Defeat Strength Demystified
When I first joined the EM List twenty years ago the main topic of debate
was margins vs winning votes for measuring defeat strength. It was all very
mysterious to me ... to a mathematician the symmetry of margins was
appealing ... and as a a sympathizer of underdog minorities to me it
seemed callous to totally disregard the losing votes when they might help
resolve a Condorcet cycle. On the other hand, there was the point of view
that when there are competing majorities, the proposition supported by the
greatest majority is the one most likely to be true. However a cynic might
question this altruistic truth seeking assumption and assert that it's not
so much a question of right or wrong but of who can get their way.
Which brings us to game theory, which looks at elections as multiplayer
games with the players (voters or voter factions) strategically trying to
optimize their expected personal or factional "utilities" given the rules
of the game as well as the information they have about the preferences,
desires, or "utilities" of the other players.
Once I became aware of this point of view, I saw the futility of Borda's
assumption of honest voters, and the irrelevance of Saari's appeal to
geometric symmetry in Borda's defense. Also it made it more obvious why the
standard use of Cardinal Ratings/Score/Range/Grade ballots might just as
well be replaced by simple Approval, since they all have the same optimal
strategy ... only the naive voter would vote strictly between the extremes.
[Of course there are some extremely sophisticated voters who might factor
in an externality that we could call the "ultimate utility of supporting
eternal truth" ... not part of the limited scope of the voting game proper
... perhaps something more along the lines of Pascal's wager.]
After this point of view soaked in ... the defeat strength debate started
to make more sense. In fact, a paramount ranked voting strategy problem is
the insincere "burial" of a second choice to give added support to a first
choice. This problem is especially evident in pairwise methods like Borda
and Condorcet. But this kind of attack against a sincere Condorcet
candidate is easier to defend against when defeat strength is measured by
winning votes.
Once this fact soaked in to my newbie psyche, I saw the wisdom of the
Ossipoff camp with its impressive array of defense criteria based on
winning votes.
Eventually Mike O. went on to bigger and better things but a few years ago
he made a brief, but passionate, return to the EM List when the
Possibilities of Hope seemed to include a real possibility of election
reform. As we weighed the merits of various methods it suddenly became
apparent that we didn't have a Condorcet method that was immune to both
burial abd "Chicken," a ploy that had not concerned us much in the past but
now loomed larger.
O course IRV came up as a method that was immune to both Burial and
Chicken, but at the expense of the Condorcet Criterion. A flurry of
activity on the EM list searched for a hybrid between IRV and Condorcet
similar to what we have seen since the resurrection of IRV as RCV.
BTR-IRV and Benham were the leading contenders, but neither of these
inspired the fire in anybody from the glory days of the List. A few of us
toyed with a hybrid between Condorcet and Approval called Approval Sorted
Margins (ASM) that gave a way of defending against both Burial and Chicken,
but nobody took it seriously because unlike the automatic defense under IRV
it required awareness of the problem to know when to lower the approval of
a potential chicken defector ... furthermore the addition of approval into
the mix went against the Universal Domain purity ethos in the form of
ranked ballots only.
It was soon pointed out that margins automatically defends against chicken
ploys, and it was already well known that with minimal precaution wv
defends against burial, neither requiring any approval lever ... but nobody
quite managed to combine them into one holy grail ... because, as I
recently (last week) showed, the limitation to Universal Domain makes it
impossible. However, the method under Universal Domain requiring the least
vigilance to defend against both of these kinds of attacks is Fractional
Approval Sorted Margins. [Here the margins referred to are approval
differences, not pairwise defeat margins.] The defensive maneuvers required
are truncations or raising to equal top in the respective cases of Chicken
or Burial.
Now here is a suggestion for a minimal departure from Universal Domain that
makes both Burial and Chicken gambits too risky to be practical with added
benefit of potentially settling the wv versus margins debate once and for
all!
[But probably not before the debate about round or flat earth:-)]
To each ranked preference ballot append a check box labeled "symmetric
completion?"
Here we are making use of the equivalence of margins and wv under symmetric
completion of the ballots.
If more than half of the voters check the optional box, then defeat
strength will be according to margins ... otherwise wv is used.
Another more elegant way to finesse this thang is to symmetrically complete
those ballots having checked boxes, and then tally all of the resulting
ballots (checked or not) by wv rules.
The symmetric completion of a ballot takes place operationally at the
pairwise matrix stage ... if candidates i and j are ranked equally on a
ballot, then that ballot normally contributes nothing to row i or row j of
the pairwise matrix. But under symmetric completion it contributes 1/2 to
both the (i, j) and the (j, i) entries of the pairwise matrix.
I hope this has been interesting and stimulating to the imagination of
possibilities ... not the end of all debate... which would be more of a
tragedy than a triumph!
