"Margins Sorted Approval" poll candidate
One of my nominations and my top choice in the current poll:
Margins Sorted Approval (specified cutoff):
*Voters rank from the top however many candidates they wish and can also
specify an approval
cutoff/threshold. Default approval is only for candidates ranked below
no others (i.e. ranked top
or equal-top).
A Forrest Simmons invention. Candidates are listed in approval score
order and if any adjacent pairs
are pairwise out of order then this is corrected by flipping the
out-of-order pair with the smallest
margin. If there is a tie for this we flip the less approved pair.
Repeat until there are no adjacent pairs
of candidates that are pairwise out of order, then elect the
highest-ordered candidate.*
I'm going to compare it with another of my nominations, another
Condorcet method that collects the
same information from the voters:
Smith//Approval (specified cutoff):
Voters rank from the top however many candidates they wish and can also
specify an approval
cutoff/threshold. Default approval is only for candidates ranked below
no others (i.e. ranked top
or equal-top).
The most approved member of the Smith set wins.
Although it asks voters for a bit more information than other Condorcet
methods like Ranked Pairs,
Schulze, MinMax etcetera, I think it is a lot easier than them to
explain and sell than them.
Condorcet//Approval (explicit) was discussed here in April 2002 by Adam
Tarr. I find voluntarily (in a
Condorcet method) electing a candidate outside the Smith set to be weird
and unacceptable, but all the
examples he gave that I saw apply just as well to Smith//Approval(explicit).
Now why do I prefer Margins Sorted Approval?
The main reason is that it is quite a lot less vulnerable to Burial
strategy. Say there are three candidates
and most of the voters normally truncate. Say A is the predicted FPP
and Condorcet winner, B is the
predicted FPP runner-up and C is coming last by quite a big margin.
In that case the voters most likely to be tempted to try a Burial
strategy will be the B supporters against
A, using no-threat C as the "bus".
43 A|
03 A>B| ("strategically naive" voters)
44 B|>C (sincere is B or B>A)
10 C|
The B>C Buriers have given A a pairwise defeat, so now there is an
A>B>C>A cycle.
The approval scores: B 47, A 46, C 10.
Now if this was Smith//Approval the 3 A>B| voters would have blown the
election for A by approving B.
But ASM notices that both approval-score adjacent pairs (B-A and A-C)
are pairwise out of order and by far
the smallest of the two approval-score margins is that between B and A
and so flips that order to give
A>B>C. Now neither pair is pairwise "out of order" so that order is
final and A comfortably wins.
Now to borrow an old example with none of the voters truncating:
49 A|> C (sincere is A or A>B)
06 B>A|
06 B|>A
06 B|>C
06 B>C|
27 C>B|
Now there is a cycle A>C>B>A and the approval scores are A 55, B 51, C 33.
Again Smith//Approval has a problem, the Burying strategists have succeeded.
But again Approval Sorted Margins fixes it. Both adjacent approval-score
adjacent pairs (A-B and B-C)
are out pairwise order and the A-B margin (4) is smaller than the B-C
margin (18) so we flip the A-B pair
to give the order B>A>C. Now neither adjacent pair is pairwise out of
order so that order is final and
B (the sincere Condorcet winner) wins.
The other reason I prefer Margins Sorted Approval to Smith//Approval
(explicit) is mostly aesthetic.
I find it much more elegant (even beautiful). It would meet as many
monotonicity criteria as it is possible
for a Condorcet method to meet. Without even trying, it meets Reverse
Symmetry.
By comparison I find Smith//Approval(explicit) a bit clunky.
Unfortunately Benham and Woodall and Gross Loser Elimination and "almost
Condorcet" RCIPE and
Hare (aka IRV) all fail Mono-raise (aka Monotonicity).
In both my examples above, the three Winning Votes methods in the poll
(Ranked Pairs and Schulze and
MinMax and maybe "Max Strength Transitive Beatpath") all elect the
Burier's favourite.
In the second example that is also true of Benham and Woodall and Gross
Loser Elimination.
Chris Benham
http://lists.electorama.com/pipermail/election-methods-electorama.com//2002-April/073341.html
I think that if you give people a ballot that looks like grades, they will
tend to assign candidates grades that reflect their cardinal rankings for
those candidates, provided they don't have strategic incentive to do
otherwise. If lack of slots becomes a problem, we could switch to 1-10
rankings. If a tendency to spread the candidates out tends to skew the
results, we could go with the "none of the below" candidate in ranked
ballots. But for the time being, I think the 6-slot ballot would do fine,
and if I were to advocate this method I'd go with the 6-slot ballot.
At any rate, I was just looking at how well this technique responds to
certain strategic voting scenarios. In an earlier message (March 20) I
suggested that Approval Completed Condorcet ("ACC" from here on out) passes
SFC and SDSC from Mike's criterion. It doesn't pass the "Generalized"
versions unless one slips in a Smith set requirement explicitly, which I
argued against in that message.
I'm now going to compare ACC to margins and winning votes Condorcet
methods, using the example that has become my signature example on this
list. The following are the sincere preferences of my example electorate:
49: Bush>Gore>Nader
12: Gore>Bush>Nader
12: Gore>Nader>Bush
27: Nader>Gore>Bush
If everyone votes sincerely, then Gore is the Condorcet winner. The
problem arises when the Bush voters swap Nader and Gore on their ballots
(in margins they can achieve the same effect by truncating, but I'll ignore
that for this analysis). So the new "preferences" are
49: Bush>Nader>Gore
12: Gore>Bush>Nader
12: Gore>Nader>Bush
27: Nader>Gore>Bush
In margins-based methods, the only way for Gore to still win the election
is for the Nader voters to bury Nader behind Gore. The stable equilibrium
ballots become:
49: Bush>Nader>Gore
12: Gore>Bush>Nader
39: Gore>Nader>Bush
And this allows Gore to still carry the election. This sort of equilibrium
is what Mike is talking about when he says that margins methods are
"falsifying".
In winning votes methods, the Nader camp can vote equal first-place
rankings rather than swap Gore and Nader entirely. The stable result is
therefore:
49: Bush>Nader>Gore
12: Gore>Bush>Nader
12: Gore>Nader>Bush
27: Nader=Gore>Bush
In ACC... we first have to define where the approval cutoffs on the ballots
are. Since the approval tally is only used to break cyclic ties, clearly
the Bush camp has no incentive to Approve of anyone except Bush. I'm going
to make the assumption that since Gore and Bush are the apparent front
runners in this race (the only two with a decent shot at election), every
voter will approve one and not the other. This is the logical approval
cutoff to use, based on the approval strategy threads that have been
circulating on the list of late. So the ballots could look something like
this: (>> denotes approval cutoff)
49: Bush>>Nader>Gore
12: Gore>>Bush>Nader
6: Gore>>Nader>Bush
6: Gore>Nader>>Bush
27: Nader>Gore>>Bush
In this case, Gore wins the approval runoff 51-49-33. So not only did ACC
avoid the need for defensive order-reversal like margins methods, but it
avoided the need for defensive equal-ranking like winning votes
methods. This is a super result: totally strategy-free voting for the
majority side.
There is a dark side to this result, though. Say that some of the
Gore>Bush>Nader voters were extremely non-strategic and decided to approve
both Bush and Gore. So the votes now look like:
49: Bush>>Nader>Gore
6: Gore>Bush>>Nader
6: Gore>>Bush>Nader
6: Gore>>Nader>Bush
6: Gore>Nader>>Bush
27: Nader>Gore>>Bush
Now, Bush wins the approval runoff 55-51-33. This is where ACC's favorite
betrayal scenario comes in. Since Bush wins the approval vote, the only
way the majority can guarantee a Gore win is to make Gore the initial
Condorcet winner, which requires that the Nader camp vote Gore in first place:
49: Bush>>Nader>Gore
6: Gore>Bush>>Nader
6: Gore>>Bush>Nader
6: Gore>>Nader>Bush
33: Gore>Nader>>Bush
So this is more or less the same as the margins method equilibrium.
In summary, if the voters are fairly logical in the placement of their
approval cutoff, then ACC seems almost uniquely free of strategy
considerations. If the underlying approval votes do not back up the
sincere Condorcet winner, however, then ACC becomes just as vulnerable to
strategic manipulation as the margins methods are, if not more so.
Comments?
-Adam
An example can be found where one particular method does better than
another.
3 candidates;
CW, BF, & Bus
(BF is buriers’ favorite. Bus 🚌 is the candidate under whom they bury CW.)
To test wv Condorcet for burial deterrence, I checked 24 cases:
All 6 faction-size orderings for the 3 candidates.
and
4 ways for the middle CW’s voters to rank the other 2, with regard to which
they rank in 2nd place:
Neither
BF
Bus
Half one & half the other
The faction-sizes are kept as close together as possible, because equal
sizes is the middle about which the variation happens, & is probably the
most likely single configuration.
Divide the number of burial’s backfires by the number of its successes, for
the backfire/success ratio…abbreviated
b/s.
For wv Condorcet, b/s = 10.
What is it for Margins-Sorted Approval?
On Thu, Apr 18, 2024 at 10:14 Chris Benham cbenhamau@yahoo.com.au wrote:
One of my nominations and my top choice in the current poll:
Margins Sorted Approval (specified cutoff):
*Voters rank from the top however many candidates they wish and can also
specify an approval
cutoff/threshold. Default approval is only for candidates ranked below no
others (i.e. ranked top
or equal-top).
A Forrest Simmons invention. Candidates are listed in approval score order
and if any adjacent pairs
are pairwise out of order then this is corrected by flipping the
out-of-order pair with the smallest
margin. If there is a tie for this we flip the less approved pair. Repeat
until there are no adjacent pairs
of candidates that are pairwise out of order, then elect the
highest-ordered candidate.*
I'm going to compare it with another of my nominations, another Condorcet
method that collects the
same information from the voters:
Smith//Approval (specified cutoff):
Voters rank from the top however many candidates they wish and can also
specify an approval
cutoff/threshold. Default approval is only for candidates ranked below no
others (i.e. ranked top
or equal-top).
The most approved member of the Smith set wins.
Although it asks voters for a bit more information than other Condorcet
methods like Ranked Pairs,
Schulze, MinMax etcetera, I think it is a lot easier than them to explain
and sell than them.
Condorcet//Approval (explicit) was discussed here in April 2002 by Adam
Tarr. I find voluntarily (in a
Condorcet method) electing a candidate outside the Smith set to be weird
and unacceptable, but all the
examples he gave that I saw apply just as well to
Smith//Approval(explicit).
Now why do I prefer Margins Sorted Approval?
The main reason is that it is quite a lot less vulnerable to Burial
strategy. Say there are three candidates
and most of the voters normally truncate. Say A is the predicted FPP and
Condorcet winner, B is the
predicted FPP runner-up and C is coming last by quite a big margin.
In that case the voters most likely to be tempted to try a Burial strategy
will be the B supporters against
A, using no-threat C as the "bus".
43 A|
03 A>B| ("strategically naive" voters)
44 B|>C (sincere is B or B>A)
10 C|
The B>C Buriers have given A a pairwise defeat, so now there is an A>B>C>A
cycle.
The approval scores: B 47, A 46, C 10.
Now if this was Smith//Approval the 3 A>B| voters would have blown the
election for A by approving B.
But ASM notices that both approval-score adjacent pairs (B-A and A-C) are
pairwise out of order and by far
the smallest of the two approval-score margins is that between B and A
and so flips that order to give
A>B>C. Now neither pair is pairwise "out of order" so that order is
final and A comfortably wins.
