> If the definition was "If the number of ballots ranking A as the first
> preference is greater than the number of ballots on which another
> candidate B is ranked anything other than last or joint last (either
> explicitly or through implication on a truncated ballot), then A's
> probability of winning must be no less than B's." then I'd be less
> critical of it. I think the way it's worded implies an approval
> cut-off even if in practice it makes no difference.
>
> Toby
>
>
> ------------------------------------------------------------------------
> *From:* C.Benham <cbenham@adam.com.au>
> *To:* Toby Pereira <tdp201b@yahoo.co.uk>; "cbenham@adam.com.au"
> <cbenham@adam.com.au>; "election-methods@lists.electorama.com"
> <election-methods@lists.electorama.com>
> *Sent:* Sunday, 26 May 2019, 20:19
> *Subject:* Re: [EM] Losing Votes (equal-ranking whole)
>
> Toby,
>
> If you try to give that calculator a truncated ballot it will just
> turn it into the sort of ballot you like.
>
> How do you think equally-ranked ballots should be counted in a
> pairwise comparison? A half-vote to
> each or zero to both?
>
> So you can't actually point to any election example where the
> Plurality criterion bars from winning the candidate
> that you think should have won?
> 46: A
> 44: B>C
> 10: C
> Returning to this, are you happy with B winning? And if not, why not?
>
> Chris Benham
>
> On 27/05/2019 3:38 am, Toby Pereira wrote:
> By unranked candidates, I meant the ones that had not had any sort of
> "vote" - the ones not explicitly listed by the voter. If there are
> three candidates in an election, A, B, and C, I might like A but
> absolutely hate the others. My vote might simply be:
>
> A
>
> On the other hand, while I might still absolutely hate B and C, I
> might still hate C more. So my vote might be:
>
> A>B
>
> But just because I have ranked B on my ballot, this should not be
> taken as any sort of endorsement of B or a vote "for" B.
>
> My vote could also be:
>
> A>B>C
>
> Does adding C on the end mean that I have in some sense voted for C? I
> don't think there would actually be any methods where adding C on the
> end would have any effect on how the winner is calculated, but the
> plurality criterion would presumably in theory find it acceptable to
> do so.
>
> But this is more a philosophical objection to the assumptions implicit
> in the plurality criterion than an an objection to the results that a
> method obeying the criterion would produce in practice. But anyway, I
> put my thoughts about the plurality criterion a while ago (as did
> Juho) here:
> http://election-methods.5485.n7.nabble.com/EM-Fwd-Ordering-defeats-in-Minimax-td34236.html#a34247
>
> But anyway, thank you for the link to the calculator.
>
> Toby
>
>
>
>
> ------------------------------------------------------------------------
> *From:* Chris Benham <cbenhamau@yahoo.com.au>
> <mailto:cbenhamau@yahoo.com.au>
> *To:* "tdp201b@yahoo.co.uk" <mailto:tdp201b@yahoo.co.uk>
> <tdp201b@yahoo.co.uk> <mailto:tdp201b@yahoo.co.uk>;
> "cbenham@adam.com.au" <mailto:cbenham@adam.com.au>
> <cbenham@adam.com.au> <mailto:cbenham@adam.com.au>;
> "election-methods@lists.electorama.com"
> <mailto:election-methods@lists.electorama.com>
> <election-methods@lists.electorama.com>
> <mailto:election-methods@lists.electorama.com>
> *Sent:* Sunday, 26 May 2019, 18:08
> *Subject:* Re: [EM] Losing Votes (equal-ranking whole)
>
> Toby,
>
> You would like this old online ranked-ballot voting calculator:
>
> https://www.cse.wustl.edu/~legrand/rbvote/calc.html
>
> What do you think are the "false premises" that the Plurality
> criterion is based on??? It was coined with the assumption
> that voters could only strictly rank from the top however many
> candidates they wish, and those not truncated had in
> some sense been "voted for". It says that if A has more first-place
> votes than B has any sort of votes then B can't win.
> No explicit mention of "unranked candidates".
>
> (Adapting it to ballots that allow equal-ranking at the top,?? "first
> preferences" refers to first-preference score on the
> ballots symmetrically completed, at least at the top, ballots).
> To sensibly claim that it is a "mistake" for an algorithm to do (or
> apparently "assume") something, I think you need to
> point to something wrong with an actual result of it doing so.
>
> My answer to your question is no.
> Chris Benham
>
>
> On 27/05/2019 1:04 am, Toby Pereira wrote:
> I think it's a mistake to assume some sort of approval of a ranked
> candidate. If it's not explicitly part of a method then you should not
> infer it. As far as I'm concerned:
>
> 46: A
> 44: B>C
> 10: C
>
> Is the same as:
>
> 46: A>B=C
> 44: B>C>A
> 10: C>A=B
>
> Presented with these ballots, does this change who you think the
> winner should be?
>
> This isn't a defence of margins by me or an argument against anything
> else in your post, but I think the plurality criterion, by talking
> about unranked candidates, is based on false premises.
>
> Toby
>
> On Sat, 25 May 2019 at 15:31, C.Benham
> <cbenham@adam.com.au> <mailto:cbenham@adam.com.au> wrote:
> There are several Condorcet algorithms that decide the winner by
> weighing "defeat strengths" and they
> are all equivalent to MinMax when there are no more than 3 candidates.
>
> The ones I have in mind that are equal or very nearly equal in
> merit are
> River, Schulze, Ranked Pairs, Smith//MinMax.
> In public political elections they are very very unlikely to give
> different winners. River and Smith//MinMax seem to me
> to be the easiest to understand and explain and use. The other two
> are
> perhaps a bit more elegant and have their
> enthusiastic supporters.
>
> This is to make the case that measuring pairwise defeat strength
> by the
> number of votes on the losing side with above-bottom
> equal-ranking contributing a whole vote to each side (and
> otherwise as
> with normal Winning Votes) is much better than either
> Winning Votes or Margins.
>
> The case for Losing Votes(erw) against Margins is that it (in common
> with WV) it meets the Plurality criterion and the Non-Drastic
> Defense criterion.
>
> The case for Losing Votes(erw) against Winning Votes is that it meets
> the Chicken Dilemma criterion and that is much less likely
> to fail to elect a positionally dominant uncovered candidate. (I
> don't
> see how it can fail to elect such a candidate in the 3-candidate
> case.)
>
> For those who think that Margins might be acceptable:
>
> 46: A
> 44: B>C
> 10: C
>
> A>B 46-44 (margin=2), B>C 44-10 (margin=34), C>A 54-46 (margin=8).
>
> Using Losing Votes (erw) as the measure of defeat strength, the
> weakest
> defeat is the one with the most votes on the losing side.
> That is the C>A defeat so MinMax drops that and A wins. Conversely
> the
> strongest defeat is the one with the fewest votes on the
> losing side. That is the B>C defeat so River and Ranked Pairs lock
> that. The second strongest is the A>B defeat so those methods
> also lock that. All but one candidate has been thereby
> disqualified so B
> wins, or we ignore the third pairwise defeat because that
> makes a cycle, so give a final order A>B>C and A wins.
>
> To meet both of the Plurality criterion and the Chicken Dilemma
> criterion A must win.
>
> Winning Votes elects C, violating Chicken Dilemma (which it has to
> do to
> meet the previously fashionable Minimal Defense criterion).
>
> Margins elects B. This fails the Plurality criterion because A has
> more
> exclusive first-place votes than B has any sort of above-bottom
> votes. It is also an egregious and outrageous failure of
> Later-no-Help
> (assuming that if all the ballots just vote for one candidate we
> elect the plurality winner).
>
> To anyone who is remotely positionally or strategically minded or has
> any common sense and isn't blind to everything except the
> Margins pairwise matrix, B is clearly the weakest candidate and a
> completely unacceptable winner.
>
> 35: A
> 10: A=B
> 30: B>C
> 25: C
>
> A>B 45-40 (erw, "normally" 35-30, margin=5), B>C 40-25 (margin=15),
> C>A 55-45 (margin=10).
>
> Voted at least equal-top (or Top Ratings) scores: A45, B40, C25.
> Voted above bottom (or Approval) scores: A45, B40, C55
>
> An old Kevin Venzke example. B is neither the most top-rated
> candidate
> or the most approved candidate and is
> pairwise-beaten and positionally dominated by A (the most top-rated).