Thanks Forest, I found this post to be very interesting and informative.
I'll add that I recently read that here in Oregon votes must be
delegated as whole votes, not fractions or decimals. This means that
your clever idea of "voting" for or against "symmetric completion" would
not be allowed in Oregon unless it delegated the half counts in balanced
pairs.
Again, thanks for your forest-instead-of-the-trees perspective of
margins versus winning votes.
Richard Fobes
The VoteFair guy
On 9/15/2021 9:09 PM, Forest Simmons wrote:
When I first joined the EM List twenty years ago the main topic of
debate was margins vs winning votes for measuring defeat strength. It
was all very mysterious to me ... to a mathematician the symmetry of
margins was appealing ... and as a a sympathizer of underdog minorities
to me it seemed callous to totally disregard the losing votes when they
might help resolve a Condorcet cycle. On the other hand, there was the
point of view that when there are competing majorities, the proposition
supported by the greatest majority is the one most likely to be true.
However a cynic might question this altruistic truth seeking assumption
and assert that it's not so much a question of right or wrong but of who
can get their way.
Which brings us to game theory, which looks at elections as multiplayer
games with the players (voters or voter factions) strategically trying
to optimize their expected personal or factional "utilities" given the
rules of the game as well as the information they have about the
preferences, desires, or "utilities" of the other players.
Once I became aware of this point of view, I saw the futility of Borda's
assumption of honest voters, and the irrelevance of Saari's appeal to
geometric symmetry in Borda's defense. Also it made it more obvious why
the standard use of Cardinal Ratings/Score/Range/Grade ballots might
just as well be replaced by simple Approval, since they all have the
same optimal strategy ... only the naive voter would vote strictly
between the extremes.
[Of course there are some extremely sophisticated voters who might
factor in an externality that we could call the "ultimate utility of
supporting eternal truth" ... not part of the limited scope of the
voting game proper ... perhaps something more along the lines of
Pascal's wager.]
After this point of view soaked in ... the defeat strength debate
started to make more sense. In fact, a paramount ranked voting strategy
problem is the insincere "burial" of a second choice to give added
support to a first choice. This problem is especially evident in
pairwise methods like Borda and Condorcet. But this kind of attack
against a sincere Condorcet candidate is easier to defend against when
defeat strength is measured by winning votes.
Once this fact soaked in to my newbie psyche, I saw the wisdom of the
Ossipoff camp with its impressive array of defense criteria based on
winning votes.
Eventually Mike O. went on to bigger and better things but a few years
ago he made a brief, but passionate, return to the EM List when the
Possibilities of Hope seemed to include a real possibility of election
reform. As we weighed the merits of various methods it suddenly became
apparent that we didn't have a Condorcet method that was immune to both
burial abd "Chicken," a ploy that had not concerned us much in the past
but now loomed larger.
O course IRV came up as a method that was immune to both Burial and
Chicken, but at the expense of the Condorcet Criterion. A flurry of
activity on the EM list searched for a hybrid between IRV and Condorcet
similar to what we have seen since the resurrection of IRV as RCV.
BTR-IRV and Benham were the leading contenders, but neither of these
inspired the fire in anybody from the glory days of the List. A few of
us toyed with a hybrid between Condorcet and Approval called Approval
Sorted Margins (ASM) that gave a way of defending against both Burial
and Chicken, but nobody took it seriously because unlike the automatic
defense under IRV it required awareness of the problem to know when to
lower the approval of a potential chicken defector ... furthermore the
addition of approval into the mix went against the Universal Domain
purity ethos in the form of ranked ballots only.
It was soon pointed out that margins automatically defends against
chicken ploys, and it was already well known that with minimal
precaution wv defends against burial, neither requiring any approval
lever ... but nobody quite managed to combine them into one holy grail
... because, as I recently (last week) showed, the limitation to
Universal Domain makes it impossible. However, the method under
Universal Domain requiring the least vigilance to defend against both of
these kinds of attacks is Fractional Approval Sorted Margins. [Here the
margins referred to are approval differences, not pairwise defeat
margins.] The defensive maneuvers required are truncations or raising to
equal top in the respective cases of Chicken or Burial.
Now here is a suggestion for a minimal departure from Universal Domain
that makes both Burial and Chicken gambits too risky to be practical
with added benefit of potentially settling the wv versus margins debate
once and for all!
[But probably not before the debate about round or flat earth:-)]
To each ranked preference ballot append a check box labeled "symmetric
completion?"
Here we are making use of the equivalence of margins and wv under
symmetric completion of the ballots.
If more than half of the voters check the optional box, then defeat
strength will be according to margins ... otherwise wv is used.