Now to borrow an old example with none of the voters truncating:
49 A|> C (sincere is A or A>B)
06 B>A|
06 B|>A
06 B|>C
06 B>C|
27 C>B|
Now there is a cycle A>C>B>A and the approval scores are A 55, B 51, C 33.
Again Smith//Approval has a problem, the Burying strategists have
succeeded.
But again Approval Sorted Margins fixes it. Both adjacent approval-score
adjacent pairs (A-B and B-C)
are out pairwise order and the A-B margin (4) is smaller than the B-C
margin (18) so we flip the A-B pair
to give the order B>A>C. Now neither adjacent pair is pairwise out of
order so that order is final and
B (the sincere Condorcet winner) wins.
The other reason I prefer Margins Sorted Approval to Smith//Approval
(explicit) is mostly aesthetic.
I find it much more elegant (even beautiful). It would meet as many
monotonicity criteria as it is possible
for a Condorcet method to meet. Without even trying, it meets Reverse
Symmetry.
By comparison I find Smith//Approval(explicit) a bit clunky.
Unfortunately Benham and Woodall and Gross Loser Elimination and "almost
Condorcet" RCIPE and
Hare (aka IRV) all fail Mono-raise (aka Monotonicity).
In both my examples above, the three Winning Votes methods in the poll
(Ranked Pairs and Schulze and
MinMax and maybe "Max Strength Transitive Beatpath") all elect the
Burier's favourite.
In the second example that is also true of Benham and Woodall and Gross
Loser Elimination.
Chris Benham
http://lists.electorama.com/pipermail/election-methods-electorama.com//2002-April/073341.html
I think that if you give people a ballot that looks like grades, they will
tend to assign candidates grades that reflect their cardinal rankings for
those candidates, provided they don't have strategic incentive to do
otherwise. If lack of slots becomes a problem, we could switch to 1-10
rankings. If a tendency to spread the candidates out tends to skew the
results, we could go with the "none of the below" candidate in ranked
ballots. But for the time being, I think the 6-slot ballot would do fine,
and if I were to advocate this method I'd go with the 6-slot ballot.
At any rate, I was just looking at how well this technique responds to
certain strategic voting scenarios. In an earlier message (March 20) I
suggested that Approval Completed Condorcet ("ACC" from here on out) passes
SFC and SDSC from Mike's criterion. It doesn't pass the "Generalized"
versions unless one slips in a Smith set requirement explicitly, which I
argued against in that message.
I'm now going to compare ACC to margins and winning votes Condorcet
methods, using the example that has become my signature example on this
list. The following are the sincere preferences of my example electorate:
49: Bush>Gore>Nader
12: Gore>Bush>Nader
12: Gore>Nader>Bush
27: Nader>Gore>Bush
If everyone votes sincerely, then Gore is the Condorcet winner. The
problem arises when the Bush voters swap Nader and Gore on their ballots
(in margins they can achieve the same effect by truncating, but I'll ignore
that for this analysis). So the new "preferences" are
49: Bush>Nader>Gore
12: Gore>Bush>Nader
12: Gore>Nader>Bush
27: Nader>Gore>Bush
In margins-based methods, the only way for Gore to still win the election
is for the Nader voters to bury Nader behind Gore. The stable equilibrium
ballots become:
49: Bush>Nader>Gore
12: Gore>Bush>Nader
39: Gore>Nader>Bush
And this allows Gore to still carry the election. This sort of equilibrium
is what Mike is talking about when he says that margins methods are
"falsifying".
In winning votes methods, the Nader camp can vote equal first-place
rankings rather than swap Gore and Nader entirely. The stable result is
therefore:
49: Bush>Nader>Gore
12: Gore>Bush>Nader
12: Gore>Nader>Bush
27: Nader=Gore>Bush
In ACC... we first have to define where the approval cutoffs on the ballots
are. Since the approval tally is only used to break cyclic ties, clearly
the Bush camp has no incentive to Approve of anyone except Bush. I'm going
to make the assumption that since Gore and Bush are the apparent front
runners in this race (the only two with a decent shot at election), every
voter will approve one and not the other. This is the logical approval
cutoff to use, based on the approval strategy threads that have been
circulating on the list of late. So the ballots could look something like
this: (>> denotes approval cutoff)
49: Bush>>Nader>Gore
12: Gore>>Bush>Nader
6: Gore>>Nader>Bush
6: Gore>Nader>>Bush
27: Nader>Gore>>Bush
In this case, Gore wins the approval runoff 51-49-33. So not only did ACC
avoid the need for defensive order-reversal like margins methods, but it
avoided the need for defensive equal-ranking like winning votes
methods. This is a super result: totally strategy-free voting for the
majority side.
There is a dark side to this result, though. Say that some of the
Gore>Bush>Nader voters were extremely non-strategic and decided to approve
both Bush and Gore. So the votes now look like:
49: Bush>>Nader>Gore
6: Gore>Bush>>Nader
6: Gore>>Bush>Nader
6: Gore>>Nader>Bush
6: Gore>Nader>>Bush
27: Nader>Gore>>Bush
Now, Bush wins the approval runoff 55-51-33. This is where ACC's favorite
betrayal scenario comes in. Since Bush wins the approval vote, the only
way the majority can guarantee a Gore win is to make Gore the initial
Condorcet winner, which requires that the Nader camp vote Gore in first place:
49: Bush>>Nader>Gore
6: Gore>Bush>>Nader
6: Gore>>Bush>Nader
6: Gore>>Nader>Bush
33: Gore>Nader>>Bush
So this is more or less the same as the margins method equilibrium.
In summary, if the voters are fairly logical in the placement of their
approval cutoff, then ACC seems almost uniquely free of strategy
considerations. If the underlying approval votes do not back up the
sincere Condorcet winner, however, then ACC becomes just as vulnerable to
strategic manipulation as the margins methods are, if not more so.
Comments?
-Adam
-
Does Margins-Sorted Approval meet Minimal-Defense?
-
Can offense-truncation by one faction take the win from a CW ranked in
2nd place by the other faction?
Answers for wv: 1) Yes. 2) No.
On Thu, Apr 18, 2024 at 14:17 Michael Ossipoff email9648742@gmail.com
wrote:
An example can be found where one particular method does better than
another.
3 candidates;
CW, BF, & Bus
(BF is buriers’ favorite. Bus 🚌 is the candidate under whom they bury CW.)
To test wv Condorcet for burial deterrence, I checked 24 cases:
All 6 faction-size orderings for the 3 candidates.
and
4 ways for the middle CW’s voters to rank the other 2, with regard to
which they rank in 2nd place:
Neither
BF
Bus
Half one & half the other
The faction-sizes are kept as close together as possible, because equal
sizes is the middle about which the variation happens, & is probably the
most likely single configuration.
Divide the number of burial’s backfires by the number of its successes,
for the backfire/success ratio…abbreviated
b/s.
For wv Condorcet, b/s = 10.
What is it for Margins-Sorted Approval?
On Thu, Apr 18, 2024 at 10:14 Chris Benham cbenhamau@yahoo.com.au wrote:
One of my nominations and my top choice in the current poll:
Margins Sorted Approval (specified cutoff):
*Voters rank from the top however many candidates they wish and can also
specify an approval
cutoff/threshold. Default approval is only for candidates ranked below no
others (i.e. ranked top
or equal-top).
A Forrest Simmons invention. Candidates are listed in approval score
order and if any adjacent pairs
are pairwise out of order then this is corrected by flipping the
out-of-order pair with the smallest
margin. If there is a tie for this we flip the less approved pair. Repeat
until there are no adjacent pairs
of candidates that are pairwise out of order, then elect the
highest-ordered candidate.*
I'm going to compare it with another of my nominations, another Condorcet
method that collects the
same information from the voters:
Smith//Approval (specified cutoff):
Voters rank from the top however many candidates they wish and can also
specify an approval
cutoff/threshold. Default approval is only for candidates ranked below no
others (i.e. ranked top
or equal-top).
The most approved member of the Smith set wins.
Although it asks voters for a bit more information than other Condorcet
methods like Ranked Pairs,
Schulze, MinMax etcetera, I think it is a lot easier than them to explain
and sell than them.
Condorcet//Approval (explicit) was discussed here in April 2002 by Adam
Tarr. I find voluntarily (in a
Condorcet method) electing a candidate outside the Smith set to be weird
and unacceptable, but all the
examples he gave that I saw apply just as well to
Smith//Approval(explicit).
Now why do I prefer Margins Sorted Approval?
The main reason is that it is quite a lot less vulnerable to Burial
strategy. Say there are three candidates
and most of the voters normally truncate. Say A is the predicted FPP and
Condorcet winner, B is the
predicted FPP runner-up and C is coming last by quite a big margin.
In that case the voters most likely to be tempted to try a Burial
strategy will be the B supporters against
A, using no-threat C as the "bus".
43 A|
03 A>B| ("strategically naive" voters)
44 B|>C (sincere is B or B>A)
10 C|
The B>C Buriers have given A a pairwise defeat, so now there is an
A>B>C>A cycle.
The approval scores: B 47, A 46, C 10.
Now if this was Smith//Approval the 3 A>B| voters would have blown the
election for A by approving B.
But ASM notices that both approval-score adjacent pairs (B-A and A-C) are
pairwise out of order and by far
the smallest of the two approval-score margins is that between B and A
and so flips that order to give
A>B>C. Now neither pair is pairwise "out of order" so that order is
final and A comfortably wins.
Now to borrow an old example with none of the voters truncating:
49 A|> C (sincere is A or A>B)
06 B>A|
06 B|>A
06 B|>C
06 B>C|
27 C>B|
Now there is a cycle A>C>B>A and the approval scores are A 55, B 51, C
33.
Again Smith//Approval has a problem, the Burying strategists have
succeeded.
But again Approval Sorted Margins fixes it. Both adjacent approval-score
adjacent pairs (A-B and B-C)
are out pairwise order and the A-B margin (4) is smaller than the B-C
margin (18) so we flip the A-B pair
to give the order B>A>C. Now neither adjacent pair is pairwise out of
order so that order is final and
B (the sincere Condorcet winner) wins.
The other reason I prefer Margins Sorted Approval to Smith//Approval
(explicit) is mostly aesthetic.
I find it much more elegant (even beautiful). It would meet as many
monotonicity criteria as it is possible
for a Condorcet method to meet. Without even trying, it meets Reverse
Symmetry.
By comparison I find Smith//Approval(explicit) a bit clunky.
Unfortunately Benham and Woodall and Gross Loser Elimination and "almost
Condorcet" RCIPE and
Hare (aka IRV) all fail Mono-raise (aka Monotonicity).
In both my examples above, the three Winning Votes methods in the poll
(Ranked Pairs and Schulze and
MinMax and maybe "Max Strength Transitive Beatpath") all elect the
Burier's favourite.
In the second example that is also true of Benham and Woodall and Gross
Loser Elimination.
Chris Benham
http://lists.electorama.com/pipermail/election-methods-electorama.com//2002-April/073341.html
I think that if you give people a ballot that looks like grades, they will
tend to assign candidates grades that reflect their cardinal rankings for
those candidates, provided they don't have strategic incentive to do
otherwise. If lack of slots becomes a problem, we could switch to 1-10
rankings. If a tendency to spread the candidates out tends to skew the
results, we could go with the "none of the below" candidate in ranked
ballots. But for the time being, I think the 6-slot ballot would do fine,
and if I were to advocate this method I'd go with the 6-slot ballot.
At any rate, I was just looking at how well this technique responds to
certain strategic voting scenarios. In an earlier message (March 20) I
suggested that Approval Completed Condorcet ("ACC" from here on out) passes
SFC and SDSC from Mike's criterion. It doesn't pass the "Generalized"
versions unless one slips in a Smith set requirement explicitly, which I
argued against in that message.