>
> Winning Votes and Margins both elect the clearly weakest candidate, B.
> Losing Votes(erw) elects A.
>
> For those who prefer to have a method comply with Minimal Defense
> (which
> says that if on more than half the ballots
> C is voted above A and A no higher than equal-bottom then A can't
> win)
> rather than Chicken Dilemma another method
> I prefer to WV is Smith//Approval which here elects C.
>
> 25: A>B
> 26: B>C
> 23: C>A
> 26: C
>
> C>A 75-25 (margin=50), A>B 48-26 (margin=22), B>C 51-49 (margin=2).
>
> Voted at least equal-top (or Top Ratings) scores: C49, B26, A25.
> Voted above bottom (or Approval) scores: C75, B51, A48.
>
> C is an overwhelmingly positionally dominant uncovered candidate.
> Margins and Losing Votes elect C.
> WV and IRV elect B.
>
> Now say we change 4 of the 26 C ballots to A>C, thereby making C a
> bit
> weaker.
>
> 25: A>B
> 26: B>C
> 23: C>A
> 22: C
> 04: A>C
>
> C>A 71-29 (margin=42), A>B 52-26 (margin=26), B>C 51-49 (margin=2).
>
> Voted at least equal-top (or Top Ratings) scores: C45, B26, A29.
> Voted above bottom (or Approval) scores: C75, B51, A52.
>
>
> The weakening of C has caused WV and IRV to change from B to C, now
> agreeing with LV and Margins.
> Assuming the change was from sincere to insincere, those very lucky
> and/or very well informed 4 voters
> have pulled off a Push-over strategy.
>
> This is a failure of Mono-raise-delete (more obvious if we reverse
> the
> order of the two situations), which
> is one of Woodall's mononicity criteria that he says is incompatible
> with Condorcet.
>
> Nonetheless in this case C is still the positionally dominant
> uncovered
> candidate and Losing Votes (erw)
> and Margins both still elect C.
>
> Steve Eppley's old example to illustrate (I think his) Non-Drastic
> Defense criterion, which says that if
> on more than half the ballots B is voted no lower than equal-top and
> above A then A can't win.
>
> 46: A>C (sincere may be A>B)
> 10: B>A
> 10: B>C
> 34: C=B (the "defenders", sincere may be C>B)
>
> B>A 54-46 (m=8), A>C 56-44 (m=12), C>B (80-54 erw, "normally"
> 46-20, m=26).
>
> Voted at least equal-top (or Top Ratings) scores: B54, A46, C34.
> Voted above bottom (or Approval) scores: B54, A56, C90.
>
> B is the only candidate top-rated on more than half the ballots. More
> than half the voters voted B
> above A and B not lower than equal-top. Margins and Losing Votes
> without my recommended
> "above-bottom equal-ranking whole" bit elect A, violating the
> Non-Drastic Defense criterion.
>
> Losing Votes (erw) and WV elect B.
>
> If anyone has some counter-examples where they think that Winning
> Votes
> does better than
> Losing Votes (erw), I'd be interested in seeing them.
>
> Chris Benham
>
>
>
>
>
>
>
>
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FJ
Faran, James
Sat, Jun 1, 2019 12:15 PM
51 A>B>C>D
49 B>C>D>A
Is A a better choice than B?
-
Yes. Plurality demands it. Moreover, B beats C and D on all ballots, so C and D can be ignored and the pairwise race is all that's left.
-
No. A is ranked bottom on 49% of ballots, B ranked at least second on 100%, top on almost half.
Are C and D Irrelevant Alternatives?
Jim Faran
On Jun 1, 2019 5:28 AM, "C.Benham" cbenham@adam.com.au wrote:
Toby,
I didn't coin the Plurality criterion, and I do somewhat prefer your suggested alternative wording. To take account of equal-top ranking being
allowed, I would specify the fractional interpretation of "number of ballots ranking A as the first preference". The original coiner of the criterion
was operating on the assumption that no equal-ranking would be allowed (except at the bottom implied by truncation which would be allowed)
and perhaps also that no-one would needlessly mark a candidate strictly bottom when they could just truncate.
I think in part the criterion is tailor-made for voters accustomed to and content with plurality voting, and after some new election on ballots
that allow voters to rank the candidates is used, they want to know why B won while their favourite candidate A was voted (alone) in first place
on more ballots than B was voted above bottom. And I like the criterion because I agree that there can't be a good enough answer.
A standard (and possible criterion) I like says that if A both positionally dominates and pairwise beats B then B can't win. That implies Plurality.
35: A
10: A=B
30: B>C
25: C
Here no ballots vote A or B below equal-top. A has more top (or first) place votes than B so positionally dominates and pairwise beats B.
Do you think B is an acceptable winner?
Chris Benham
On 29/05/2019 10:37 pm, Toby Pereira wrote:
I don't have a definite answer to the question of equally ranked ballots, and to me I suppose it's still an open question exactly what the best way forwards is, even if you make a good argument against margins.
I don't have an example where the plurality criterion bars from winning the candidate that I think should have won. Looking at the definition on the Wikipedia: "If the number of ballots ranking A as the first preference is greater than the number of ballots on which another candidate B is given any preference, then A's probability of winning must be no less than B's.", it's more that I would disagree with the terminology "given any preference."
If the definition was "If the number of ballots ranking A as the first preference is greater than the number of ballots on which another candidate B is ranked anything other than last or joint last (either explicitly or through implication on a truncated ballot), then A's probability of winning must be no less than B's." then I'd be less critical of it. I think the way it's worded implies an approval cut-off even if in practice it makes no difference.
Toby
From: C.Benham cbenham@adam.com.aumailto:cbenham@adam.com.au
To: Toby Pereira tdp201b@yahoo.co.ukmailto:tdp201b@yahoo.co.uk; "cbenham@adam.com.au"mailto:cbenham@adam.com.au cbenham@adam.com.aumailto:cbenham@adam.com.au; "election-methods@lists.electorama.com"mailto:election-methods@lists.electorama.com election-methods@lists.electorama.commailto:election-methods@lists.electorama.com
Sent: Sunday, 26 May 2019, 20:19
Subject: Re: [EM] Losing Votes (equal-ranking whole)
Toby,
If you try to give that calculator a truncated ballot it will just turn it into the sort of ballot you like.
How do you think equally-ranked ballots should be counted in a pairwise comparison? A half-vote to
each or zero to both?
So you can't actually point to any election example where the Plurality criterion bars from winning the candidate
that you think should have won?
46: A
44: B>C
10: C
Returning to this, are you happy with B winning? And if not, why not?
Chris Benham
On 27/05/2019 3:38 am, Toby Pereira wrote:
By unranked candidates, I meant the ones that had not had any sort of "vote" - the ones not explicitly listed by the voter. If there are three candidates in an election, A, B, and C, I might like A but absolutely hate the others. My vote might simply be:
A
On the other hand, while I might still absolutely hate B and C, I might still hate C more. So my vote might be:
A>B
But just because I have ranked B on my ballot, this should not be taken as any sort of endorsement of B or a vote "for" B.
My vote could also be:
A>B>C
Does adding C on the end mean that I have in some sense voted for C? I don't think there would actually be any methods where adding C on the end would have any effect on how the winner is calculated, but the plurality criterion would presumably in theory find it acceptable to do so.
But this is more a philosophical objection to the assumptions implicit in the plurality criterion than an an objection to the results that a method obeying the criterion would produce in practice. But anyway, I put my thoughts about the plurality criterion a while ago (as did Juho) here: http://election-methods.5485.n7.nabble.com/EM-Fwd-Ordering-defeats-in-Minimax-td34236.html#a34247
But anyway, thank you for the link to the calculator.