Another more elegant way to finesse this thang is to symmetrically
complete those ballots having checked boxes, and then tally all of the
resulting ballots (checked or not) by wv rules.
The symmetric completion of a ballot takes place operationally at the
pairwise matrix stage ... if candidates i and j are ranked equally on a
ballot, then that ballot normally contributes nothing to row i or row j
of the pairwise matrix. But under symmetric completion it contributes
1/2 to both the (i, j) and the (j, i) entries of the pairwise matrix.
I hope this has been interesting and stimulating to the imagination of
possibilities ... not the end of all debate... which would be more of a
tragedy than a triumph!
Election-Methods mailing list - see https://electorama.com/em for list info
As someone who is quite new to the list, I found this really interesting
and I really learned a lot. Thanks.
On Wed, Sep 15, 2021 at 11:09 PM Forest Simmons forest.simmons21@gmail.com
wrote:
When I first joined the EM List twenty years ago the main topic of debate
was margins vs winning votes for measuring defeat strength. It was all very
mysterious to me ... to a mathematician the symmetry of margins was
appealing ... and as a a sympathizer of underdog minorities to me it
seemed callous to totally disregard the losing votes when they might help
resolve a Condorcet cycle. On the other hand, there was the point of view
that when there are competing majorities, the proposition supported by the
greatest majority is the one most likely to be true. However a cynic might
question this altruistic truth seeking assumption and assert that it's not
so much a question of right or wrong but of who can get their way.
Which brings us to game theory, which looks at elections as multiplayer
games with the players (voters or voter factions) strategically trying to
optimize their expected personal or factional "utilities" given the rules
of the game as well as the information they have about the preferences,
desires, or "utilities" of the other players.
Once I became aware of this point of view, I saw the futility of Borda's
assumption of honest voters, and the irrelevance of Saari's appeal to
geometric symmetry in Borda's defense. Also it made it more obvious why the
standard use of Cardinal Ratings/Score/Range/Grade ballots might just as
well be replaced by simple Approval, since they all have the same optimal
strategy ... only the naive voter would vote strictly between the extremes.
[Of course there are some extremely sophisticated voters who might factor
in an externality that we could call the "ultimate utility of supporting
eternal truth" ... not part of the limited scope of the voting game proper
... perhaps something more along the lines of Pascal's wager.]
After this point of view soaked in ... the defeat strength debate started
to make more sense. In fact, a paramount ranked voting strategy problem is
the insincere "burial" of a second choice to give added support to a first
choice. This problem is especially evident in pairwise methods like Borda
and Condorcet. But this kind of attack against a sincere Condorcet
candidate is easier to defend against when defeat strength is measured by
winning votes.
Once this fact soaked in to my newbie psyche, I saw the wisdom of the
Ossipoff camp with its impressive array of defense criteria based on
winning votes.
Eventually Mike O. went on to bigger and better things but a few years ago
he made a brief, but passionate, return to the EM List when the
Possibilities of Hope seemed to include a real possibility of election
reform. As we weighed the merits of various methods it suddenly became
apparent that we didn't have a Condorcet method that was immune to both
burial abd "Chicken," a ploy that had not concerned us much in the past but
now loomed larger.
O course IRV came up as a method that was immune to both Burial and
Chicken, but at the expense of the Condorcet Criterion. A flurry of
activity on the EM list searched for a hybrid between IRV and Condorcet
similar to what we have seen since the resurrection of IRV as RCV.
BTR-IRV and Benham were the leading contenders, but neither of these
inspired the fire in anybody from the glory days of the List. A few of us
toyed with a hybrid between Condorcet and Approval called Approval Sorted
Margins (ASM) that gave a way of defending against both Burial and Chicken,
but nobody took it seriously because unlike the automatic defense under IRV
it required awareness of the problem to know when to lower the approval of
a potential chicken defector ... furthermore the addition of approval into
the mix went against the Universal Domain purity ethos in the form of
ranked ballots only.
It was soon pointed out that margins automatically defends against chicken
ploys, and it was already well known that with minimal precaution wv
defends against burial, neither requiring any approval lever ... but nobody
quite managed to combine them into one holy grail ... because, as I
recently (last week) showed, the limitation to Universal Domain makes it
impossible. However, the method under Universal Domain requiring the least
vigilance to defend against both of these kinds of attacks is Fractional
Approval Sorted Margins. [Here the margins referred to are approval
differences, not pairwise defeat margins.] The defensive maneuvers required
are truncations or raising to equal top in the respective cases of Chicken
or Burial.
Now here is a suggestion for a minimal departure from Universal Domain
that makes both Burial and Chicken gambits too risky to be practical with
added benefit of potentially settling the wv versus margins debate once and
for all!