I'm now going to compare ACC to margins and winning votes Condorcet
methods, using the example that has become my signature example on this
list. The following are the sincere preferences of my example electorate:
49: Bush>Gore>Nader
12: Gore>Bush>Nader
12: Gore>Nader>Bush
27: Nader>Gore>Bush
If everyone votes sincerely, then Gore is the Condorcet winner. The
problem arises when the Bush voters swap Nader and Gore on their ballots
(in margins they can achieve the same effect by truncating, but I'll ignore
that for this analysis). So the new "preferences" are
49: Bush>Nader>Gore
12: Gore>Bush>Nader
12: Gore>Nader>Bush
27: Nader>Gore>Bush
In margins-based methods, the only way for Gore to still win the election
is for the Nader voters to bury Nader behind Gore. The stable equilibrium
ballots become:
49: Bush>Nader>Gore
12: Gore>Bush>Nader
39: Gore>Nader>Bush
And this allows Gore to still carry the election. This sort of equilibrium
is what Mike is talking about when he says that margins methods are
"falsifying".
In winning votes methods, the Nader camp can vote equal first-place
rankings rather than swap Gore and Nader entirely. The stable result is
therefore:
49: Bush>Nader>Gore
12: Gore>Bush>Nader
12: Gore>Nader>Bush
27: Nader=Gore>Bush
In ACC... we first have to define where the approval cutoffs on the ballots
are. Since the approval tally is only used to break cyclic ties, clearly
the Bush camp has no incentive to Approve of anyone except Bush. I'm going
to make the assumption that since Gore and Bush are the apparent front
runners in this race (the only two with a decent shot at election), every
voter will approve one and not the other. This is the logical approval
cutoff to use, based on the approval strategy threads that have been
circulating on the list of late. So the ballots could look something like
this: (>> denotes approval cutoff)
49: Bush>>Nader>Gore
12: Gore>>Bush>Nader
6: Gore>>Nader>Bush
6: Gore>Nader>>Bush
27: Nader>Gore>>Bush
In this case, Gore wins the approval runoff 51-49-33. So not only did ACC
avoid the need for defensive order-reversal like margins methods, but it
avoided the need for defensive equal-ranking like winning votes
methods. This is a super result: totally strategy-free voting for the
majority side.
There is a dark side to this result, though. Say that some of the
Gore>Bush>Nader voters were extremely non-strategic and decided to approve
both Bush and Gore. So the votes now look like:
49: Bush>>Nader>Gore
6: Gore>Bush>>Nader
6: Gore>>Bush>Nader
6: Gore>>Nader>Bush
6: Gore>Nader>>Bush
27: Nader>Gore>>Bush
Now, Bush wins the approval runoff 55-51-33. This is where ACC's favorite
betrayal scenario comes in. Since Bush wins the approval vote, the only
way the majority can guarantee a Gore win is to make Gore the initial
Condorcet winner, which requires that the Nader camp vote Gore in first place:
49: Bush>>Nader>Gore
6: Gore>Bush>>Nader
6: Gore>>Bush>Nader
6: Gore>>Nader>Bush
33: Gore>Nader>>Bush
So this is more or less the same as the margins method equilibrium.
In summary, if the voters are fairly logical in the placement of their
approval cutoff, then ACC seems almost uniquely free of strategy
considerations. If the underlying approval votes do not back up the
sincere Condorcet winner, however, then ACC becomes just as vulnerable to
strategic manipulation as the margins methods are, if not more so.
Comments?
-Adam
Stephen Eppley https://electowiki.org/wiki/Stephen_Eppleygives this
official definition:
If more than half of the voters prefer alternative y over
alternative x, then that majority must have some way of voting
that ensures x will not be elected and does not require any of
them to rank y equal to or over any alternatives preferred over y.
This definition is most similar to that ofSDSC
https://electowiki.org/wiki/SDSC.
https://electowiki.org/wiki/Strong_Defensive_Strategy_criterion
The answer to your first question (based on the definition I copied
above) is yes. That is obviously implied by its compliance with Double
Defeat. All that "majority" has to do is approve Y and not X. Double
Defeat says that a candidate that is pairwise beaten by a more approved
candidate can't win.
The answer to your second question is yes if the other faction doesn't
approve the CW and no if it does. Like in this old example:
49 A (sincere is A>B)
24 B (the "sincere CW" but the faction may be defecting against C)
27 C>B
If the C>B voters approve B then the approval order is B>A>C and since B
pairwise beats A and A pairwise beats C that order is final and B wins.
But if they don't then the approval order is A>C>B and that order is
final and A wins.
The faction-sizes are kept as close together as possible, because
equal sizes is the middle about which the variation happens, & is
probably the most likely single configuration.
I don't that is always a good idea. If the faction sizes are close
together then surely the risk for the Buriers of their strategy
back-firing would be a lot greater than if the "bus" faction is quite a
bit smaller than theirs. Also of course two large parties and one small
one more closely resembles the current political landscape.
An example can be found where one particular method does better than
another.
Good. I look forward to seeing your example where Winning Votes does
better than Approval Sorted Margins.
I don't know the answer to your last question.
Chris B.
On 19/04/2024 6:56 am, Michael Ossipoff wrote:
-
Does Margins-Sorted Approval meet Minimal-Defense?
-
Can offense-truncation by one faction take the win from a CW ranked
in 2nd place by the other faction?
Answers for wv: 1) Yes. 2) No.
On Thu, Apr 18, 2024 at 14:17 Michael Ossipoff
email9648742@gmail.com wrote:
An example can be found where one particular method does better
than another.
3 candidates;
CW, BF, & Bus
(BF is buriers’ favorite. Bus 🚌 is the candidate under whom they
bury CW.)
To test wv Condorcet for burial deterrence, I checked 24 cases:
All 6 faction-size orderings for the 3 candidates.
and
4 ways for the middle CW’s voters to rank the other 2, with regard
to which they rank in 2nd place:
Neither
BF
Bus
Half one & half the other
The faction-sizes are kept as close together as possible, because
equal sizes is the middle about which the variation happens, & is
probably the most likely single configuration.
Divide the number of burial’s backfires by the number of its
successes, for the backfire/success ratio…abbreviated
b/s.
For wv Condorcet, b/s = 10.
What is it for Margins-Sorted Approval?
On Thu, Apr 18, 2024 at 10:14 Chris Benham
<cbenhamau@yahoo.com.au> wrote:
One of my nominations and my top choice in the current poll:
Margins Sorted Approval (specified cutoff):
*Voters rank from the top however many candidates they wish
and can also specify an approval
cutoff/threshold. Default approval is only for candidates
ranked below no others (i.e. ranked top
or equal-top).
A Forrest Simmons invention. Candidates are listed in approval
score order and if any adjacent pairs
are pairwise out of order then this is corrected by flipping
the out-of-order pair with the smallest
margin. If there is a tie for this we flip the less approved
pair. Repeat until there are no adjacent pairs
of candidates that are pairwise out of order, then elect the
highest-ordered candidate.*
I'm going to compare it with another of my nominations,
another Condorcet method that collects the
same information from the voters:
Smith//Approval (specified cutoff):
*Voters rank from the top however many candidates they wish
and can also specify an approval
cutoff/threshold. Default approval is only for candidates
ranked below no others (i.e. ranked top
or equal-top).
The most approved member of the Smith set wins.*
Although it asks voters for a bit more information than other
Condorcet methods like Ranked Pairs,
Schulze, MinMax etcetera, I think it is a lot easier than them
to explain and sell than them.
Condorcet//Approval (explicit) was discussed here in April
2002 by Adam Tarr. I find voluntarily (in a
Condorcet method) electing a candidate outside the Smith set
to be weird and unacceptable, but all the
examples he gave that I saw apply just as well to
Smith//Approval(explicit).
Now why do I prefer Margins Sorted Approval?
The main reason is that it is quite a lot less vulnerable to
Burial strategy. Say there are three candidates
and most of the voters normally truncate. Say A is the
predicted FPP and Condorcet winner, B is the
predicted FPP runner-up and C is coming last by quite a big
margin.
In that case the voters most likely to be tempted to try a
Burial strategy will be the B supporters against
A, using no-threat C as the "bus".
43 A|
03 A>B| ("strategically naive" voters)
44 B|>C (sincere is B or B>A)
10 C|
The B>C Buriers have given A a pairwise defeat, so now there
is an A>B>C>A cycle.
The approval scores: B 47, A 46, C 10.
Now if this was Smith//Approval the 3 A>B| voters would have
blown the election for A by approving B.
But ASM notices that both approval-score adjacent pairs (B-A
and A-C) are pairwise out of order and by far
the smallest of the two approval-score margins is that between
B and A and so flips that order to give
A>B>C. Now neither pair is pairwise "out of order" so that
order is final and A comfortably wins.
Now to borrow an old example with none of the voters truncating:
49 A|> C (sincere is A or A>B)
06 B>A|
06 B|>A
06 B|>C
06 B>C|
27 C>B|
Now there is a cycle A>C>B>A and the approval scores are A 55,
B 51, C 33.
Again Smith//Approval has a problem, the Burying strategists
have succeeded.
But again Approval Sorted Margins fixes it. Both adjacent
approval-score adjacent pairs (A-B and B-C)
are out pairwise order and the A-B margin (4) is smaller than
the B-C margin (18) so we flip the A-B pair
to give the order B>A>C. Now neither adjacent pair is
pairwise out of order so that order is final and
B (the sincere Condorcet winner) wins.
The other reason I prefer Margins Sorted Approval to
Smith//Approval (explicit) is mostly aesthetic.
I find it much more elegant (even beautiful). It would meet as
many monotonicity criteria as it is possible
for a Condorcet method to meet. Without even trying, it meets
Reverse Symmetry.
By comparison I find Smith//Approval(explicit) a bit clunky.
Unfortunately Benham and Woodall and Gross Loser Elimination
and "almost Condorcet" RCIPE and
Hare (aka IRV) all fail Mono-raise (aka Monotonicity).
In both my examples above, the three Winning Votes methods in
the poll (Ranked Pairs and Schulze and
MinMax and maybe "Max Strength Transitive Beatpath") all elect
the Burier's favourite.
In the second example that is also true of Benham and Woodall
and Gross Loser Elimination.
Chris Benham
http://lists.electorama.com/pipermail/election-methods-electorama.com//2002-April/073341.html
I think that if you give people a ballot that looks like grades, they will
tend to assign candidates grades that reflect their cardinal rankings for
those candidates, provided they don't have strategic incentive to do
otherwise. If lack of slots becomes a problem, we could switch to 1-10
rankings. If a tendency to spread the candidates out tends to skew the
results, we could go with the "none of the below" candidate in ranked
ballots. But for the time being, I think the 6-slot ballot would do fine,
and if I were to advocate this method I'd go with the 6-slot ballot.
At any rate, I was just looking at how well this technique responds to
certain strategic voting scenarios. In an earlier message (March 20) I
suggested that Approval Completed Condorcet ("ACC" from here on out) passes
SFC and SDSC from Mike's criterion. It doesn't pass the "Generalized"
versions unless one slips in a Smith set requirement explicitly, which I
argued against in that message.