Toby
From: Chris Benham cbenhamau@yahoo.com.aumailto:cbenhamau@yahoo.com.au
To: "tdp201b@yahoo.co.uk"mailto:tdp201b@yahoo.co.uk tdp201b@yahoo.co.ukmailto:tdp201b@yahoo.co.uk; "cbenham@adam.com.au"mailto:cbenham@adam.com.au cbenham@adam.com.aumailto:cbenham@adam.com.au; "election-methods@lists.electorama.com"mailto:election-methods@lists.electorama.com election-methods@lists.electorama.commailto:election-methods@lists.electorama.com
Sent: Sunday, 26 May 2019, 18:08
Subject: Re: [EM] Losing Votes (equal-ranking whole)
Toby,
You would like this old online ranked-ballot voting calculator:
https://www.cse.wustl.edu/~legrand/rbvote/calc.html
What do you think are the "false premises" that the Plurality criterion is based on??? It was coined with the assumption
that voters could only strictly rank from the top however many candidates they wish, and those not truncated had in
some sense been "voted for". It says that if A has more first-place votes than B has any sort of votes then B can't win.
No explicit mention of "unranked candidates".
(Adapting it to ballots that allow equal-ranking at the top,?? "first preferences" refers to first-preference score on the
ballots symmetrically completed, at least at the top, ballots).
To sensibly claim that it is a "mistake" for an algorithm to do (or apparently "assume") something, I think you need to
point to something wrong with an actual result of it doing so.
My answer to your question is no.
Chris Benham
On 27/05/2019 1:04 am, Toby Pereira wrote:
I think it's a mistake to assume some sort of approval of a ranked candidate. If it's not explicitly part of a method then you should not infer it. As far as I'm concerned:
46: A
44: B>C
10: C
Is the same as:
46: A>B=C
44: B>C>A
10: C>A=B
Presented with these ballots, does this change who you think the winner should be?
This isn't a defence of margins by me or an argument against anything else in your post, but I think the plurality criterion, by talking about unranked candidates, is based on false premises.
Toby
On Sat, 25 May 2019 at 15:31, C.Benham
cbenham@adam.com.aumailto:cbenham@adam.com.au wrote:
There are several Condorcet algorithms that decide the winner by
weighing "defeat strengths" and they
are all equivalent to MinMax when there are no more than 3 candidates.
The ones I have in mind that are equal or very nearly equal in merit are
River, Schulze, Ranked Pairs, Smith//MinMax.
In public political elections they are very very unlikely to give
different winners. River and Smith//MinMax seem to me
to be the easiest to understand and explain and use. The other two are
perhaps a bit more elegant and have their
enthusiastic supporters.
This is to make the case that measuring pairwise defeat strength by the
number of votes on the losing side with above-bottom
equal-ranking contributing a whole vote to each side (and otherwise as
with normal Winning Votes) is much better than either
Winning Votes or Margins.
The case for Losing Votes(erw) against Margins is that it (in common
with WV) it meets the Plurality criterion and the Non-Drastic
Defense criterion.
The case for Losing Votes(erw) against Winning Votes is that it meets
the Chicken Dilemma criterion and that is much less likely
to fail to elect a positionally dominant uncovered candidate. (I don't
see how it can fail to elect such a candidate in the 3-candidate case.)
For those who think that Margins might be acceptable:
46: A
44: B>C
10: C
A>B 46-44 (margin=2), B>C 44-10 (margin=34), C>A 54-46 (margin=8).
Using Losing Votes (erw) as the measure of defeat strength, the weakest
defeat is the one with the most votes on the losing side.
That is the C>A defeat so MinMax drops that and A wins. Conversely the
strongest defeat is the one with the fewest votes on the
losing side. That is the B>C defeat so River and Ranked Pairs lock
that. The second strongest is the A>B defeat so those methods
also lock that. All but one candidate has been thereby disqualified so B
wins, or we ignore the third pairwise defeat because that
makes a cycle, so give a final order A>B>C and A wins.
To meet both of the Plurality criterion and the Chicken Dilemma
criterion A must win.
Winning Votes elects C, violating Chicken Dilemma (which it has to do to
meet the previously fashionable Minimal Defense criterion).
Margins elects B. This fails the Plurality criterion because A has more
exclusive first-place votes than B has any sort of above-bottom
votes. It is also an egregious and outrageous failure of Later-no-Help
(assuming that if all the ballots just vote for one candidate we
elect the plurality winner).
To anyone who is remotely positionally or strategically minded or has
any common sense and isn't blind to everything except the
Margins pairwise matrix, B is clearly the weakest candidate and a
completely unacceptable winner.
35: A
10: A=B
30: B>C
25: C
A>B 45-40 (erw, "normally" 35-30, margin=5), B>C 40-25 (margin=15),
C>A 55-45 (margin=10).
Voted at least equal-top (or Top Ratings) scores: A45, B40, C25.
Voted above bottom (or Approval) scores: A45, B40, C55
An old Kevin Venzke example. B is neither the most top-rated candidate
or the most approved candidate and is
pairwise-beaten and positionally dominated by A (the most top-rated).
Winning Votes and Margins both elect the clearly weakest candidate, B.
Losing Votes(erw) elects A.
For those who prefer to have a method comply with Minimal Defense (which
says that if on more than half the ballots
C is voted above A and A no higher than equal-bottom then A can't win)
rather than Chicken Dilemma another method
I prefer to WV is Smith//Approval which here elects C.
25: A>B
26: B>C
23: C>A
26: C
C>A 75-25 (margin=50), A>B 48-26 (margin=22), B>C 51-49 (margin=2).
Voted at least equal-top (or Top Ratings) scores: C49, B26, A25.
Voted above bottom (or Approval) scores: C75, B51, A48.
C is an overwhelmingly positionally dominant uncovered candidate.
Margins and Losing Votes elect C.
WV and IRV elect B.
Now say we change 4 of the 26 C ballots to A>C, thereby making C a bit
weaker.
25: A>B
26: B>C
23: C>A
22: C
04: A>C
C>A 71-29 (margin=42), A>B 52-26 (margin=26), B>C 51-49 (margin=2).
Voted at least equal-top (or Top Ratings) scores: C45, B26, A29.
Voted above bottom (or Approval) scores: C75, B51, A52.
The weakening of C has caused WV and IRV to change from B to C, now
agreeing with LV and Margins.
Assuming the change was from sincere to insincere, those very lucky
and/or very well informed 4 voters
have pulled off a Push-over strategy.
This is a failure of Mono-raise-delete (more obvious if we reverse the
order of the two situations), which
is one of Woodall's mononicity criteria that he says is incompatible
with Condorcet.
Nonetheless in this case C is still the positionally dominant uncovered
candidate and Losing Votes (erw)
and Margins both still elect C.
Steve Eppley's old example to illustrate (I think his) Non-Drastic
Defense criterion, which says that if
on more than half the ballots B is voted no lower than equal-top and
above A then A can't win.
46: A>C (sincere may be A>B)
10: B>A
10: B>C
34: C=B (the "defenders", sincere may be C>B)
B>A 54-46 (m=8), A>C 56-44 (m=12), C>B (80-54 erw, "normally" 46-20, m=26).
Voted at least equal-top (or Top Ratings) scores: B54, A46, C34.
Voted above bottom (or Approval) scores: B54, A56, C90.
B is the only candidate top-rated on more than half the ballots. More
than half the voters voted B
above A and B not lower than equal-top. Margins and Losing Votes
without my recommended
"above-bottom equal-ranking whole" bit elect A, violating the
Non-Drastic Defense criterion.
Losing Votes (erw) and WV elect B.
If anyone has some counter-examples where they think that Winning Votes
does better than
Losing Votes (erw), I'd be interested in seeing them.
Chris Benham
Election-Methods mailing list - see https://electorama.com/em for list info
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https://mail.yahoo.com/neo/launch?.src=ym&reason=myc&soc_src=mail&soc_trk=ma#DAB4FAD8-2DD7-40BB-A1B8-4E2AA1F9FDF2
51 A>B>C>D
49 B>C>D>A
Is A a better choice than B?
1. Yes. Plurality demands it. Moreover, B beats C and D on all ballots, so C and D can be ignored and the pairwise race is all that's left.
2. No. A is ranked bottom on 49% of ballots, B ranked at least second on 100%, top on almost half.
Are C and D Irrelevant Alternatives?
Jim Faran
On Jun 1, 2019 5:28 AM, "C.Benham" <cbenham@adam.com.au> wrote:
Toby,
I didn't coin the Plurality criterion, and I do somewhat prefer your suggested alternative wording. To take account of equal-top ranking being
allowed, I would specify the fractional interpretation of "number of ballots ranking A as the first preference". The original coiner of the criterion
was operating on the assumption that no equal-ranking would be allowed (except at the bottom implied by truncation which would be allowed)
and perhaps also that no-one would needlessly mark a candidate strictly bottom when they could just truncate.