[But probably not before the debate about round or flat earth:-)]
To each ranked preference ballot append a check box labeled "symmetric
completion?"
Here we are making use of the equivalence of margins and wv under
symmetric completion of the ballots.
If more than half of the voters check the optional box, then defeat
strength will be according to margins ... otherwise wv is used.
Another more elegant way to finesse this thang is to symmetrically
complete those ballots having checked boxes, and then tally all of the
resulting ballots (checked or not) by wv rules.
The symmetric completion of a ballot takes place operationally at the
pairwise matrix stage ... if candidates i and j are ranked equally on a
ballot, then that ballot normally contributes nothing to row i or row j of
the pairwise matrix. But under symmetric completion it contributes 1/2 to
both the (i, j) and the (j, i) entries of the pairwise matrix.
I hope this has been interesting and stimulating to the imagination of
possibilities ... not the end of all debate... which would be more of a
tragedy than a triumph!
Election-Methods mailing list - see https://electorama.com/em for list
info
--
Dr. Daniel Carrera
Postdoctoral Research Associate
Iowa State University
Daniel,
I'm glad you liked it ... you must have a much greater attention span than
average:-)
Forest
El jue., 16 de sep. de 2021 12:46 p. m., Daniel Carrera dcarrera@gmail.com
escribió:
As someone who is quite new to the list, I found this really interesting
and I really learned a lot. Thanks.
On Wed, Sep 15, 2021 at 11:09 PM Forest Simmons <
forest.simmons21@gmail.com> wrote:
When I first joined the EM List twenty years ago the main topic of debate
was margins vs winning votes for measuring defeat strength. It was all very
mysterious to me ... to a mathematician the symmetry of margins was
appealing ... and as a a sympathizer of underdog minorities to me it
seemed callous to totally disregard the losing votes when they might help
resolve a Condorcet cycle. On the other hand, there was the point of view
that when there are competing majorities, the proposition supported by the
greatest majority is the one most likely to be true. However a cynic might
question this altruistic truth seeking assumption and assert that it's not
so much a question of right or wrong but of who can get their way.
Which brings us to game theory, which looks at elections as multiplayer
games with the players (voters or voter factions) strategically trying to
optimize their expected personal or factional "utilities" given the rules
of the game as well as the information they have about the preferences,
desires, or "utilities" of the other players.
Once I became aware of this point of view, I saw the futility of Borda's
assumption of honest voters, and the irrelevance of Saari's appeal to
geometric symmetry in Borda's defense. Also it made it more obvious why the
standard use of Cardinal Ratings/Score/Range/Grade ballots might just as
well be replaced by simple Approval, since they all have the same optimal
strategy ... only the naive voter would vote strictly between the extremes.
[Of course there are some extremely sophisticated voters who might factor
in an externality that we could call the "ultimate utility of supporting
eternal truth" ... not part of the limited scope of the voting game proper
... perhaps something more along the lines of Pascal's wager.]
After this point of view soaked in ... the defeat strength debate started
to make more sense. In fact, a paramount ranked voting strategy problem is
the insincere "burial" of a second choice to give added support to a first
choice. This problem is especially evident in pairwise methods like Borda
and Condorcet. But this kind of attack against a sincere Condorcet
candidate is easier to defend against when defeat strength is measured by
winning votes.
Once this fact soaked in to my newbie psyche, I saw the wisdom of the
Ossipoff camp with its impressive array of defense criteria based on
winning votes.
Eventually Mike O. went on to bigger and better things but a few years
ago he made a brief, but passionate, return to the EM List when the
Possibilities of Hope seemed to include a real possibility of election
reform. As we weighed the merits of various methods it suddenly became
apparent that we didn't have a Condorcet method that was immune to both
burial abd "Chicken," a ploy that had not concerned us much in the past but
now loomed larger.
O course IRV came up as a method that was immune to both Burial and
Chicken, but at the expense of the Condorcet Criterion. A flurry of
activity on the EM list searched for a hybrid between IRV and Condorcet
similar to what we have seen since the resurrection of IRV as RCV.
BTR-IRV and Benham were the leading contenders, but neither of these
inspired the fire in anybody from the glory days of the List. A few of us
toyed with a hybrid between Condorcet and Approval called Approval Sorted
Margins (ASM) that gave a way of defending against both Burial and Chicken,
but nobody took it seriously because unlike the automatic defense under IRV
it required awareness of the problem to know when to lower the approval of
a potential chicken defector ... furthermore the addition of approval into
the mix went against the Universal Domain purity ethos in the form of
ranked ballots only.