I'm now going to compare ACC to margins and winning votes Condorcet
methods, using the example that has become my signature example on this
list. The following are the sincere preferences of my example electorate:
49: Bush>Gore>Nader
12: Gore>Bush>Nader
12: Gore>Nader>Bush
27: Nader>Gore>Bush
If everyone votes sincerely, then Gore is the Condorcet winner. The
problem arises when the Bush voters swap Nader and Gore on their ballots
(in margins they can achieve the same effect by truncating, but I'll ignore
that for this analysis). So the new "preferences" are
49: Bush>Nader>Gore
12: Gore>Bush>Nader
12: Gore>Nader>Bush
27: Nader>Gore>Bush
In margins-based methods, the only way for Gore to still win the election
is for the Nader voters to bury Nader behind Gore. The stable equilibrium
ballots become:
49: Bush>Nader>Gore
12: Gore>Bush>Nader
39: Gore>Nader>Bush
And this allows Gore to still carry the election. This sort of equilibrium
is what Mike is talking about when he says that margins methods are
"falsifying".
In winning votes methods, the Nader camp can vote equal first-place
rankings rather than swap Gore and Nader entirely. The stable result is
therefore:
49: Bush>Nader>Gore
12: Gore>Bush>Nader
12: Gore>Nader>Bush
27: Nader=Gore>Bush
In ACC... we first have to define where the approval cutoffs on the ballots
are. Since the approval tally is only used to break cyclic ties, clearly
the Bush camp has no incentive to Approve of anyone except Bush. I'm going
to make the assumption that since Gore and Bush are the apparent front
runners in this race (the only two with a decent shot at election), every
voter will approve one and not the other. This is the logical approval
cutoff to use, based on the approval strategy threads that have been
circulating on the list of late. So the ballots could look something like
this: (>> denotes approval cutoff)
49: Bush>>Nader>Gore
12: Gore>>Bush>Nader
6: Gore>>Nader>Bush
6: Gore>Nader>>Bush
27: Nader>Gore>>Bush
In this case, Gore wins the approval runoff 51-49-33. So not only did ACC
avoid the need for defensive order-reversal like margins methods, but it
avoided the need for defensive equal-ranking like winning votes
methods. This is a super result: totally strategy-free voting for the
majority side.
There is a dark side to this result, though. Say that some of the
Gore>Bush>Nader voters were extremely non-strategic and decided to approve
both Bush and Gore. So the votes now look like:
49: Bush>>Nader>Gore
6: Gore>Bush>>Nader
6: Gore>>Bush>Nader
6: Gore>>Nader>Bush
6: Gore>Nader>>Bush
27: Nader>Gore>>Bush
Now, Bush wins the approval runoff 55-51-33. This is where ACC's favorite
betrayal scenario comes in. Since Bush wins the approval vote, the only
way the majority can guarantee a Gore win is to make Gore the initial
Condorcet winner, which requires that the Nader camp vote Gore in first place:
49: Bush>>Nader>Gore
6: Gore>Bush>>Nader
6: Gore>>Bush>Nader
6: Gore>>Nader>Bush
33: Gore>Nader>>Bush
So this is more or less the same as the margins method equilibrium.
In summary, if the voters are fairly logical in the placement of their
approval cutoff, then ACC seems almost uniquely free of strategy
considerations. If the underlying approval votes do not back up the
sincere Condorcet winner, however, then ACC becomes just as vulnerable to
strategic manipulation as the margins methods are, if not more so.
Comments?
-Adam
If a single example can’t be found in which wv Condorcet does better than
Approval-Sorted Margins, then of course I’ll admit that Approval-Sorted
Margins is better.
I have a few questions about Margins-Sorted-Approval:
If I want to propose it to (say) a city-council or an initiative-committee
or focus-group, someone will ask what it’s advantage is…in what way it’s
better. What valuable property does it offer that other methods don’t?
What’s the answer to that inevitable question?
…& there’s the matter of motivation. What is it about double sorting that
motivates it?
It makes sense to start with Approval-ordering & then adjust to fix the
most important pairwise contradictions by switching. But aren’t the *
biggest* margins more important than the smallest ones? Then why fix the
smallest-margin mis-orderings first? & what’s special about adjacency in
the Approval-ordering? Isn’t the biggest pairwise contradiction most
important even between candidates not adjacent in the Approval-ordering?
…& why margins instead of wv, losing-votes, or any of the various measures
of a pairwise-defeat? In my experience, wv has been the important
defeat-measure for strategic protection.
On Sat, Apr 20, 2024 at 11:03 Chris Benham cbenhamau@yahoo.com.au wrote:
Mike O.,
https://electowiki.org/wiki/Minimal_Defense_criterion
Stephen Eppley https://electowiki.org/wiki/Stephen_Eppley gives this
official definition:
If more than half of the voters prefer alternative y over alternative x,
then that majority must have some way of voting that ensures x will not be
elected and does not require any of them to rank y equal to or over any
alternatives preferred over y.
This definition is most similar to that of SDSC
https://electowiki.org/wiki/SDSC.
https://electowiki.org/wiki/Strong_Defensive_Strategy_criterion
The answer to your first question (based on the definition I copied above)
is yes. That is obviously implied by its compliance with Double Defeat. All
that "majority" has to do is approve Y and not X. Double Defeat says that a
candidate that is pairwise beaten by a more approved candidate can't win.
The answer to your second question is yes if the other faction doesn't
approve the CW and no if it does. Like in this old example:
49 A (sincere is A>B)
24 B (the "sincere CW" but the faction may be defecting against C)
27 C>B
If the C>B voters approve B then the approval order is B>A>C and since B
pairwise beats A and A pairwise beats C that order is final and B wins.
But if they don't then the approval order is A>C>B and that order is final
and A wins.
The faction-sizes are kept as close together as possible, because equal
sizes is the middle about which the variation happens, & is probably the
most likely single configuration.
I don't that is always a good idea. If the faction sizes are close
together then surely the risk for the Buriers of their strategy back-firing
would be a lot greater than if the "bus" faction is quite a bit smaller
than theirs. Also of course two large parties and one small one more
closely resembles the current political landscape.
An example can be found where one particular method does better than
another.
Good. I look forward to seeing your example where Winning Votes does
better than Approval Sorted Margins.
I don't know the answer to your last question.
Chris B.
On 19/04/2024 6:56 am, Michael Ossipoff wrote:
-
Does Margins-Sorted Approval meet Minimal-Defense?
-
Can offense-truncation by one faction take the win from a CW ranked in
2nd place by the other faction?
Answers for wv: 1) Yes. 2) No.
On Thu, Apr 18, 2024 at 14:17 Michael Ossipoff email9648742@gmail.com
wrote:
An example can be found where one particular method does better than
another.
3 candidates;
CW, BF, & Bus
(BF is buriers’ favorite. Bus 🚌 is the candidate under whom they bury
CW.)
To test wv Condorcet for burial deterrence, I checked 24 cases:
All 6 faction-size orderings for the 3 candidates.
and
4 ways for the middle CW’s voters to rank the other 2, with regard to
which they rank in 2nd place:
Neither
BF
Bus
Half one & half the other
The faction-sizes are kept as close together as possible, because equal
sizes is the middle about which the variation happens, & is probably the
most likely single configuration.
Divide the number of burial’s backfires by the number of its successes,
for the backfire/success ratio…abbreviated
b/s.
For wv Condorcet, b/s = 10.
What is it for Margins-Sorted Approval?
On Thu, Apr 18, 2024 at 10:14 Chris Benham cbenhamau@yahoo.com.au
wrote:
One of my nominations and my top choice in the current poll:
Margins Sorted Approval (specified cutoff):
*Voters rank from the top however many candidates they wish and can also
specify an approval
cutoff/threshold. Default approval is only for candidates ranked below
no others (i.e. ranked top
or equal-top).
A Forrest Simmons invention. Candidates are listed in approval score
order and if any adjacent pairs
are pairwise out of order then this is corrected by flipping the
out-of-order pair with the smallest
margin. If there is a tie for this we flip the less approved pair.
Repeat until there are no adjacent pairs
of candidates that are pairwise out of order, then elect the
highest-ordered candidate.*
I'm going to compare it with another of my nominations, another
Condorcet method that collects the
same information from the voters:
Smith//Approval (specified cutoff):
Voters rank from the top however many candidates they wish and can also
specify an approval
cutoff/threshold. Default approval is only for candidates ranked below
no others (i.e. ranked top
or equal-top).
The most approved member of the Smith set wins.
Although it asks voters for a bit more information than other Condorcet
methods like Ranked Pairs,
Schulze, MinMax etcetera, I think it is a lot easier than them to
explain and sell than them.
Condorcet//Approval (explicit) was discussed here in April 2002 by Adam
Tarr. I find voluntarily (in a
Condorcet method) electing a candidate outside the Smith set to be weird
and unacceptable, but all the
examples he gave that I saw apply just as well to
Smith//Approval(explicit).
Now why do I prefer Margins Sorted Approval?
The main reason is that it is quite a lot less vulnerable to Burial
strategy. Say there are three candidates
and most of the voters normally truncate. Say A is the predicted FPP
and Condorcet winner, B is the
predicted FPP runner-up and C is coming last by quite a big margin.
In that case the voters most likely to be tempted to try a Burial
strategy will be the B supporters against
A, using no-threat C as the "bus".
43 A|
03 A>B| ("strategically naive" voters)
44 B|>C (sincere is B or B>A)
10 C|
The B>C Buriers have given A a pairwise defeat, so now there is an
A>B>C>A cycle.
The approval scores: B 47, A 46, C 10.
Now if this was Smith//Approval the 3 A>B| voters would have blown the
election for A by approving B.
But ASM notices that both approval-score adjacent pairs (B-A and A-C)
are pairwise out of order and by far
the smallest of the two approval-score margins is that between B and A
and so flips that order to give
A>B>C. Now neither pair is pairwise "out of order" so that order is
final and A comfortably wins.
Now to borrow an old example with none of the voters truncating:
49 A|> C (sincere is A or A>B)
06 B>A|
06 B|>A
06 B|>C
06 B>C|
27 C>B|
Now there is a cycle A>C>B>A and the approval scores are A 55, B 51, C
33.
Again Smith//Approval has a problem, the Burying strategists have
succeeded.
But again Approval Sorted Margins fixes it. Both adjacent approval-score
adjacent pairs (A-B and B-C)
are out pairwise order and the A-B margin (4) is smaller than the B-C
margin (18) so we flip the A-B pair
to give the order B>A>C. Now neither adjacent pair is pairwise out of
order so that order is final and
B (the sincere Condorcet winner) wins.
The other reason I prefer Margins Sorted Approval to Smith//Approval
(explicit) is mostly aesthetic.
I find it much more elegant (even beautiful). It would meet as many
monotonicity criteria as it is possible
for a Condorcet method to meet. Without even trying, it meets Reverse
Symmetry.
By comparison I find Smith//Approval(explicit) a bit clunky.
Unfortunately Benham and Woodall and Gross Loser Elimination and "almost
Condorcet" RCIPE and
Hare (aka IRV) all fail Mono-raise (aka Monotonicity).
In both my examples above, the three Winning Votes methods in the poll
(Ranked Pairs and Schulze and
MinMax and maybe "Max Strength Transitive Beatpath") all elect the
Burier's favourite.
In the second example that is also true of Benham and Woodall and Gross
Loser Elimination.
Chris Benham
http://lists.electorama.com/pipermail/election-methods-electorama.com//2002-April/073341.html
I think that if you give people a ballot that looks like grades, they will
tend to assign candidates grades that reflect their cardinal rankings for
those candidates, provided they don't have strategic incentive to do
otherwise. If lack of slots becomes a problem, we could switch to 1-10
rankings. If a tendency to spread the candidates out tends to skew the
results, we could go with the "none of the below" candidate in ranked
ballots. But for the time being, I think the 6-slot ballot would do fine,
and if I were to advocate this method I'd go with the 6-slot ballot.