I think in part the criterion is tailor-made for voters accustomed to and content with plurality voting, and after some new election on ballots
that allow voters to rank the candidates is used, they want to know why B won while their favourite candidate A was voted (alone) in first place
on more ballots than B was voted above bottom. And I like the criterion because I agree that there can't be a good enough answer.
A standard (and possible criterion) I like says that if A both positionally dominates and pairwise beats B then B can't win. That implies Plurality.
35: A
10: A=B
30: B>C
25: C
Here no ballots vote A or B below equal-top. A has more top (or first) place votes than B so positionally dominates and pairwise beats B.
Do you think B is an acceptable winner?
Chris Benham
On 29/05/2019 10:37 pm, Toby Pereira wrote:
I don't have a definite answer to the question of equally ranked ballots, and to me I suppose it's still an open question exactly what the best way forwards is, even if you make a good argument against margins.
I don't have an example where the plurality criterion bars from winning the candidate that I think should have won. Looking at the definition on the Wikipedia: "If the number of ballots ranking A as the first preference is greater than the number of ballots on which another candidate B is given any preference, then A's probability of winning must be no less than B's.", it's more that I would disagree with the terminology "given any preference."
If the definition was "If the number of ballots ranking A as the first preference is greater than the number of ballots on which another candidate B is ranked anything other than last or joint last (either explicitly or through implication on a truncated ballot), then A's probability of winning must be no less than B's." then I'd be less critical of it. I think the way it's worded implies an approval cut-off even if in practice it makes no difference.
Toby
________________________________
From: C.Benham <cbenham@adam.com.au><mailto:cbenham@adam.com.au>
To: Toby Pereira <tdp201b@yahoo.co.uk><mailto:tdp201b@yahoo.co.uk>; "cbenham@adam.com.au"<mailto:cbenham@adam.com.au> <cbenham@adam.com.au><mailto:cbenham@adam.com.au>; "election-methods@lists.electorama.com"<mailto:election-methods@lists.electorama.com> <election-methods@lists.electorama.com><mailto:election-methods@lists.electorama.com>
Sent: Sunday, 26 May 2019, 20:19
Subject: Re: [EM] Losing Votes (equal-ranking whole)
Toby,
If you try to give that calculator a truncated ballot it will just turn it into the sort of ballot you like.
How do you think equally-ranked ballots should be counted in a pairwise comparison? A half-vote to
each or zero to both?
So you can't actually point to any election example where the Plurality criterion bars from winning the candidate
that you think should have won?
46: A
44: B>C
10: C
Returning to this, are you happy with B winning? And if not, why not?
Chris Benham
On 27/05/2019 3:38 am, Toby Pereira wrote:
By unranked candidates, I meant the ones that had not had any sort of "vote" - the ones not explicitly listed by the voter. If there are three candidates in an election, A, B, and C, I might like A but absolutely hate the others. My vote might simply be:
A
On the other hand, while I might still absolutely hate B and C, I might still hate C more. So my vote might be:
A>B
But just because I have ranked B on my ballot, this should not be taken as any sort of endorsement of B or a vote "for" B.
My vote could also be:
A>B>C
Does adding C on the end mean that I have in some sense voted for C? I don't think there would actually be any methods where adding C on the end would have any effect on how the winner is calculated, but the plurality criterion would presumably in theory find it acceptable to do so.
But this is more a philosophical objection to the assumptions implicit in the plurality criterion than an an objection to the results that a method obeying the criterion would produce in practice. But anyway, I put my thoughts about the plurality criterion a while ago (as did Juho) here: http://election-methods.5485.n7.nabble.com/EM-Fwd-Ordering-defeats-in-Minimax-td34236.html#a34247
But anyway, thank you for the link to the calculator.
Toby
________________________________
From: Chris Benham <cbenhamau@yahoo.com.au><mailto:cbenhamau@yahoo.com.au>
To: "tdp201b@yahoo.co.uk"<mailto:tdp201b@yahoo.co.uk> <tdp201b@yahoo.co.uk><mailto:tdp201b@yahoo.co.uk>; "cbenham@adam.com.au"<mailto:cbenham@adam.com.au> <cbenham@adam.com.au><mailto:cbenham@adam.com.au>; "election-methods@lists.electorama.com"<mailto:election-methods@lists.electorama.com> <election-methods@lists.electorama.com><mailto:election-methods@lists.electorama.com>
Sent: Sunday, 26 May 2019, 18:08
Subject: Re: [EM] Losing Votes (equal-ranking whole)
Toby,
You would like this old online ranked-ballot voting calculator:
https://www.cse.wustl.edu/~legrand/rbvote/calc.html
What do you think are the "false premises" that the Plurality criterion is based on??? It was coined with the assumption
that voters could only strictly rank from the top however many candidates they wish, and those not truncated had in
some sense been "voted for". It says that if A has more first-place votes than B has any sort of votes then B can't win.
No explicit mention of "unranked candidates".
(Adapting it to ballots that allow equal-ranking at the top,?? "first preferences" refers to first-preference score on the
ballots symmetrically completed, at least at the top, ballots).
To sensibly claim that it is a "mistake" for an algorithm to do (or apparently "assume") something, I think you need to
point to something wrong with an actual result of it doing so.
My answer to your question is no.
Chris Benham
On 27/05/2019 1:04 am, Toby Pereira wrote:
I think it's a mistake to assume some sort of approval of a ranked candidate. If it's not explicitly part of a method then you should not infer it. As far as I'm concerned:
46: A
44: B>C
10: C
Is the same as:
46: A>B=C
44: B>C>A
10: C>A=B
Presented with these ballots, does this change who you think the winner should be?
This isn't a defence of margins by me or an argument against anything else in your post, but I think the plurality criterion, by talking about unranked candidates, is based on false premises.
Toby
On Sat, 25 May 2019 at 15:31, C.Benham
<cbenham@adam.com.au><mailto:cbenham@adam.com.au> wrote:
There are several Condorcet algorithms that decide the winner by
weighing "defeat strengths" and they
are all equivalent to MinMax when there are no more than 3 candidates.
The ones I have in mind that are equal or very nearly equal in merit are
River, Schulze, Ranked Pairs, Smith//MinMax.
In public political elections they are very very unlikely to give
different winners. River and Smith//MinMax seem to me
to be the easiest to understand and explain and use. The other two are
perhaps a bit more elegant and have their
enthusiastic supporters.
This is to make the case that measuring pairwise defeat strength by the
number of votes on the losing side with above-bottom
equal-ranking contributing a whole vote to each side (and otherwise as
with normal Winning Votes) is much better than either
Winning Votes or Margins.
The case for Losing Votes(erw) against Margins is that it (in common
with WV) it meets the Plurality criterion and the Non-Drastic
Defense criterion.
The case for Losing Votes(erw) against Winning Votes is that it meets
the Chicken Dilemma criterion and that is much less likely
to fail to elect a positionally dominant uncovered candidate. (I don't
see how it can fail to elect such a candidate in the 3-candidate case.)
For those who think that Margins might be acceptable:
46: A
44: B>C
10: C
A>B 46-44 (margin=2), B>C 44-10 (margin=34), C>A 54-46 (margin=8).
Using Losing Votes (erw) as the measure of defeat strength, the weakest
defeat is the one with the most votes on the losing side.
That is the C>A defeat so MinMax drops that and A wins. Conversely the
strongest defeat is the one with the fewest votes on the
losing side. That is the B>C defeat so River and Ranked Pairs lock
that. The second strongest is the A>B defeat so those methods
also lock that. All but one candidate has been thereby disqualified so B
wins, or we ignore the third pairwise defeat because that
makes a cycle, so give a final order A>B>C and A wins.
To meet both of the Plurality criterion and the Chicken Dilemma
criterion A must win.
Winning Votes elects C, violating Chicken Dilemma (which it has to do to
meet the previously fashionable Minimal Defense criterion).
Margins elects B. This fails the Plurality criterion because A has more
exclusive first-place votes than B has any sort of above-bottom
votes. It is also an egregious and outrageous failure of Later-no-Help
(assuming that if all the ballots just vote for one candidate we
elect the plurality winner).