It was soon pointed out that margins automatically defends against
chicken ploys, and it was already well known that with minimal precaution
wv defends against burial, neither requiring any approval lever ... but
nobody quite managed to combine them into one holy grail ... because, as I
recently (last week) showed, the limitation to Universal Domain makes it
impossible. However, the method under Universal Domain requiring the least
vigilance to defend against both of these kinds of attacks is Fractional
Approval Sorted Margins. [Here the margins referred to are approval
differences, not pairwise defeat margins.] The defensive maneuvers required
are truncations or raising to equal top in the respective cases of Chicken
or Burial.
Now here is a suggestion for a minimal departure from Universal Domain
that makes both Burial and Chicken gambits too risky to be practical with
added benefit of potentially settling the wv versus margins debate once and
for all!
[But probably not before the debate about round or flat earth:-)]
To each ranked preference ballot append a check box labeled "symmetric
completion?"
Here we are making use of the equivalence of margins and wv under
symmetric completion of the ballots.
If more than half of the voters check the optional box, then defeat
strength will be according to margins ... otherwise wv is used.
Another more elegant way to finesse this thang is to symmetrically
complete those ballots having checked boxes, and then tally all of the
resulting ballots (checked or not) by wv rules.
The symmetric completion of a ballot takes place operationally at the
pairwise matrix stage ... if candidates i and j are ranked equally on a
ballot, then that ballot normally contributes nothing to row i or row j of
the pairwise matrix. But under symmetric completion it contributes 1/2 to
both the (i, j) and the (j, i) entries of the pairwise matrix.
I hope this has been interesting and stimulating to the imagination of
possibilities ... not the end of all debate... which would be more of a
tragedy than a triumph!
Election-Methods mailing list - see https://electorama.com/em for list
info
--
Dr. Daniel Carrera
Postdoctoral Research Associate
Iowa State University
Hi Forest,
I may have to make a couple of responses to this post, but I at least want to reply to this line:"It was soon pointed out that margins automatically defends against chicken ploys"
Now I don't support either the chicken dilemma criterion ("CDC"), the theory behind it, or margins. But I must defend margins' honor here. Margins doesn't conform to CDC in any remarkable way.
The CDC applies in only one type of scenario, which has 3 candidates, so this is easy to analyze. These are your options for whom to elect:
A: The candidate of the "faithful", non-truncating wing of the majority, who got defected on by the B voters. With support from only one faction, electing A will likely violate Plurality, so it's very rare to elect A here. Raynaud would do it.B: The candidate of the defecting wing of the majority. This will be the only candidate with any sort of majority. Many, many methods will elect B in order to avoid turning A into a spoiler candidate, and making the A voters regret their votes for A. CDC says in contrast that B must lose, as their punishment for truncating A (since CDC assumes that they actually like A).C: The minority opposition candidate. The disunity of the majority will cause C to be elected in methods like FPP, IRV, and DSC. This is the outcome that CDC is probably arguing for.
So the CDC says "B loses." WV (and any SDSC method, like Bucklin) elects B every time. So that gives you one extreme on the spectrum.
Margins is not on the other side. It can elect ANY of those three candidates depending on the margins. In a real world scenario it's probably going to be B or C, with similar likelihood, but it's still possible to set the numbers so that the tightest margin is between A and C, so that A is elected.
Whether margins is more on the B side or more on the C side depends on which pair of numbers you think is likely to be closer (in absolute terms): The size of the combined majority vs. the size of the minority, or the sizes of the two factions within the majority.
Note that the supposed value of CDC is not directly from its outcome, but from its effect on incentives. It is not supposed to be a "good thing" in itself that the minority candidate wins. This outcome is literally supposed to be a disaster, a punishment, intended to incentivize the majority to not truncate. It's worth asking, if you reduce your compliance with CDC to 50%, do you still get 50% of the benefit? What do we expect that means?
When we implement 100% of the incentive, the disasters "shouldn't" happen because people stop defecting. If you drop the incentive to 50%, so that defecting works half the time, isn't it inevitable that we would start seeing disasters, too, when the voters miscalculate their strategy? It seems to me that to only partially satisfy CDC might well be the worst option. You will spoil elections to teach somebody a lesson, but the lesson can't be learned due to other conflicting incentives.
In conclusion, I don't think a method should be offered as a CD mitigator unless it elects C almost all the time in this scenario.
Kevin
Le mercredi 15 septembre 2021, 23:09:57 UTC−5, Forest Simmons <forest.simmons21@gmail.com> a écrit :
When I first joined the EM List twenty years ago the main topic of debate was margins vs winning votes for measuring defeat strength. It was all very mysterious to me ... to a mathematician the symmetry of margins was appealing ... and as a a sympathizer of underdog minorities to me it seemed callous to totally disregard the losing votes when they might help resolve a Condorcet cycle. On the other hand, there was the point of view that when there are competing majorities, the proposition supported by the greatest majority is the one most likely to be true. However a cynic might question this altruistic truth seeking assumption and assert that it's not so much a question of right or wrong but of who can get their way.