At any rate, I was just looking at how well this technique responds to
certain strategic voting scenarios. In an earlier message (March 20) I
suggested that Approval Completed Condorcet ("ACC" from here on out) passes
SFC and SDSC from Mike's criterion. It doesn't pass the "Generalized"
versions unless one slips in a Smith set requirement explicitly, which I
argued against in that message.
I'm now going to compare ACC to margins and winning votes Condorcet
methods, using the example that has become my signature example on this
list. The following are the sincere preferences of my example electorate:
49: Bush>Gore>Nader
12: Gore>Bush>Nader
12: Gore>Nader>Bush
27: Nader>Gore>Bush
If everyone votes sincerely, then Gore is the Condorcet winner. The
problem arises when the Bush voters swap Nader and Gore on their ballots
(in margins they can achieve the same effect by truncating, but I'll ignore
that for this analysis). So the new "preferences" are
49: Bush>Nader>Gore
12: Gore>Bush>Nader
12: Gore>Nader>Bush
27: Nader>Gore>Bush
In margins-based methods, the only way for Gore to still win the election
is for the Nader voters to bury Nader behind Gore. The stable equilibrium
ballots become:
49: Bush>Nader>Gore
12: Gore>Bush>Nader
39: Gore>Nader>Bush
And this allows Gore to still carry the election. This sort of equilibrium
is what Mike is talking about when he says that margins methods are
"falsifying".
In winning votes methods, the Nader camp can vote equal first-place
rankings rather than swap Gore and Nader entirely. The stable result is
therefore:
49: Bush>Nader>Gore
12: Gore>Bush>Nader
12: Gore>Nader>Bush
27: Nader=Gore>Bush
In ACC... we first have to define where the approval cutoffs on the ballots
are. Since the approval tally is only used to break cyclic ties, clearly
the Bush camp has no incentive to Approve of anyone except Bush. I'm going
to make the assumption that since Gore and Bush are the apparent front
runners in this race (the only two with a decent shot at election), every
voter will approve one and not the other. This is the logical approval
cutoff to use, based on the approval strategy threads that have been
circulating on the list of late. So the ballots could look something like
this: (>> denotes approval cutoff)
49: Bush>>Nader>Gore
12: Gore>>Bush>Nader
6: Gore>>Nader>Bush
6: Gore>Nader>>Bush
27: Nader>Gore>>Bush
In this case, Gore wins the approval runoff 51-49-33. So not only did ACC
avoid the need for defensive order-reversal like margins methods, but it
avoided the need for defensive equal-ranking like winning votes
methods. This is a super result: totally strategy-free voting for the
majority side.
There is a dark side to this result, though. Say that some of the
Gore>Bush>Nader voters were extremely non-strategic and decided to approve
both Bush and Gore. So the votes now look like:
49: Bush>>Nader>Gore
6: Gore>Bush>>Nader
6: Gore>>Bush>Nader
6: Gore>>Nader>Bush
6: Gore>Nader>>Bush
27: Nader>Gore>>Bush
Now, Bush wins the approval runoff 55-51-33. This is where ACC's favorite
betrayal scenario comes in. Since Bush wins the approval vote, the only
way the majority can guarantee a Gore win is to make Gore the initial
Condorcet winner, which requires that the Nader camp vote Gore in first place:
49: Bush>>Nader>Gore
6: Gore>Bush>>Nader
6: Gore>>Bush>Nader
6: Gore>>Nader>Bush
33: Gore>Nader>>Bush
So this is more or less the same as the margins method equilibrium.
In summary, if the voters are fairly logical in the placement of their
approval cutoff, then ACC seems almost uniquely free of strategy
considerations. If the underlying approval votes do not back up the
sincere Condorcet winner, however, then ACC becomes just as vulnerable to
strategic manipulation as the margins methods are, if not more so.
Comments?
-Adam
Margins Sorted Approval (explicit) doesn't use any information other
than the approval scores and the plain win-loss-draw results of (usually
only some of) the pairwise contests based on the rankings.
So the "margins" referred to are about the approval scores of adjacent
pairs of candidates in the approval order. There are no "winning votes"
or "losing votes".
Most of the time we can operate Margins Sorted Approval without even
finding out if there is a cycle or not. If the Condorcet winner is the
least approved candidate then it will work its way up to the top of the
final order and we'll know that it pairwise beat all the other
candidates. Otherwise there is no need for us to know the pairwise
result between the candidate at the top of the final order and the
candidate at the bottom (and maybe other pairwise results if there are
more than three candidates.)
This makes it quite a bit easier to operate than Smith//Approval and
some other methods.
I admit that it might be a bit of a challenge to explain and sell to an
at all sceptical non-expert audience. Smith//Approval is much easier in
that way.
Chris
On 21/04/2024 4:37 am, Michael Ossipoff wrote:
If a single example can’t be found in which wv Condorcet does better
than Approval-Sorted Margins, then of course I’ll admit that
Approval-Sorted Margins is better.
I have a few questions about Margins-Sorted-Approval:
If I want to propose it to (say) a city-council or an
initiative-committee or focus-group, someone will ask what it’s
advantage is…in what way it’s better. What valuable property does it
offer that other methods don’t?
What’s the answer to that inevitable question?
…& there’s the matter of motivation. What is it about double sorting
that motivates it?
It makes sense to start with Approval-ordering & then adjust to fix
the most important pairwise contradictions by switching. But aren’t
the * biggest* margins more important than the smallest ones? Then why
fix the smallest-margin mis-orderings first? & what’s special about
adjacency in the Approval-ordering? Isn’t the biggest pairwise
contradiction most important even between candidates not adjacent in
the Approval-ordering?
…& why margins instead of wv, losing-votes, or any of the various
measures of a pairwise-defeat? In my experience, wv has been the
important defeat-measure for strategic protection.
On Sat, Apr 20, 2024 at 11:03 Chris Benham cbenhamau@yahoo.com.au wrote:
Mike O.,
https://electowiki.org/wiki/Minimal_Defense_criterion
Stephen Eppley <https://electowiki.org/wiki/Stephen_Eppley>gives
this official definition:
If more than half of the voters prefer alternative y over
alternative x, then that majority must have some way of
voting that ensures x will not be elected and does not
require any of them to rank y equal to or over any
alternatives preferred over y.
This definition is most similar to that ofSDSC
<https://electowiki.org/wiki/SDSC>.
https://electowiki.org/wiki/Strong_Defensive_Strategy_criterion
The answer to your first question (based on the definition I
copied above) is yes. That is obviously implied by its compliance
with Double Defeat. All that "majority" has to do is approve Y and
not X. Double Defeat says that a candidate that is pairwise beaten
by a more approved candidate can't win.
The answer to your second question is yes if the other faction
doesn't approve the CW and no if it does. Like in this old example:
49 A (sincere is A>B)
24 B (the "sincere CW" but the faction may be defecting against C)
27 C>B
If the C>B voters approve B then the approval order is B>A>C and
since B pairwise beats A and A pairwise beats C that order is
final and B wins.
But if they don't then the approval order is A>C>B and that order
is final and A wins.
The faction-sizes are kept as close together as possible, because
equal sizes is the middle about which the variation happens, & is
probably the most likely single configuration.
I don't that is always a good idea. If the faction sizes are close
together then surely the risk for the Buriers of their strategy
back-firing would be a lot greater than if the "bus" faction is
quite a bit smaller than theirs. Also of course two large parties
and one small one more closely resembles the current political
landscape.
An example can be found where one particular method does better
than another.
Good. I look forward to seeing your example where Winning Votes
does better than Approval Sorted Margins.
I don't know the answer to your last question.
Chris B.
On 19/04/2024 6:56 am, Michael Ossipoff wrote:
1) Does Margins-Sorted Approval meet Minimal-Defense?
2) Can offense-truncation by one faction take the win from a CW
ranked in 2nd place by the other faction?
Answers for wv: 1) Yes. 2) No.
On Thu, Apr 18, 2024 at 14:17 Michael Ossipoff
<email9648742@gmail.com> wrote:
An example can be found where one particular method does
better than another.
3 candidates;
CW, BF, & Bus
(BF is buriers’ favorite. Bus 🚌 is the candidate under whom
they bury CW.)
To test wv Condorcet for burial deterrence, I checked 24 cases:
All 6 faction-size orderings for the 3 candidates.
and
4 ways for the middle CW’s voters to rank the other 2, with
regard to which they rank in 2nd place:
Neither
BF
Bus
Half one & half the other
The faction-sizes are kept as close together as possible,
because equal sizes is the middle about which the variation
happens, & is probably the most likely single configuration.
Divide the number of burial’s backfires by the number of its
successes, for the backfire/success ratio…abbreviated
b/s.
For wv Condorcet, b/s = 10.
What is it for Margins-Sorted Approval?
On Thu, Apr 18, 2024 at 10:14 Chris Benham
<cbenhamau@yahoo.com.au> wrote:
One of my nominations and my top choice in the current poll:
Margins Sorted Approval (specified cutoff):
*Voters rank from the top however many candidates they
wish and can also specify an approval
cutoff/threshold. Default approval is only for candidates
ranked below no others (i.e. ranked top
or equal-top).
A Forrest Simmons invention. Candidates are listed in
approval score order and if any adjacent pairs
are pairwise out of order then this is corrected by
flipping the out-of-order pair with the smallest
margin. If there is a tie for this we flip the less
approved pair. Repeat until there are no adjacent pairs
of candidates that are pairwise out of order, then elect
the highest-ordered candidate.*
I'm going to compare it with another of my nominations,
another Condorcet method that collects the
same information from the voters:
Smith//Approval (specified cutoff):
*Voters rank from the top however many candidates they
wish and can also specify an approval
cutoff/threshold. Default approval is only for candidates
ranked below no others (i.e. ranked top
or equal-top).
The most approved member of the Smith set wins.*
Although it asks voters for a bit more information than
other Condorcet methods like Ranked Pairs,
Schulze, MinMax etcetera, I think it is a lot easier than
them to explain and sell than them.
Condorcet//Approval (explicit) was discussed here in
April 2002 by Adam Tarr. I find voluntarily (in a
Condorcet method) electing a candidate outside the Smith
set to be weird and unacceptable, but all the
examples he gave that I saw apply just as well to
Smith//Approval(explicit).
Now why do I prefer Margins Sorted Approval?
The main reason is that it is quite a lot less vulnerable
to Burial strategy. Say there are three candidates
and most of the voters normally truncate. Say A is the
predicted FPP and Condorcet winner, B is the
predicted FPP runner-up and C is coming last by quite a
big margin.
In that case the voters most likely to be tempted to try
a Burial strategy will be the B supporters against
A, using no-threat C as the "bus".
43 A|
03 A>B| ("strategically naive" voters)
44 B|>C (sincere is B or B>A)
10 C|
The B>C Buriers have given A a pairwise defeat, so now
there is an A>B>C>A cycle.
The approval scores: B 47, A 46, C 10.
Now if this was Smith//Approval the 3 A>B| voters would
have blown the election for A by approving B.
But ASM notices that both approval-score adjacent pairs
(B-A and A-C) are pairwise out of order and by far
the smallest of the two approval-score margins is that
between B and A and so flips that order to give
A>B>C. Now neither pair is pairwise "out of order" so
that order is final and A comfortably wins.
Now to borrow an old example with none of the voters
truncating:
49 A|> C (sincere is A or A>B)
06 B>A|
06 B|>A
06 B|>C
06 B>C|
27 C>B|
Now there is a cycle A>C>B>A and the approval scores are
A 55, B 51, C 33.
Again Smith//Approval has a problem, the Burying
strategists have succeeded.