To anyone who is remotely positionally or strategically minded or has
any common sense and isn't blind to everything except the
Margins pairwise matrix, B is clearly the weakest candidate and a
completely unacceptable winner.
35: A
10: A=B
30: B>C
25: C
A>B 45-40 (erw, "normally" 35-30, margin=5), B>C 40-25 (margin=15),
C>A 55-45 (margin=10).
Voted at least equal-top (or Top Ratings) scores: A45, B40, C25.
Voted above bottom (or Approval) scores: A45, B40, C55
An old Kevin Venzke example. B is neither the most top-rated candidate
or the most approved candidate and is
pairwise-beaten and positionally dominated by A (the most top-rated).
Winning Votes and Margins both elect the clearly weakest candidate, B.
Losing Votes(erw) elects A.
For those who prefer to have a method comply with Minimal Defense (which
says that if on more than half the ballots
C is voted above A and A no higher than equal-bottom then A can't win)
rather than Chicken Dilemma another method
I prefer to WV is Smith//Approval which here elects C.
25: A>B
26: B>C
23: C>A
26: C
C>A 75-25 (margin=50), A>B 48-26 (margin=22), B>C 51-49 (margin=2).
Voted at least equal-top (or Top Ratings) scores: C49, B26, A25.
Voted above bottom (or Approval) scores: C75, B51, A48.
C is an overwhelmingly positionally dominant uncovered candidate.
Margins and Losing Votes elect C.
WV and IRV elect B.
Now say we change 4 of the 26 C ballots to A>C, thereby making C a bit
weaker.
25: A>B
26: B>C
23: C>A
22: C
04: A>C
C>A 71-29 (margin=42), A>B 52-26 (margin=26), B>C 51-49 (margin=2).
Voted at least equal-top (or Top Ratings) scores: C45, B26, A29.
Voted above bottom (or Approval) scores: C75, B51, A52.
The weakening of C has caused WV and IRV to change from B to C, now
agreeing with LV and Margins.
Assuming the change was from sincere to insincere, those very lucky
and/or very well informed 4 voters
have pulled off a Push-over strategy.
This is a failure of Mono-raise-delete (more obvious if we reverse the
order of the two situations), which
is one of Woodall's mononicity criteria that he says is incompatible
with Condorcet.
Nonetheless in this case C is still the positionally dominant uncovered
candidate and Losing Votes (erw)
and Margins both still elect C.
Steve Eppley's old example to illustrate (I think his) Non-Drastic
Defense criterion, which says that if
on more than half the ballots B is voted no lower than equal-top and
above A then A can't win.
46: A>C (sincere may be A>B)
10: B>A
10: B>C
34: C=B (the "defenders", sincere may be C>B)
B>A 54-46 (m=8), A>C 56-44 (m=12), C>B (80-54 erw, "normally" 46-20, m=26).
Voted at least equal-top (or Top Ratings) scores: B54, A46, C34.
Voted above bottom (or Approval) scores: B54, A56, C90.
B is the only candidate top-rated on more than half the ballots. More
than half the voters voted B
above A and B not lower than equal-top. Margins and Losing Votes
without my recommended
"above-bottom equal-ranking whole" bit elect A, violating the
Non-Drastic Defense criterion.
Losing Votes (erw) and WV elect B.
If anyone has some counter-examples where they think that Winning Votes
does better than
Losing Votes (erw), I'd be interested in seeing them.
Chris Benham
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C
C.Benham
Sat, Jun 1, 2019 12:46 PM
Jim,
Yes.
Chris Benham
On 1/06/2019 9:45 pm, Faran, James wrote:
51 A>B>C>D
49 B>C>D>A
Is A a better choice than B?
-
Yes. Plurality demands it. Moreover, B beats C and D on all
ballots, so C and D can be ignored and the pairwise race is all that's
left.
-
No. A is ranked bottom on 49% of ballots, B ranked at least second
on 100%, top on almost half.
Are C and D Irrelevant Alternatives?
Jim Faran
On Jun 1, 2019 5:28 AM, "C.Benham" cbenham@adam.com.au wrote:
Toby,
I didn't coin the Plurality criterion, and I do somewhat prefer your
suggested alternative wording. To take account of equal-top ranking being
allowed, I would specify the fractional interpretation of "number of
ballots ranking A as the first preference". The original coiner of
the criterion
was operating on the assumption that no equal-ranking would be
allowed (except at the bottom implied by truncation which would be
allowed)
and perhaps also that no-one would needlessly mark a candidate
strictly bottom when they could just truncate.
I think in part the criterion is tailor-made for voters accustomed to
and content with plurality voting, and after some new election on ballots
that allow voters to rank the candidates is used, they want to know
why B won while their favourite candidate A was voted (alone) in first
place
on more ballots than B was voted above bottom. And I like the
criterion because I agree that there can't be a good enough answer.
A standard (and possible criterion) I like says that if A both
positionally dominates and pairwise beats B then B can't win. That
implies Plurality.
35: A
10: A=B
30: B>C
25: C
Here no ballots vote A or B below equal-top. A has more top (or first)
place votes than B so positionally dominates and pairwise beats B.
Do you think B is an acceptable winner?
Chris Benham
On 29/05/2019 10:37 pm, Toby Pereira wrote:
I don't have a definite answer to the question of equally ranked
ballots, and to me I suppose it's still an open question exactly what
the best way forwards is, even if you make a good argument against
margins.
I don't have an example where the plurality criterion bars from
winning the candidate that I think should have won. Looking at the
definition on the Wikipedia: "If the number of ballots ranking A as
the first preference is greater than the number of ballots on which
another candidate B is given any preference, then A's probability of
winning must be no less than B's.", it's more that I would disagree
with the terminology "given any preference."
If the definition was "If the number of ballots ranking A as the
first preference is greater than the number of ballots on which
another candidate B is ranked anything other than last or joint last
(either explicitly or through implication on a truncated ballot),
then A's probability of winning must be no less than B's." then I'd
be less critical of it. I think the way it's worded implies an
approval cut-off even if in practice it makes no difference.
Toby
From: C.Benham cbenham@adam.com.au
To: Toby Pereira tdp201b@yahoo.co.uk; "cbenham@adam.com.au"
cbenham@adam.com.au; "election-methods@lists.electorama.com"
election-methods@lists.electorama.com
Sent: Sunday, 26 May 2019, 20:19
Subject: Re: [EM] Losing Votes (equal-ranking whole)
Toby,
If you try to give that calculator a truncated ballot it will just
turn it into the sort of ballot you like.
How do you think equally-ranked ballots should be counted in a
pairwise comparison? A half-vote to
each or zero to both?
So you can't actually point to any election example where the
Plurality criterion bars from winning the candidate
that you think should have won?
46: A
44: B>C
10: C
Returning to this, are you happy with B winning? And if not, why not?
Chris Benham
On 27/05/2019 3:38 am, Toby Pereira wrote:
By unranked candidates, I meant the ones that had not had any sort of
"vote" - the ones not explicitly listed by the voter. If there are
three candidates in an election, A, B, and C, I might like A but
absolutely hate the others. My vote might simply be:
A
On the other hand, while I might still absolutely hate B and C, I
might still hate C more. So my vote might be:
A>B
But just because I have ranked B on my ballot, this should not be
taken as any sort of endorsement of B or a vote "for" B.
My vote could also be:
A>B>C
Does adding C on the end mean that I have in some sense voted for C?
I don't think there would actually be any methods where adding C on
the end would have any effect on how the winner is calculated, but
the plurality criterion would presumably in theory find it acceptable
to do so.
But this is more a philosophical objection to the assumptions
implicit in the plurality criterion than an an objection to the
results that a method obeying the criterion would produce in
practice. But anyway, I put my thoughts about the plurality criterion
a while ago (as did Juho) here:
http://election-methods.5485.n7.nabble.com/EM-Fwd-Ordering-defeats-in-Minimax-td34236.html#a34247
But anyway, thank you for the link to the calculator.