Which brings us to game theory, which looks at elections as multiplayer games with the players (voters or voter factions) strategically trying to optimize their expected personal or factional "utilities" given the rules of the game as well as the information they have about the preferences, desires, or "utilities" of the other players.
Once I became aware of this point of view, I saw the futility of Borda's assumption of honest voters, and the irrelevance of Saari's appeal to geometric symmetry in Borda's defense. Also it made it more obvious why the standard use of Cardinal Ratings/Score/Range/Grade ballots might just as well be replaced by simple Approval, since they all have the same optimal strategy ... only the naive voter would vote strictly between the extremes.
[Of course there are some extremely sophisticated voters who might factor in an externality that we could call the "ultimate utility of supporting eternal truth" ... not part of the limited scope of the voting game proper ... perhaps something more along the lines of Pascal's wager.]
After this point of view soaked in ... the defeat strength debate started to make more sense. In fact, a paramount ranked voting strategy problem is the insincere "burial" of a second choice to give added support to a first choice. This problem is especially evident in pairwise methods like Borda and Condorcet. But this kind of attack against a sincere Condorcet candidate is easier to defend against when defeat strength is measured by winning votes.
Once this fact soaked in to my newbie psyche, I saw the wisdom of the Ossipoff camp with its impressive array of defense criteria based on winning votes.
Eventually Mike O. went on to bigger and better things but a few years ago he made a brief, but passionate, return to the EM List when the Possibilities of Hope seemed to include a real possibility of election reform. As we weighed the merits of various methods it suddenly became apparent that we didn't have a Condorcet method that was immune to both burial abd "Chicken," a ploy that had not concerned us much in the past but now loomed larger.
O course IRV came up as a method that was immune to both Burial and Chicken, but at the expense of the Condorcet Criterion. A flurry of activity on the EM list searched for a hybrid between IRV and Condorcet similar to what we have seen since the resurrection of IRV as RCV.
BTR-IRV and Benham were the leading contenders, but neither of these inspired the fire in anybody from the glory days of the List. A few of us toyed with a hybrid between Condorcet and Approval called Approval Sorted Margins (ASM) that gave a way of defending against both Burial and Chicken, but nobody took it seriously because unlike the automatic defense under IRV it required awareness of the problem to know when to lower the approval of a potential chicken defector ... furthermore the addition of approval into the mix went against the Universal Domain purity ethos in the form of ranked ballots only.
It was soon pointed out that margins automatically defends against chicken ploys, and it was already well known that with minimal precaution wv defends against burial, neither requiring any approval lever ... but nobody quite managed to combine them into one holy grail ... because, as I recently (last week) showed, the limitation to Universal Domain makes it impossible. However, the method under Universal Domain requiring the least vigilance to defend against both of these kinds of attacks is Fractional Approval Sorted Margins. [Here the margins referred to are approval differences, not pairwise defeat margins.] The defensive maneuvers required are truncations or raising to equal top in the respective cases of Chicken or Burial.
Now here is a suggestion for a minimal departure from Universal Domain that makes both Burial and Chicken gambits too risky to be practical with added benefit of potentially settling the wv versus margins debate once and for all!
[But probably not before the debate about round or flat earth:-)]
To each ranked preference ballot append a check box labeled "symmetric completion?"
Here we are making use of the equivalence of margins and wv under symmetric completion of the ballots.
If more than half of the voters check the optional box, then defeat strength will be according to margins ... otherwise wv is used.
Another more elegant way to finesse this thang is to symmetrically complete those ballots having checked boxes, and then tally all of the resulting ballots (checked or not) by wv rules.
The symmetric completion of a ballot takes place operationally at the pairwise matrix stage ... if candidates i and j are ranked equally on a ballot, then that ballot normally contributes nothing to row i or row j of the pairwise matrix. But under symmetric completion it contributes 1/2 to both the (i, j) and the (j, i) entries of the pairwise matrix.
I hope this has been interesting and stimulating to the imagination of possibilities ... not the end of all debate... which would be more of a tragedy than a triumph!
Election-Methods mailing list - see https://electorama.com/em for list info
Hi Forest,
A few extra thoughts.
Le mercredi 15 septembre 2021, 23:09:57 UTC−5, Forest Simmons <forest.simmons21@gmail.com> a écrit :
Once I became aware of this point of view, I saw the futility of Borda's assumption of honest voters, and the irrelevance of
Saari's appeal to geometric symmetry in Borda's defense. Also it made it more obvious why the standard use of Cardinal >Ratings/Score/Range/Grade ballots might just as well be replaced by simple Approval, since they all have the same optimal>strategy ... only the naive voter would vote strictly between the extremes.