But again Approval Sorted Margins fixes it. Both adjacent
approval-score adjacent pairs (A-B and B-C)
are out pairwise order and the A-B margin (4) is smaller
than the B-C margin (18) so we flip the A-B pair
to give the order B>A>C. Now neither adjacent pair is
pairwise out of order so that order is final and
B (the sincere Condorcet winner) wins.
The other reason I prefer Margins Sorted Approval to
Smith//Approval (explicit) is mostly aesthetic.
I find it much more elegant (even beautiful). It would
meet as many monotonicity criteria as it is possible
for a Condorcet method to meet. Without even trying, it
meets Reverse Symmetry.
By comparison I find Smith//Approval(explicit) a bit clunky.
Unfortunately Benham and Woodall and Gross Loser
Elimination and "almost Condorcet" RCIPE and
Hare (aka IRV) all fail Mono-raise (aka Monotonicity).
In both my examples above, the three Winning Votes
methods in the poll (Ranked Pairs and Schulze and
MinMax and maybe "Max Strength Transitive Beatpath") all
elect the Burier's favourite.
In the second example that is also true of Benham and
Woodall and Gross Loser Elimination.
Chris Benham
http://lists.electorama.com/pipermail/election-methods-electorama.com//2002-April/073341.html
I think that if you give people a ballot that looks like grades, they will
tend to assign candidates grades that reflect their cardinal rankings for
those candidates, provided they don't have strategic incentive to do
otherwise. If lack of slots becomes a problem, we could switch to 1-10
rankings. If a tendency to spread the candidates out tends to skew the
results, we could go with the "none of the below" candidate in ranked
ballots. But for the time being, I think the 6-slot ballot would do fine,
and if I were to advocate this method I'd go with the 6-slot ballot.
At any rate, I was just looking at how well this technique responds to
certain strategic voting scenarios. In an earlier message (March 20) I
suggested that Approval Completed Condorcet ("ACC" from here on out) passes
SFC and SDSC from Mike's criterion. It doesn't pass the "Generalized"
versions unless one slips in a Smith set requirement explicitly, which I
argued against in that message.
I'm now going to compare ACC to margins and winning votes Condorcet
methods, using the example that has become my signature example on this
list. The following are the sincere preferences of my example electorate:
49: Bush>Gore>Nader
12: Gore>Bush>Nader
12: Gore>Nader>Bush
27: Nader>Gore>Bush
If everyone votes sincerely, then Gore is the Condorcet winner. The
problem arises when the Bush voters swap Nader and Gore on their ballots
(in margins they can achieve the same effect by truncating, but I'll ignore
that for this analysis). So the new "preferences" are
49: Bush>Nader>Gore
12: Gore>Bush>Nader
12: Gore>Nader>Bush
27: Nader>Gore>Bush
In margins-based methods, the only way for Gore to still win the election
is for the Nader voters to bury Nader behind Gore. The stable equilibrium
ballots become:
49: Bush>Nader>Gore
12: Gore>Bush>Nader
39: Gore>Nader>Bush
And this allows Gore to still carry the election. This sort of equilibrium
is what Mike is talking about when he says that margins methods are
"falsifying".
In winning votes methods, the Nader camp can vote equal first-place
rankings rather than swap Gore and Nader entirely. The stable result is
therefore:
49: Bush>Nader>Gore
12: Gore>Bush>Nader
12: Gore>Nader>Bush
27: Nader=Gore>Bush
In ACC... we first have to define where the approval cutoffs on the ballots
are. Since the approval tally is only used to break cyclic ties, clearly
the Bush camp has no incentive to Approve of anyone except Bush. I'm going
to make the assumption that since Gore and Bush are the apparent front
runners in this race (the only two with a decent shot at election), every
voter will approve one and not the other. This is the logical approval
cutoff to use, based on the approval strategy threads that have been
circulating on the list of late. So the ballots could look something like
this: (>> denotes approval cutoff)
49: Bush>>Nader>Gore
12: Gore>>Bush>Nader
6: Gore>>Nader>Bush
6: Gore>Nader>>Bush
27: Nader>Gore>>Bush
In this case, Gore wins the approval runoff 51-49-33. So not only did ACC
avoid the need for defensive order-reversal like margins methods, but it
avoided the need for defensive equal-ranking like winning votes
methods. This is a super result: totally strategy-free voting for the
majority side.
There is a dark side to this result, though. Say that some of the
Gore>Bush>Nader voters were extremely non-strategic and decided to approve
both Bush and Gore. So the votes now look like:
49: Bush>>Nader>Gore
6: Gore>Bush>>Nader
6: Gore>>Bush>Nader
6: Gore>>Nader>Bush
6: Gore>Nader>>Bush
27: Nader>Gore>>Bush
Now, Bush wins the approval runoff 55-51-33. This is where ACC's favorite
betrayal scenario comes in. Since Bush wins the approval vote, the only
way the majority can guarantee a Gore win is to make Gore the initial
Condorcet winner, which requires that the Nader camp vote Gore in first place:
49: Bush>>Nader>Gore
6: Gore>Bush>>Nader
6: Gore>>Bush>Nader
6: Gore>>Nader>Bush
33: Gore>Nader>>Bush
So this is more or less the same as the margins method equilibrium.
In summary, if the voters are fairly logical in the placement of their
approval cutoff, then ACC seems almost uniquely free of strategy
considerations. If the underlying approval votes do not back up the
sincere Condorcet winner, however, then ACC becomes just as vulnerable to
strategic manipulation as the margins methods are, if not more so.
Comments?
-Adam
A question I forgot to answer:
It makes sense to start with Approval-ordering & then adjust to fix
the most important pairwise contradictions by switching. But aren’t
the * biggest* margins more important than the smallest ones? Then why
fix the smallest-margin mis-orderings first?
Our aim it produce a "beat chain" (if that's the right term) where every
candidate beats the next-lowest in the order down to the bottom, which
is most in harmony with the approval order. No out-of-order pair of
adjacent candidates is going to be left out of order.
As we switch the smaller-margin out-of-order adjacent pairs the
larger-margin ones will strongly tend to go away, with the result that
the final order will be more in harmony with the approval order.
My earlier incomplete answer to Michael O.'s questions:
Margins Sorted Approval (explicit) doesn't use any information other
than the approval scores and the plain win-loss-draw results of
(usually only some of) the pairwise contests based on the rankings.
So the "margins" referred to are about the approval scores of adjacent
pairs of candidates in the approval order. There are no "winning
votes" or "losing votes".
Most of the time we can operate Margins Sorted Approval without even
finding out if there is a cycle or not. If the Condorcet winner is
the least approved candidate then it will work its way up to the top
of the final order and we'll know that it pairwise beat all the other
candidates. Otherwise there is no need for us to know the pairwise
result between the candidate at the top of the final order and the
candidate at the bottom (and maybe other pairwise results if there are
more than three candidates.)
This makes it quite a bit easier to operate than Smith//Approval and
some other methods.
I admit that it might be a bit of a challenge to explain and sell to
an at all sceptical non-expert audience. Smith//Approval is much
easier in that way.
Chris
On 21/04/2024 4:37 am, Michael Ossipoff wrote:
If a single example can’t be found in which wv Condorcet does better
than Approval-Sorted Margins, then of course I’ll admit that
Approval-Sorted Margins is better.
I have a few questions about Margins-Sorted-Approval:
If I want to propose it to (say) a city-council or an
initiative-committee or focus-group, someone will ask what it’s
advantage is…in what way it’s better. What valuable property does it
offer that other methods don’t?
What’s the answer to that inevitable question?
…& there’s the matter of motivation. What is it about double sorting
that motivates it?
It makes sense to start with Approval-ordering & then adjust to fix
the most important pairwise contradictions by switching. But aren’t
the * biggest* margins more important than the smallest ones? Then why
fix the smallest-margin mis-orderings first? & what’s special about
adjacency in the Approval-ordering? Isn’t the biggest pairwise
contradiction most important even between candidates not adjacent in
the Approval-ordering?
…& why margins instead of wv, losing-votes, or any of the various
measures of a pairwise-defeat? In my experience, wv has been the
important defeat-measure for strategic protection.
On Sat, Apr 20, 2024 at 11:03 Chris Benham cbenhamau@yahoo.com.au wrote:
Mike O.,
https://electowiki.org/wiki/Minimal_Defense_criterion
Stephen Eppley <https://electowiki.org/wiki/Stephen_Eppley>gives
this official definition:
If more than half of the voters prefer alternative y over
alternative x, then that majority must have some way of
voting that ensures x will not be elected and does not
require any of them to rank y equal to or over any
alternatives preferred over y.
This definition is most similar to that ofSDSC
<https://electowiki.org/wiki/SDSC>.
https://electowiki.org/wiki/Strong_Defensive_Strategy_criterion
The answer to your first question (based on the definition I
copied above) is yes. That is obviously implied by its compliance
with Double Defeat. All that "majority" has to do is approve Y and
not X. Double Defeat says that a candidate that is pairwise beaten
by a more approved candidate can't win.
The answer to your second question is yes if the other faction
doesn't approve the CW and no if it does. Like in this old example:
49 A (sincere is A>B)
24 B (the "sincere CW" but the faction may be defecting against C)
27 C>B
If the C>B voters approve B then the approval order is B>A>C and
since B pairwise beats A and A pairwise beats C that order is
final and B wins.
But if they don't then the approval order is A>C>B and that order
is final and A wins.
The faction-sizes are kept as close together as possible, because
equal sizes is the middle about which the variation happens, & is
probably the most likely single configuration.
I don't that is always a good idea. If the faction sizes are close
together then surely the risk for the Buriers of their strategy
back-firing would be a lot greater than if the "bus" faction is
quite a bit smaller than theirs. Also of course two large parties
and one small one more closely resembles the current political
landscape.
An example can be found where one particular method does better
than another.
Good. I look forward to seeing your example where Winning Votes
does better than Approval Sorted Margins.
I don't know the answer to your last question.
Chris B.
On 19/04/2024 6:56 am, Michael Ossipoff wrote:
1) Does Margins-Sorted Approval meet Minimal-Defense?
2) Can offense-truncation by one faction take the win from a CW
ranked in 2nd place by the other faction?
Answers for wv: 1) Yes. 2) No.
On Thu, Apr 18, 2024 at 14:17 Michael Ossipoff
<email9648742@gmail.com> wrote:
An example can be found where one particular method does
better than another.
3 candidates;
CW, BF, & Bus
(BF is buriers’ favorite. Bus 🚌 is the candidate under whom
they bury CW.)
To test wv Condorcet for burial deterrence, I checked 24 cases:
All 6 faction-size orderings for the 3 candidates.
and
4 ways for the middle CW’s voters to rank the other 2, with
regard to which they rank in 2nd place:
Neither
BF
Bus
Half one & half the other
The faction-sizes are kept as close together as possible,
because equal sizes is the middle about which the variation
happens, & is probably the most likely single configuration.
Divide the number of burial’s backfires by the number of its
successes, for the backfire/success ratio…abbreviated
b/s.
For wv Condorcet, b/s = 10.
What is it for Margins-Sorted Approval?
On Thu, Apr 18, 2024 at 10:14 Chris Benham
<cbenhamau@yahoo.com.au> wrote:
One of my nominations and my top choice in the current poll:
Margins Sorted Approval (specified cutoff):
*Voters rank from the top however many candidates they
wish and can also specify an approval
cutoff/threshold. Default approval is only for candidates
ranked below no others (i.e. ranked top
or equal-top).