Toby
From: Chris Benham cbenhamau@yahoo.com.au
mailto:cbenhamau@yahoo.com.au
To: "tdp201b@yahoo.co.uk" mailto:tdp201b@yahoo.co.uk
tdp201b@yahoo.co.uk mailto:tdp201b@yahoo.co.uk;
"cbenham@adam.com.au" mailto:cbenham@adam.com.au
cbenham@adam.com.au mailto:cbenham@adam.com.au;
"election-methods@lists.electorama.com"
mailto:election-methods@lists.electorama.com
election-methods@lists.electorama.com
mailto:election-methods@lists.electorama.com
Sent: Sunday, 26 May 2019, 18:08
Subject: Re: [EM] Losing Votes (equal-ranking whole)
Toby,
You would like this old online ranked-ballot voting calculator:
https://www.cse.wustl.edu/~legrand/rbvote/calc.html
What do you think are the "false premises" that the Plurality
criterion is based on??? It was coined with the assumption
that voters could only strictly rank from the top however many
candidates they wish, and those not truncated had in
some sense been "voted for". It says that if A has more first-place
votes than B has any sort of votes then B can't win.
No explicit mention of "unranked candidates".
(Adapting it to ballots that allow equal-ranking at the top,?? "first
preferences" refers to first-preference score on the
ballots symmetrically completed, at least at the top, ballots).
To sensibly claim that it is a "mistake" for an algorithm to do (or
apparently "assume") something, I think you need to
point to something wrong with an actual result of it doing so.
My answer to your question is no.
Chris Benham
On 27/05/2019 1:04 am, Toby Pereira wrote:
I think it's a mistake to assume some sort of approval of a ranked
candidate. If it's not explicitly part of a method then you should
not infer it. As far as I'm concerned:
46: A
44: B>C
10: C
Is the same as:
46: A>B=C
44: B>C>A
10: C>A=B
Presented with these ballots, does this change who you think the
winner should be?
This isn't a defence of margins by me or an argument against anything
else in your post, but I think the plurality criterion, by talking
about unranked candidates, is based on false premises.
Toby
On Sat, 25 May 2019 at 15:31, C.Benham
<cbenham@adam.com.au> <mailto:cbenham@adam.com.au> wrote:
There are several Condorcet algorithms that decide the winner by
weighing "defeat strengths" and they
are all equivalent to MinMax when there are no more than 3
candidates.
The ones I have in mind that are equal or very nearly equal in
merit are
River, Schulze, Ranked Pairs, Smith//MinMax.
In public political elections they are very very unlikely to give
different winners. River and Smith//MinMax seem to me
to be the easiest to understand and explain and use. The other
two are
perhaps a bit more elegant and have their
enthusiastic supporters.
This is to make the case that measuring pairwise defeat strength
by the
number of votes on the losing side with above-bottom
equal-ranking contributing a whole vote to each side (and
otherwise as
with normal Winning Votes) is much better than either
Winning Votes or Margins.
The case for Losing Votes(erw) against Margins is that it (in common
with WV) it meets the Plurality criterion and the Non-Drastic
Defense criterion.
The case for Losing Votes(erw) against Winning Votes is that it
meets
the Chicken Dilemma criterion and that is much less likely
to fail to elect a positionally dominant uncovered candidate. (I
don't
see how it can fail to elect such a candidate in the 3-candidate
case.)
For those who think that Margins might be acceptable:
46: A
44: B>C
10: C
A>B 46-44 (margin=2), B>C 44-10 (margin=34), C>A 54-46 (margin=8).
Using Losing Votes (erw) as the measure of defeat strength, the
weakest
defeat is the one with the most votes on the losing side.
That is the C>A defeat so MinMax drops that and A wins.
Conversely the
strongest defeat is the one with the fewest votes on the
losing side. That is the B>C defeat so River and Ranked Pairs lock
that. The second strongest is the A>B defeat so those methods
also lock that. All but one candidate has been thereby
disqualified so B
wins, or we ignore the third pairwise defeat because that
makes a cycle, so give a final order A>B>C and A wins.
To meet both of the Plurality criterion and the Chicken Dilemma
criterion A must win.
Winning Votes elects C, violating Chicken Dilemma (which it has
to do to
meet the previously fashionable Minimal Defense criterion).
Margins elects B. This fails the Plurality criterion because A
has more
exclusive first-place votes than B has any sort of above-bottom
votes. It is also an egregious and outrageous failure of
Later-no-Help
(assuming that if all the ballots just vote for one candidate we
elect the plurality winner).
To anyone who is remotely positionally or strategically minded or
has
any common sense and isn't blind to everything except the
Margins pairwise matrix, B is clearly the weakest candidate and a
completely unacceptable winner.
35: A
10: A=B
30: B>C
25: C
A>B 45-40 (erw, "normally" 35-30, margin=5), B>C 40-25 (margin=15),
C>A 55-45 (margin=10).
Voted at least equal-top (or Top Ratings) scores: A45, B40, C25.
Voted above bottom (or Approval) scores: A45, B40, C55
An old Kevin Venzke example. B is neither the most top-rated
candidate
or the most approved candidate and is
pairwise-beaten and positionally dominated by A (the most top-rated).
Winning Votes and Margins both elect the clearly weakest
candidate, B.
Losing Votes(erw) elects A.
For those who prefer to have a method comply with Minimal Defense
(which
says that if on more than half the ballots
C is voted above A and A no higher than equal-bottom then A can't
win)
rather than Chicken Dilemma another method
I prefer to WV is Smith//Approval which here elects C.
25: A>B
26: B>C
23: C>A
26: C
C>A 75-25 (margin=50), A>B 48-26 (margin=22), B>C 51-49 (margin=2).
Voted at least equal-top (or Top Ratings) scores: C49, B26, A25.
Voted above bottom (or Approval) scores: C75, B51, A48.
C is an overwhelmingly positionally dominant uncovered candidate.
Margins and Losing Votes elect C.
WV and IRV elect B.
Now say we change 4 of the 26 C ballots to A>C, thereby making C
a bit
weaker.
25: A>B
26: B>C
23: C>A
22: C
04: A>C
C>A 71-29 (margin=42), A>B 52-26 (margin=26), B>C 51-49 (margin=2).
Voted at least equal-top (or Top Ratings) scores: C45, B26, A29.
Voted above bottom (or Approval) scores: C75, B51, A52.
The weakening of C has caused WV and IRV to change from B to C, now
agreeing with LV and Margins.
Assuming the change was from sincere to insincere, those very lucky
and/or very well informed 4 voters
have pulled off a Push-over strategy.
This is a failure of Mono-raise-delete (more obvious if we
reverse the
order of the two situations), which
is one of Woodall's mononicity criteria that he says is incompatible
with Condorcet.
Nonetheless in this case C is still the positionally dominant
uncovered
candidate and Losing Votes (erw)
and Margins both still elect C.
Steve Eppley's old example to illustrate (I think his) Non-Drastic
Defense criterion, which says that if
on more than half the ballots B is voted no lower than equal-top and
above A then A can't win.
46: A>C (sincere may be A>B)
10: B>A
10: B>C
34: C=B (the "defenders", sincere may be C>B)
B>A 54-46 (m=8), A>C 56-44 (m=12), C>B (80-54 erw, "normally"
46-20, m=26).
Voted at least equal-top (or Top Ratings) scores: B54, A46, C34.
Voted above bottom (or Approval) scores: B54, A56, C90.
B is the only candidate top-rated on more than half the ballots.
More
than half the voters voted B
above A and B not lower than equal-top. Margins and Losing Votes
without my recommended
"above-bottom equal-ranking whole" bit elect A, violating the
Non-Drastic Defense criterion.
Losing Votes (erw) and WV elect B.
If anyone has some counter-examples where they think that Winning
Votes
does better than
Losing Votes (erw), I'd be interested in seeing them.
Chris Benham
----
Election-Methods mailing list - see https://electorama.com/em
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Jim,
Yes.
Chris Benham
On 1/06/2019 9:45 pm, Faran, James wrote:
> 51 A>B>C>D
> 49 B>C>D>A
>
> Is A a better choice than B?
>
> 1. Yes. Plurality demands it. Moreover, B beats C and D on all
> ballots, so C and D can be ignored and the pairwise race is all that's
> left.
>
> 2. No. A is ranked bottom on 49% of ballots, B ranked at least second
> on 100%, top on almost half.
>
> Are C and D Irrelevant Alternatives?