After this point of view soaked in ... the defeat strength debate started to make more sense. In fact, a paramount ranked>voting strategy problem is the insincere "burial" of a second choice to give added support to a first choice. This problem is>especially evident in pairwise methods like Borda and Condorcet. But this kind of attack against a sincere Condorcet candidate>is easier to defend against when defeat strength is measured by winning votes.>
Once this fact soaked in to my newbie psyche, I saw the wisdom of the Ossipoff camp with its impressive array of defense>criteria based on winning votes.
I think it was confusing and unhelpful that these criteria were usually explained in the context of burial.A criterion like SDSC (Strong Defensive Strategy Criterion) can really be viewed as a guarantee forcertain voters that compromise will not be needed, much like FBC. Some methods satisfying SDSC don'teven have burial, yet the property is not irrelevant. Implicit Approval on rank ballots is an easy example,or Bucklin.
It certainly seems like I am the last member of the "Ossipoff camp." What I would say is that WV itselfdoesn't matter. Only its practical implications matter. Minimize spoilers, minimize people regretting thatthey voted for their favorite candidate. People use such arguments to argue for Condorcet itself. Whytoss them out when choosing how to resolve a cycle?
Eventually Mike O. went on to bigger and better things but a few years ago he made a brief, but passionate, return to the EM>List when the Possibilities of Hope seemed to include a real possibility of election reform. As we weighed the merits of various>methods it suddenly became apparent that we didn't have a Condorcet method that was immune to both burial abd "Chicken,">a ploy that had not concerned us much in the past but now loomed larger.
For my part, the chicken dilemma was always a concern for me when designing methods. It hasweighed on my mind more heavily in recent years, though, I will say.
The problem has always been that there was not, and in my view still IS not, any real solution on thetable. At least if limited to the UD methods. My best idea is that defection without burial just not beallowed, which raises other questions.
For me, Mike's proposed CDC is a complete disaster. It is expensive, it involves mind-reading, itprobably would achieve an outcome other than its intended one, it is barely defined, and its definitionseems to make a sneaky concession to Condorcet methods that strikes me as unwarranted giventhe goal of the criterion. (Namely, one of the two factions is ALLOWED to defect! What??)
So, I was disappointed by this development.
Now here is a suggestion for a minimal departure from Universal Domain that makes both Burial and Chicken gambits too
risky to be practical with added benefit of potentially settling the wv versus margins debate once and for all!>
[But probably not before the debate about round or flat earth:-)]>
To each ranked preference ballot append a check box labeled "symmetric completion?"
I'd love to know on what basis the voter makes this decision. There is no need to request that hisOWN ballot be symmetrically completed, so it must have something to do with his assessmentof the race.
But I suppose your idea is to introduce so much uncertainty that no one wants to use any insincere strategy. I'm not sure how well that works. It seems pretty clear that this method would have to havemore compromise incentive than WV, and uncertainty about the method's resolution would probablydrive further compromise incentive, as people seek to minimize risk.
Kevin
Kevin!
Thanks for setting me straight on that!
I was thinking that unlike Burial, Chicken could not work with complete
rankings, so that symmetric completion would be a defense ... and the more
complete, the greater the risk to the defectors ...and also that symmetric
completion makes wv more like margins ... all in an effort to find an
method versatile enough to defend against both kinds of attacks, like ASM
does, but without using explicit Approval.
Bottom line: no Universal Domain compliant method is sufficiently
versatile, and a lever that allows voters to blend margins with wv is not
the right violation of UD to do the job ... so far the best known solution
requires some incorporation of approval as in ASM.
El sáb., 18 de sep. de 2021 12:24 p. m., Kevin Venzke stepjak@yahoo.fr
escribió:
Hi Forest,
I may have to make a couple of responses to this post, but I at least want
to reply to this line:
"It was soon pointed out that margins automatically defends against
chicken ploys"
Now I don't support either the chicken dilemma criterion ("CDC"), the
theory behind it, or margins. But I must defend margins' honor here.
Margins doesn't conform to CDC in any remarkable way.
The CDC applies in only one type of scenario, which has 3 candidates, so
this is easy to analyze. These are your options for whom to elect:
A: The candidate of the "faithful", non-truncating wing of the majority,
who got defected on by the B voters. With support from only one faction,
electing A will likely violate Plurality, so it's very rare to elect A
here. Raynaud would do it.
B: The candidate of the defecting wing of the majority. This will be the
only candidate with any sort of majority. Many, many methods will elect B
in order to avoid turning A into a spoiler candidate, and making the A
voters regret their votes for A. CDC says in contrast that B must lose, as
their punishment for truncating A (since CDC assumes that they actually
like A).