A Forrest Simmons invention. Candidates are listed in
approval score order and if any adjacent pairs
are pairwise out of order then this is corrected by
flipping the out-of-order pair with the smallest
margin. If there is a tie for this we flip the less
approved pair. Repeat until there are no adjacent pairs
of candidates that are pairwise out of order, then elect
the highest-ordered candidate.*
I'm going to compare it with another of my nominations,
another Condorcet method that collects the
same information from the voters:
Smith//Approval (specified cutoff):
*Voters rank from the top however many candidates they
wish and can also specify an approval
cutoff/threshold. Default approval is only for candidates
ranked below no others (i.e. ranked top
or equal-top).
The most approved member of the Smith set wins.*
Although it asks voters for a bit more information than
other Condorcet methods like Ranked Pairs,
Schulze, MinMax etcetera, I think it is a lot easier than
them to explain and sell than them.
Condorcet//Approval (explicit) was discussed here in
April 2002 by Adam Tarr. I find voluntarily (in a
Condorcet method) electing a candidate outside the Smith
set to be weird and unacceptable, but all the
examples he gave that I saw apply just as well to
Smith//Approval(explicit).
Now why do I prefer Margins Sorted Approval?
The main reason is that it is quite a lot less vulnerable
to Burial strategy. Say there are three candidates
and most of the voters normally truncate. Say A is the
predicted FPP and Condorcet winner, B is the
predicted FPP runner-up and C is coming last by quite a
big margin.
In that case the voters most likely to be tempted to try
a Burial strategy will be the B supporters against
A, using no-threat C as the "bus".
43 A|
03 A>B| ("strategically naive" voters)
44 B|>C (sincere is B or B>A)
10 C|
The B>C Buriers have given A a pairwise defeat, so now
there is an A>B>C>A cycle.
The approval scores: B 47, A 46, C 10.
Now if this was Smith//Approval the 3 A>B| voters would
have blown the election for A by approving B.
But ASM notices that both approval-score adjacent pairs
(B-A and A-C) are pairwise out of order and by far
the smallest of the two approval-score margins is that
between B and A and so flips that order to give
A>B>C. Now neither pair is pairwise "out of order" so
that order is final and A comfortably wins.
Now to borrow an old example with none of the voters
truncating:
49 A|> C (sincere is A or A>B)
06 B>A|
06 B|>A
06 B|>C
06 B>C|
27 C>B|
Now there is a cycle A>C>B>A and the approval scores are
A 55, B 51, C 33.
Again Smith//Approval has a problem, the Burying
strategists have succeeded.
But again Approval Sorted Margins fixes it. Both adjacent
approval-score adjacent pairs (A-B and B-C)
are out pairwise order and the A-B margin (4) is smaller
than the B-C margin (18) so we flip the A-B pair
to give the order B>A>C. Now neither adjacent pair is
pairwise out of order so that order is final and
B (the sincere Condorcet winner) wins.
The other reason I prefer Margins Sorted Approval to
Smith//Approval (explicit) is mostly aesthetic.
I find it much more elegant (even beautiful). It would
meet as many monotonicity criteria as it is possible
for a Condorcet method to meet. Without even trying, it
meets Reverse Symmetry.
By comparison I find Smith//Approval(explicit) a bit clunky.
Unfortunately Benham and Woodall and Gross Loser
Elimination and "almost Condorcet" RCIPE and
Hare (aka IRV) all fail Mono-raise (aka Monotonicity).
In both my examples above, the three Winning Votes
methods in the poll (Ranked Pairs and Schulze and
MinMax and maybe "Max Strength Transitive Beatpath") all
elect the Burier's favourite.
In the second example that is also true of Benham and
Woodall and Gross Loser Elimination.
Chris Benham
http://lists.electorama.com/pipermail/election-methods-electorama.com//2002-April/073341.html
I think that if you give people a ballot that looks like grades, they will
tend to assign candidates grades that reflect their cardinal rankings for
those candidates, provided they don't have strategic incentive to do
otherwise. If lack of slots becomes a problem, we could switch to 1-10
rankings. If a tendency to spread the candidates out tends to skew the
results, we could go with the "none of the below" candidate in ranked
ballots. But for the time being, I think the 6-slot ballot would do fine,
and if I were to advocate this method I'd go with the 6-slot ballot.
At any rate, I was just looking at how well this technique responds to
certain strategic voting scenarios. In an earlier message (March 20) I
suggested that Approval Completed Condorcet ("ACC" from here on out) passes
SFC and SDSC from Mike's criterion. It doesn't pass the "Generalized"
versions unless one slips in a Smith set requirement explicitly, which I
argued against in that message.
I'm now going to compare ACC to margins and winning votes Condorcet
methods, using the example that has become my signature example on this
list. The following are the sincere preferences of my example electorate:
49: Bush>Gore>Nader
12: Gore>Bush>Nader
12: Gore>Nader>Bush
27: Nader>Gore>Bush
If everyone votes sincerely, then Gore is the Condorcet winner. The
problem arises when the Bush voters swap Nader and Gore on their ballots
(in margins they can achieve the same effect by truncating, but I'll ignore
that for this analysis). So the new "preferences" are
49: Bush>Nader>Gore
12: Gore>Bush>Nader
12: Gore>Nader>Bush
27: Nader>Gore>Bush
In margins-based methods, the only way for Gore to still win the election
is for the Nader voters to bury Nader behind Gore. The stable equilibrium
ballots become:
49: Bush>Nader>Gore
12: Gore>Bush>Nader
39: Gore>Nader>Bush
And this allows Gore to still carry the election. This sort of equilibrium
is what Mike is talking about when he says that margins methods are
"falsifying".
In winning votes methods, the Nader camp can vote equal first-place
rankings rather than swap Gore and Nader entirely. The stable result is
therefore:
49: Bush>Nader>Gore
12: Gore>Bush>Nader
12: Gore>Nader>Bush
27: Nader=Gore>Bush
In ACC... we first have to define where the approval cutoffs on the ballots
are. Since the approval tally is only used to break cyclic ties, clearly
the Bush camp has no incentive to Approve of anyone except Bush. I'm going
to make the assumption that since Gore and Bush are the apparent front
runners in this race (the only two with a decent shot at election), every
voter will approve one and not the other. This is the logical approval
cutoff to use, based on the approval strategy threads that have been
circulating on the list of late. So the ballots could look something like
this: (>> denotes approval cutoff)
49: Bush>>Nader>Gore
12: Gore>>Bush>Nader
6: Gore>>Nader>Bush
6: Gore>Nader>>Bush
27: Nader>Gore>>Bush
In this case, Gore wins the approval runoff 51-49-33. So not only did ACC
avoid the need for defensive order-reversal like margins methods, but it
avoided the need for defensive equal-ranking like winning votes
methods. This is a super result: totally strategy-free voting for the
majority side.
There is a dark side to this result, though. Say that some of the
Gore>Bush>Nader voters were extremely non-strategic and decided to approve
both Bush and Gore. So the votes now look like:
49: Bush>>Nader>Gore
6: Gore>Bush>>Nader
6: Gore>>Bush>Nader
6: Gore>>Nader>Bush
6: Gore>Nader>>Bush
27: Nader>Gore>>Bush
Now, Bush wins the approval runoff 55-51-33. This is where ACC's favorite
betrayal scenario comes in. Since Bush wins the approval vote, the only
way the majority can guarantee a Gore win is to make Gore the initial
Condorcet winner, which requires that the Nader camp vote Gore in first place:
49: Bush>>Nader>Gore
6: Gore>Bush>>Nader
6: Gore>>Bush>Nader
6: Gore>>Nader>Bush
33: Gore>Nader>>Bush
So this is more or less the same as the margins method equilibrium.
In summary, if the voters are fairly logical in the placement of their
approval cutoff, then ACC seems almost uniquely free of strategy
considerations. If the underlying approval votes do not back up the
sincere Condorcet winner, however, then ACC becomes just as vulnerable to
strategic manipulation as the margins methods are, if not more so.
Comments?
-Adam
On Sat, Apr 20, 2024 at 12:07 PM Michael Ossipoff email9648742@gmail.com
wrote:
If a single example can’t be found in which wv Condorcet does better than
Approval-Sorted Margins, then of course I’ll admit that Approval-Sorted
Margins is better.
I have a few questions about Margins-Sorted-Approval:
If I want to propose it to (say) a city-council or an initiative-committee
or focus-group, someone will ask what it’s advantage is…in what way it’s
better. What valuable property does it offer that other methods don’t?
It is more resistant to burial and defection.
What’s the answer to that inevitable question?
…& there’s the matter of motivation. What is it about double sorting that
motivates it?
First of all, I think the name is something of a misnomer.
If all ranked candidates are approved in some way, the initial ordering is
not based on approval but rather on strong preference.
So you start with a ranking of candidates based on which candidates are
most strongly preferred. But we want to end up with list of candidates such
that each pair of candidates is in order based on their pairwise preferences.
Therefore we will have to rearrange the initial strong preference ordering
in some way, based on adjacent pairwise orderings. See below.
It makes sense to start with Approval-ordering & then adjust to fix the
most important pairwise contradictions by switching. But aren’t the *
biggest* margins more important than the smallest ones? Then why fix the
smallest-margin mis-orderings first? & what’s special about adjacency in
the Approval-ordering? Isn’t the biggest pairwise contradiction most
important even between candidates not adjacent in the Approval-ordering?
…& why margins instead of wv, losing-votes, or any of the various measures
of a pairwise-defeat? In my experience, wv has been the important
defeat-measure for strategic protection.
Remember that here margins are not based on votes in pairwise contests
but rather in comparing the strong preferences for two consecutive
candidates in the ordered ranking.
Sorting the candidate list, based on pairwise contests, can be done by
several means. Upward bubble sort gives you DMC. Downward bubble sort gives
you something different. But either of those could move candidates far from
their original strong preference ranking.
Margin sort (that is, the margin of adjacent strong preference metrics for
pairwise-out-of-order consecutive candidates) is a variation on bubble sort
that locally minimizes the change from the original strong preference
rating.
On Sat, Apr 20, 2024 at 11:03 Chris Benham cbenhamau@yahoo.com.au wrote:
Mike O.,
https://electowiki.org/wiki/Minimal_Defense_criterion
Stephen Eppley https://electowiki.org/wiki/Stephen_Eppley gives this
official definition:
If more than half of the voters prefer alternative y over alternative x,
then that majority must have some way of voting that ensures x will not be
elected and does not require any of them to rank y equal to or over any
alternatives preferred over y.
This definition is most similar to that of SDSC
https://electowiki.org/wiki/SDSC.
https://electowiki.org/wiki/Strong_Defensive_Strategy_criterion
The answer to your first question (based on the definition I copied
above) is yes. That is obviously implied by its compliance with Double
Defeat. All that "majority" has to do is approve Y and not X. Double Defeat
says that a candidate that is pairwise beaten by a more approved candidate
can't win.
The answer to your second question is yes if the other faction doesn't
approve the CW and no if it does. Like in this old example:
49 A (sincere is A>B)
24 B (the "sincere CW" but the faction may be defecting against C)
27 C>B
If the C>B voters approve B then the approval order is B>A>C and since B
pairwise beats A and A pairwise beats C that order is final and B wins.
But if they don't then the approval order is A>C>B and that order is
final and A wins.
The faction-sizes are kept as close together as possible, because equal
sizes is the middle about which the variation happens, & is probably the
most likely single configuration.
I don't that is always a good idea. If the faction sizes are close
together then surely the risk for the Buriers of their strategy back-firing
would be a lot greater than if the "bus" faction is quite a bit smaller
than theirs. Also of course two large parties and one small one more
closely resembles the current political landscape.
An example can be found where one particular method does better than
another.
Good. I look forward to seeing your example where Winning Votes does
better than Approval Sorted Margins.
I don't know the answer to your last question.
Chris B.
On 19/04/2024 6:56 am, Michael Ossipoff wrote:
-
Does Margins-Sorted Approval meet Minimal-Defense?