>
> Jim Faran
>
> On Jun 1, 2019 5:28 AM, "C.Benham" <cbenham@adam.com.au> wrote:
>
> Toby,
>
> I didn't coin the Plurality criterion, and I do somewhat prefer your
> suggested alternative wording. To take account of equal-top ranking being
> allowed, I would specify the fractional interpretation of "number of
> ballots ranking A as the first preference". The original coiner of
> the criterion
> was operating on the assumption that no equal-ranking would be
> allowed (except at the bottom implied by truncation which would be
> allowed)
> and perhaps also that no-one would needlessly mark a candidate
> strictly bottom when they could just truncate.
>
> I think in part the criterion is tailor-made for voters accustomed to
> and content with plurality voting, and after some new election on ballots
> that allow voters to rank the candidates is used, they want to know
> why B won while their favourite candidate A was voted (alone) in first
> place
> on more ballots than B was voted above bottom. And I like the
> criterion because I agree that there can't be a good enough answer.
>
> A standard (and possible criterion) I like says that if A both
> positionally dominates and pairwise beats B then B can't win. That
> implies Plurality.
>
> 35: A
> 10: A=B
> 30: B>C
> 25: C
>
> Here no ballots vote A or B below equal-top. A has more top (or first)
> place votes than B so positionally dominates and pairwise beats B.
> Do you think B is an acceptable winner?
>
> Chris Benham
>
>
>
> On 29/05/2019 10:37 pm, Toby Pereira wrote:
>> I don't have a definite answer to the question of equally ranked
>> ballots, and to me I suppose it's still an open question exactly what
>> the best way forwards is, even if you make a good argument against
>> margins.
>>
>> I don't have an example where the plurality criterion bars from
>> winning the candidate that I think should have won. Looking at the
>> definition on the Wikipedia: "If the number of ballots ranking A as
>> the first preference is greater than the number of ballots on which
>> another candidate B is given any preference, then A's probability of
>> winning must be no less than B's.", it's more that I would disagree
>> with the terminology "given any preference."
>>
>> If the definition was "If the number of ballots ranking A as the
>> first preference is greater than the number of ballots on which
>> another candidate B is ranked anything other than last or joint last
>> (either explicitly or through implication on a truncated ballot),
>> then A's probability of winning must be no less than B's." then I'd
>> be less critical of it. I think the way it's worded implies an
>> approval cut-off even if in practice it makes no difference.
>>
>> Toby
>>
>>
>> ------------------------------------------------------------------------
>> *From:* C.Benham <cbenham@adam.com.au>
>> *To:* Toby Pereira <tdp201b@yahoo.co.uk>; "cbenham@adam.com.au"
>> <cbenham@adam.com.au>; "election-methods@lists.electorama.com"
>> <election-methods@lists.electorama.com>
>> *Sent:* Sunday, 26 May 2019, 20:19
>> *Subject:* Re: [EM] Losing Votes (equal-ranking whole)
>>
>> Toby,
>>
>> If you try to give that calculator a truncated ballot it will just
>> turn it into the sort of ballot you like.
>>
>> How do you think equally-ranked ballots should be counted in a
>> pairwise comparison? A half-vote to
>> each or zero to both?
>>
>> So you can't actually point to any election example where the
>> Plurality criterion bars from winning the candidate
>> that you think should have won?
>> 46: A
>> 44: B>C
>> 10: C
>> Returning to this, are you happy with B winning? And if not, why not?
>>
>> Chris Benham
>>
>> On 27/05/2019 3:38 am, Toby Pereira wrote:
>> By unranked candidates, I meant the ones that had not had any sort of
>> "vote" - the ones not explicitly listed by the voter. If there are
>> three candidates in an election, A, B, and C, I might like A but
>> absolutely hate the others. My vote might simply be:
>>
>> A
>>
>> On the other hand, while I might still absolutely hate B and C, I
>> might still hate C more. So my vote might be:
>>
>> A>B
>>
>> But just because I have ranked B on my ballot, this should not be
>> taken as any sort of endorsement of B or a vote "for" B.
>>
>> My vote could also be:
>>
>> A>B>C
>>
>> Does adding C on the end mean that I have in some sense voted for C?
>> I don't think there would actually be any methods where adding C on
>> the end would have any effect on how the winner is calculated, but
>> the plurality criterion would presumably in theory find it acceptable
>> to do so.
>>
>> But this is more a philosophical objection to the assumptions
>> implicit in the plurality criterion than an an objection to the
>> results that a method obeying the criterion would produce in
>> practice. But anyway, I put my thoughts about the plurality criterion
>> a while ago (as did Juho) here:
>> http://election-methods.5485.n7.nabble.com/EM-Fwd-Ordering-defeats-in-Minimax-td34236.html#a34247
>>
>> But anyway, thank you for the link to the calculator.
>>
>> Toby
>>
>>
>>
>>
>> ------------------------------------------------------------------------
>> *From:* Chris Benham <cbenhamau@yahoo.com.au>
>> <mailto:cbenhamau@yahoo.com.au>
>> *To:* "tdp201b@yahoo.co.uk" <mailto:tdp201b@yahoo.co.uk>
>> <tdp201b@yahoo.co.uk> <mailto:tdp201b@yahoo.co.uk>;
>> "cbenham@adam.com.au" <mailto:cbenham@adam.com.au>
>> <cbenham@adam.com.au> <mailto:cbenham@adam.com.au>;
>> "election-methods@lists.electorama.com"
>> <mailto:election-methods@lists.electorama.com>
>> <election-methods@lists.electorama.com>
>> <mailto:election-methods@lists.electorama.com>
>> *Sent:* Sunday, 26 May 2019, 18:08
>> *Subject:* Re: [EM] Losing Votes (equal-ranking whole)
>>
>> Toby,
>>
>> You would like this old online ranked-ballot voting calculator:
>>
>> https://www.cse.wustl.edu/~legrand/rbvote/calc.html
>>
>> What do you think are the "false premises" that the Plurality
>> criterion is based on??? It was coined with the assumption
>> that voters could only strictly rank from the top however many
>> candidates they wish, and those not truncated had in
>> some sense been "voted for". It says that if A has more first-place
>> votes than B has any sort of votes then B can't win.
>> No explicit mention of "unranked candidates".
>>
>> (Adapting it to ballots that allow equal-ranking at the top,?? "first
>> preferences" refers to first-preference score on the
>> ballots symmetrically completed, at least at the top, ballots).
>> To sensibly claim that it is a "mistake" for an algorithm to do (or
>> apparently "assume") something, I think you need to
>> point to something wrong with an actual result of it doing so.
>>
>> My answer to your question is no.
>> Chris Benham
>>
>>
>> On 27/05/2019 1:04 am, Toby Pereira wrote:
>> I think it's a mistake to assume some sort of approval of a ranked
>> candidate. If it's not explicitly part of a method then you should
>> not infer it. As far as I'm concerned:
>>
>> 46: A
>> 44: B>C
>> 10: C
>>
>> Is the same as:
>>
>> 46: A>B=C
>> 44: B>C>A
>> 10: C>A=B
>>
>> Presented with these ballots, does this change who you think the
>> winner should be?
>>
>> This isn't a defence of margins by me or an argument against anything
>> else in your post, but I think the plurality criterion, by talking
>> about unranked candidates, is based on false premises.
>>
>> Toby
>>
>> On Sat, 25 May 2019 at 15:31, C.Benham
>> <cbenham@adam.com.au> <mailto:cbenham@adam.com.au> wrote:
>> There are several Condorcet algorithms that decide the winner by
>> weighing "defeat strengths" and they
>> are all equivalent to MinMax when there are no more than 3
>> candidates.
>>
>> The ones I have in mind that are equal or very nearly equal in
>> merit are
>> River, Schulze, Ranked Pairs, Smith//MinMax.
>> In public political elections they are very very unlikely to give
>> different winners. River and Smith//MinMax seem to me
>> to be the easiest to understand and explain and use. The other
>> two are
>> perhaps a bit more elegant and have their
>> enthusiastic supporters.
>>
>> This is to make the case that measuring pairwise defeat strength
>> by the
>> number of votes on the losing side with above-bottom
>> equal-ranking contributing a whole vote to each side (and
>> otherwise as
>> with normal Winning Votes) is much better than either
>> Winning Votes or Margins.