-
Can offense-truncation by one faction take the win from a CW ranked in
2nd place by the other faction?
Answers for wv: 1) Yes. 2) No.
On Thu, Apr 18, 2024 at 14:17 Michael Ossipoff email9648742@gmail.com
wrote:
An example can be found where one particular method does better than
another.
3 candidates;
CW, BF, & Bus
(BF is buriers’ favorite. Bus 🚌 is the candidate under whom they bury
CW.)
To test wv Condorcet for burial deterrence, I checked 24 cases:
All 6 faction-size orderings for the 3 candidates.
and
4 ways for the middle CW’s voters to rank the other 2, with regard to
which they rank in 2nd place:
Neither
BF
Bus
Half one & half the other
The faction-sizes are kept as close together as possible, because equal
sizes is the middle about which the variation happens, & is probably the
most likely single configuration.
Divide the number of burial’s backfires by the number of its successes,
for the backfire/success ratio…abbreviated
b/s.
For wv Condorcet, b/s = 10.
What is it for Margins-Sorted Approval?
On Thu, Apr 18, 2024 at 10:14 Chris Benham cbenhamau@yahoo.com.au
wrote:
One of my nominations and my top choice in the current poll:
Margins Sorted Approval (specified cutoff):
*Voters rank from the top however many candidates they wish and can
also specify an approval
cutoff/threshold. Default approval is only for candidates ranked below
no others (i.e. ranked top
or equal-top).
A Forrest Simmons invention. Candidates are listed in approval score
order and if any adjacent pairs
are pairwise out of order then this is corrected by flipping the
out-of-order pair with the smallest
margin. If there is a tie for this we flip the less approved pair.
Repeat until there are no adjacent pairs
of candidates that are pairwise out of order, then elect the
highest-ordered candidate.*
I'm going to compare it with another of my nominations, another
Condorcet method that collects the
same information from the voters:
Smith//Approval (specified cutoff):
Voters rank from the top however many candidates they wish and can
also specify an approval
cutoff/threshold. Default approval is only for candidates ranked below
no others (i.e. ranked top
or equal-top).
The most approved member of the Smith set wins.
Although it asks voters for a bit more information than other Condorcet
methods like Ranked Pairs,
Schulze, MinMax etcetera, I think it is a lot easier than them to
explain and sell than them.
Condorcet//Approval (explicit) was discussed here in April 2002 by
Adam Tarr. I find voluntarily (in a
Condorcet method) electing a candidate outside the Smith set to be
weird and unacceptable, but all the
examples he gave that I saw apply just as well to
Smith//Approval(explicit).
Now why do I prefer Margins Sorted Approval?
The main reason is that it is quite a lot less vulnerable to Burial
strategy. Say there are three candidates
and most of the voters normally truncate. Say A is the predicted FPP
and Condorcet winner, B is the
predicted FPP runner-up and C is coming last by quite a big margin.
In that case the voters most likely to be tempted to try a Burial
strategy will be the B supporters against
A, using no-threat C as the "bus".
43 A|
03 A>B| ("strategically naive" voters)
44 B|>C (sincere is B or B>A)
10 C|
The B>C Buriers have given A a pairwise defeat, so now there is an
A>B>C>A cycle.
The approval scores: B 47, A 46, C 10.
Now if this was Smith//Approval the 3 A>B| voters would have blown the
election for A by approving B.
But ASM notices that both approval-score adjacent pairs (B-A and A-C)
are pairwise out of order and by far
the smallest of the two approval-score margins is that between B and A
and so flips that order to give
A>B>C. Now neither pair is pairwise "out of order" so that order is
final and A comfortably wins.
Now to borrow an old example with none of the voters truncating:
49 A|> C (sincere is A or A>B)
06 B>A|
06 B|>A
06 B|>C
06 B>C|
27 C>B|
Now there is a cycle A>C>B>A and the approval scores are A 55, B 51, C
33.
Again Smith//Approval has a problem, the Burying strategists have
succeeded.
But again Approval Sorted Margins fixes it. Both adjacent
approval-score adjacent pairs (A-B and B-C)
are out pairwise order and the A-B margin (4) is smaller than the B-C
margin (18) so we flip the A-B pair
to give the order B>A>C. Now neither adjacent pair is pairwise out of
order so that order is final and
B (the sincere Condorcet winner) wins.
The other reason I prefer Margins Sorted Approval to Smith//Approval
(explicit) is mostly aesthetic.
I find it much more elegant (even beautiful). It would meet as many
monotonicity criteria as it is possible
for a Condorcet method to meet. Without even trying, it meets Reverse
Symmetry.
By comparison I find Smith//Approval(explicit) a bit clunky.
Unfortunately Benham and Woodall and Gross Loser Elimination and
"almost Condorcet" RCIPE and
Hare (aka IRV) all fail Mono-raise (aka Monotonicity).
In both my examples above, the three Winning Votes methods in the poll
(Ranked Pairs and Schulze and
MinMax and maybe "Max Strength Transitive Beatpath") all elect the
Burier's favourite.
In the second example that is also true of Benham and Woodall and Gross
Loser Elimination.
Chris Benham
http://lists.electorama.com/pipermail/election-methods-electorama.com//2002-April/073341.html
I think that if you give people a ballot that looks like grades, they will
tend to assign candidates grades that reflect their cardinal rankings for
those candidates, provided they don't have strategic incentive to do
otherwise. If lack of slots becomes a problem, we could switch to 1-10
rankings. If a tendency to spread the candidates out tends to skew the
results, we could go with the "none of the below" candidate in ranked
ballots. But for the time being, I think the 6-slot ballot would do fine,
and if I were to advocate this method I'd go with the 6-slot ballot.
At any rate, I was just looking at how well this technique responds to
certain strategic voting scenarios. In an earlier message (March 20) I
suggested that Approval Completed Condorcet ("ACC" from here on out) passes
SFC and SDSC from Mike's criterion. It doesn't pass the "Generalized"
versions unless one slips in a Smith set requirement explicitly, which I
argued against in that message.
I'm now going to compare ACC to margins and winning votes Condorcet
methods, using the example that has become my signature example on this
list. The following are the sincere preferences of my example electorate:
49: Bush>Gore>Nader
12: Gore>Bush>Nader
12: Gore>Nader>Bush
27: Nader>Gore>Bush
If everyone votes sincerely, then Gore is the Condorcet winner. The
problem arises when the Bush voters swap Nader and Gore on their ballots
(in margins they can achieve the same effect by truncating, but I'll ignore
that for this analysis). So the new "preferences" are
49: Bush>Nader>Gore
12: Gore>Bush>Nader
12: Gore>Nader>Bush
27: Nader>Gore>Bush
In margins-based methods, the only way for Gore to still win the election
is for the Nader voters to bury Nader behind Gore. The stable equilibrium
ballots become:
49: Bush>Nader>Gore
12: Gore>Bush>Nader
39: Gore>Nader>Bush
And this allows Gore to still carry the election. This sort of equilibrium
is what Mike is talking about when he says that margins methods are
"falsifying".
In winning votes methods, the Nader camp can vote equal first-place
rankings rather than swap Gore and Nader entirely. The stable result is
therefore:
49: Bush>Nader>Gore
12: Gore>Bush>Nader
12: Gore>Nader>Bush
27: Nader=Gore>Bush
In ACC... we first have to define where the approval cutoffs on the ballots
are. Since the approval tally is only used to break cyclic ties, clearly
the Bush camp has no incentive to Approve of anyone except Bush. I'm going
to make the assumption that since Gore and Bush are the apparent front
runners in this race (the only two with a decent shot at election), every
voter will approve one and not the other. This is the logical approval
cutoff to use, based on the approval strategy threads that have been
circulating on the list of late. So the ballots could look something like
this: (>> denotes approval cutoff)
49: Bush>>Nader>Gore
12: Gore>>Bush>Nader
6: Gore>>Nader>Bush
6: Gore>Nader>>Bush
27: Nader>Gore>>Bush
In this case, Gore wins the approval runoff 51-49-33. So not only did ACC
avoid the need for defensive order-reversal like margins methods, but it
avoided the need for defensive equal-ranking like winning votes
methods. This is a super result: totally strategy-free voting for the
majority side.
There is a dark side to this result, though. Say that some of the
Gore>Bush>Nader voters were extremely non-strategic and decided to approve
both Bush and Gore. So the votes now look like:
49: Bush>>Nader>Gore
6: Gore>Bush>>Nader
6: Gore>>Bush>Nader
6: Gore>>Nader>Bush
6: Gore>Nader>>Bush
27: Nader>Gore>>Bush
Now, Bush wins the approval runoff 55-51-33. This is where ACC's favorite
betrayal scenario comes in. Since Bush wins the approval vote, the only
way the majority can guarantee a Gore win is to make Gore the initial
Condorcet winner, which requires that the Nader camp vote Gore in first place:
49: Bush>>Nader>Gore
6: Gore>Bush>>Nader
6: Gore>>Bush>Nader
6: Gore>>Nader>Bush
33: Gore>Nader>>Bush
So this is more or less the same as the margins method equilibrium.
In summary, if the voters are fairly logical in the placement of their
approval cutoff, then ACC seems almost uniquely free of strategy
considerations. If the underlying approval votes do not back up the
sincere Condorcet winner, however, then ACC becomes just as vulnerable to
strategic manipulation as the margins methods are, if not more so.
Comments?
-Adam
Election-Methods mailing list - see https://electorama.com/em for list
info
A graph theorist would call it a Hamiltonian path over the tournament graph (provided that pairwise ties are drawn as edges in both directions instead of the usual no-edge convention). That isn't standard terminology when talking about voting methods, though.
One nice thing about Hamiltonian-path/beat-chain methods -- which also include Ranked Pairs and Kemeny-Young -- is that they automatically satisfy Smith. Moreover, they do so successively: first come all Smith set members, then the members of the Smith set over the remaining candidates, then...
On 4/22/24 07:59, Chris Benham wrote:
A question I forgot to answer:
It makes sense to start with Approval-ordering & then adjust to fix the most important pairwise contradictions by switching. But aren’t the * biggest* margins more important than the smallest ones? Then why fix the smallest-margin mis-orderings first?
Our aim it produce a "beat chain" (if that's the right term) where every candidate beats the next-lowest in the order down to the bottom, which is most in harmony with the approval order. No out-of-order pair of adjacent candidates is going to be left out of order.
Oh, hmm, that sounds like Split-Cycle maybe?
On Mon, Apr 22, 2024 at 1:16 PM Joshua Boehme joshua.p.boehme@gmail.com
wrote:
A graph theorist would call it a Hamiltonian path over the tournament
graph (provided that pairwise ties are drawn as edges in both directions
instead of the usual no-edge convention). That isn't standard terminology
when talking about voting methods, though.
One nice thing about Hamiltonian-path/beat-chain methods -- which also
include Ranked Pairs and Kemeny-Young -- is that they automatically satisfy
Smith. Moreover, they do so successively: first come all Smith set members,
then the members of the Smith set over the remaining candidates, then...
On 4/22/24 07:59, Chris Benham wrote:
A question I forgot to answer:
It makes sense to start with Approval-ordering & then adjust to fix the
most important pairwise contradictions by switching. But aren’t the *
biggest* margins more important than the smallest ones? Then why fix the
smallest-margin mis-orderings first?
Our aim it produce a "beat chain" (if that's the right term) where every
candidate beats the next-lowest in the order down to the bottom, which is
most in harmony with the approval order. No out-of-order pair of adjacent
candidates is going to be left out of order.
Election-Methods mailing list - see https://electorama.com/em for list
info