>>
>> The case for Losing Votes(erw) against Margins is that it (in common
>> with WV) it meets the Plurality criterion and the Non-Drastic
>> Defense criterion.
>>
>> The case for Losing Votes(erw) against Winning Votes is that it
>> meets
>> the Chicken Dilemma criterion and that is much less likely
>> to fail to elect a positionally dominant uncovered candidate. (I
>> don't
>> see how it can fail to elect such a candidate in the 3-candidate
>> case.)
>>
>> For those who think that Margins might be acceptable:
>>
>> 46: A
>> 44: B>C
>> 10: C
>>
>> A>B 46-44 (margin=2), B>C 44-10 (margin=34), C>A 54-46 (margin=8).
>>
>> Using Losing Votes (erw) as the measure of defeat strength, the
>> weakest
>> defeat is the one with the most votes on the losing side.
>> That is the C>A defeat so MinMax drops that and A wins.
>> Conversely the
>> strongest defeat is the one with the fewest votes on the
>> losing side. That is the B>C defeat so River and Ranked Pairs lock
>> that. The second strongest is the A>B defeat so those methods
>> also lock that. All but one candidate has been thereby
>> disqualified so B
>> wins, or we ignore the third pairwise defeat because that
>> makes a cycle, so give a final order A>B>C and A wins.
>>
>> To meet both of the Plurality criterion and the Chicken Dilemma
>> criterion A must win.
>>
>> Winning Votes elects C, violating Chicken Dilemma (which it has
>> to do to
>> meet the previously fashionable Minimal Defense criterion).
>>
>> Margins elects B. This fails the Plurality criterion because A
>> has more
>> exclusive first-place votes than B has any sort of above-bottom
>> votes. It is also an egregious and outrageous failure of
>> Later-no-Help
>> (assuming that if all the ballots just vote for one candidate we
>> elect the plurality winner).
>>
>> To anyone who is remotely positionally or strategically minded or
>> has
>> any common sense and isn't blind to everything except the
>> Margins pairwise matrix, B is clearly the weakest candidate and a
>> completely unacceptable winner.
>>
>> 35: A
>> 10: A=B
>> 30: B>C
>> 25: C
>>
>> A>B 45-40 (erw, "normally" 35-30, margin=5), B>C 40-25 (margin=15),
>> C>A 55-45 (margin=10).
>>
>> Voted at least equal-top (or Top Ratings) scores: A45, B40, C25.
>> Voted above bottom (or Approval) scores: A45, B40, C55
>>
>> An old Kevin Venzke example. B is neither the most top-rated
>> candidate
>> or the most approved candidate and is
>> pairwise-beaten and positionally dominated by A (the most top-rated).
>>
>> Winning Votes and Margins both elect the clearly weakest
>> candidate, B.
>> Losing Votes(erw) elects A.
>>
>> For those who prefer to have a method comply with Minimal Defense
>> (which
>> says that if on more than half the ballots
>> C is voted above A and A no higher than equal-bottom then A can't
>> win)
>> rather than Chicken Dilemma another method
>> I prefer to WV is Smith//Approval which here elects C.
>>
>> 25: A>B
>> 26: B>C
>> 23: C>A
>> 26: C
>>
>> C>A 75-25 (margin=50), A>B 48-26 (margin=22), B>C 51-49 (margin=2).
>>
>> Voted at least equal-top (or Top Ratings) scores: C49, B26, A25.
>> Voted above bottom (or Approval) scores: C75, B51, A48.
>>
>> C is an overwhelmingly positionally dominant uncovered candidate.
>> Margins and Losing Votes elect C.
>> WV and IRV elect B.
>>
>> Now say we change 4 of the 26 C ballots to A>C, thereby making C
>> a bit
>> weaker.
>>
>> 25: A>B
>> 26: B>C
>> 23: C>A
>> 22: C
>> 04: A>C
>>
>> C>A 71-29 (margin=42), A>B 52-26 (margin=26), B>C 51-49 (margin=2).
>>
>> Voted at least equal-top (or Top Ratings) scores: C45, B26, A29.
>> Voted above bottom (or Approval) scores: C75, B51, A52.
>>
>>
>> The weakening of C has caused WV and IRV to change from B to C, now
>> agreeing with LV and Margins.
>> Assuming the change was from sincere to insincere, those very lucky
>> and/or very well informed 4 voters
>> have pulled off a Push-over strategy.
>>
>> This is a failure of Mono-raise-delete (more obvious if we
>> reverse the
>> order of the two situations), which
>> is one of Woodall's mononicity criteria that he says is incompatible
>> with Condorcet.
>>
>> Nonetheless in this case C is still the positionally dominant
>> uncovered
>> candidate and Losing Votes (erw)
>> and Margins both still elect C.
>>
>> Steve Eppley's old example to illustrate (I think his) Non-Drastic
>> Defense criterion, which says that if
>> on more than half the ballots B is voted no lower than equal-top and
>> above A then A can't win.
>>
>> 46: A>C (sincere may be A>B)
>> 10: B>A
>> 10: B>C
>> 34: C=B (the "defenders", sincere may be C>B)
>>
>> B>A 54-46 (m=8), A>C 56-44 (m=12), C>B (80-54 erw, "normally"
>> 46-20, m=26).
>>
>> Voted at least equal-top (or Top Ratings) scores: B54, A46, C34.
>> Voted above bottom (or Approval) scores: B54, A56, C90.
>>
>> B is the only candidate top-rated on more than half the ballots.
>> More
>> than half the voters voted B
>> above A and B not lower than equal-top. Margins and Losing Votes
>> without my recommended
>> "above-bottom equal-ranking whole" bit elect A, violating the
>> Non-Drastic Defense criterion.
>>
>> Losing Votes (erw) and WV elect B.
>>
>> If anyone has some counter-examples where they think that Winning
>> Votes
>> does better than
>> Losing Votes (erw), I'd be interested in seeing them.
>>
>> Chris Benham
>>
>>
>>
>>
>>
>>
>>
>>
>>
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KV
Kevin Venzke
Sat, Jun 1, 2019 2:55 PM
Hi Jim,
You list good considerations. Two comments:
- The Plurality criterion doesn't actually demand that A defeat B. A's first preferences only disqualify
D. (But Majority Favorite demands an A win.)
- I would ask what are the strategic implications. If B wins because the 51 ranked B above the two
"irrelevant alternatives" then either you need A voters to be OK with losing like that, or you have to
suppose that voters may try to rank their lesser compromise choices beneath irrelevant alternatives
to avoid an unnecessary loss. We may even be seeing this tactic in the B votes below, if this in fact
is a win for B.
Kevin
Le samedi 1 juin 2019 à 07:15:33 UTC−5, Faran, James jjfaran@buffalo.edu a écrit :
51 A>B>C>D
49 B>C>D>A
Is A a better choice than B?
-
Yes. Plurality demands it. Moreover, B beats C and D on all ballots, so C and D can be ignored
and the pairwise race is all that's left.
-
No. A is ranked bottom on 49% of ballots, B ranked at least second on 100%, top on almost half.
Are C and D Irrelevant Alternatives?
Jim Faran
Hi Jim,
You list good considerations. Two comments:
1. The Plurality criterion doesn't actually demand that A defeat B. A's first preferences only disqualify
D. (But Majority Favorite demands an A win.)
2. I would ask what are the strategic implications. If B wins because the 51 ranked B above the two
"irrelevant alternatives" then either you need A voters to be OK with losing like that, or you have to
suppose that voters may try to rank their lesser compromise choices beneath irrelevant alternatives
to avoid an unnecessary loss. We may even be seeing this tactic in the B votes below, if this in fact
is a win for B.
Kevin
>Le samedi 1 juin 2019 à 07:15:33 UTC−5, Faran, James <jjfaran@buffalo.edu> a écrit :
>51 A>B>C>D
>49 B>C>D>A
>
>Is A a better choice than B?
>
>1. Yes. Plurality demands it. Moreover, B beats C and D on all ballots, so C and D can be ignored
>and the pairwise race is all that's left.
>
>2. No. A is ranked bottom on 49% of ballots, B ranked at least second on 100%, top on almost half.
>
>Are C and D Irrelevant Alternatives?
>
>Jim Faran