C: The minority opposition candidate. The disunity of the majority will
cause C to be elected in methods like FPP, IRV, and DSC. This is the
outcome that CDC is probably arguing for.
So the CDC says "B loses." WV (and any SDSC method, like Bucklin) elects B
every time. So that gives you one extreme on the spectrum.
Margins is not on the other side. It can elect ANY of those three
candidates depending on the margins. In a real world scenario it's probably
going to be B or C, with similar likelihood, but it's still possible to set
the numbers so that the tightest margin is between A and C, so that A is
elected.
Whether margins is more on the B side or more on the C side depends on
which pair of numbers you think is likely to be closer (in absolute terms):
The size of the combined majority vs. the size of the minority, or the
sizes of the two factions within the majority.
Note that the supposed value of CDC is not directly from its outcome, but
from its effect on incentives. It is not supposed to be a "good thing" in
itself that the minority candidate wins. This outcome is literally
supposed to be a disaster, a punishment, intended to incentivize the
majority to not truncate. It's worth asking, if you reduce your compliance
with CDC to 50%, do you still get 50% of the benefit? What do we expect
that means?
When we implement 100% of the incentive, the disasters "shouldn't" happen
because people stop defecting. If you drop the incentive to 50%, so that
defecting works half the time, isn't it inevitable that we would start
seeing disasters, too, when the voters miscalculate their strategy? It
seems to me that to only partially satisfy CDC might well be the worst
option. You will spoil elections to teach somebody a lesson, but the lesson
can't be learned due to other conflicting incentives.
In conclusion, I don't think a method should be offered as a CD mitigator
unless it elects C almost all the time in this scenario.
Kevin
Le mercredi 15 septembre 2021, 23:09:57 UTC−5, Forest Simmons <
forest.simmons21@gmail.com> a écrit :
When I first joined the EM List twenty years ago the main topic of debate
was margins vs winning votes for measuring defeat strength. It was all very
mysterious to me ... to a mathematician the symmetry of margins was
appealing ... and as a a sympathizer of underdog minorities to me it
seemed callous to totally disregard the losing votes when they might help
resolve a Condorcet cycle. On the other hand, there was the point of view
that when there are competing majorities, the proposition supported by the
greatest majority is the one most likely to be true. However a cynic might
question this altruistic truth seeking assumption and assert that it's not
so much a question of right or wrong but of who can get their way.
Which brings us to game theory, which looks at elections as multiplayer
games with the players (voters or voter factions) strategically trying to
optimize their expected personal or factional "utilities" given the rules
of the game as well as the information they have about the preferences,
desires, or "utilities" of the other players.
Once I became aware of this point of view, I saw the futility of Borda's
assumption of honest voters, and the irrelevance of Saari's appeal to
geometric symmetry in Borda's defense. Also it made it more obvious why the
standard use of Cardinal Ratings/Score/Range/Grade ballots might just as
well be replaced by simple Approval, since they all have the same optimal
strategy ... only the naive voter would vote strictly between the extremes.
[Of course there are some extremely sophisticated voters who might factor
in an externality that we could call the "ultimate utility of supporting
eternal truth" ... not part of the limited scope of the voting game proper
... perhaps something more along the lines of Pascal's wager.]
After this point of view soaked in ... the defeat strength debate started
to make more sense. In fact, a paramount ranked voting strategy problem is
the insincere "burial" of a second choice to give added support to a first
choice. This problem is especially evident in pairwise methods like Borda
and Condorcet. But this kind of attack against a sincere Condorcet
candidate is easier to defend against when defeat strength is measured by
winning votes.
Once this fact soaked in to my newbie psyche, I saw the wisdom of the
Ossipoff camp with its impressive array of defense criteria based on
winning votes.
Eventually Mike O. went on to bigger and better things but a few years ago
he made a brief, but passionate, return to the EM List when the
Possibilities of Hope seemed to include a real possibility of election
reform. As we weighed the merits of various methods it suddenly became
apparent that we didn't have a Condorcet method that was immune to both
burial abd "Chicken," a ploy that had not concerned us much in the past but
now loomed larger.
O course IRV came up as a method that was immune to both Burial and
Chicken, but at the expense of the Condorcet Criterion. A flurry of
activity on the EM list searched for a hybrid between IRV and Condorcet
similar to what we have seen since the resurrection of IRV as RCV.
BTR-IRV and Benham were the leading contenders, but neither of these
inspired the fire in anybody from the glory days of the List. A few of us
toyed with a hybrid between Condorcet and Approval called Approval Sorted
Margins (ASM) that gave a way of defending against both Burial and Chicken,
but nobody took it seriously because unlike the automatic defense under IRV
it required awareness of the problem to know when to lower the approval of
a potential chicken defector ... furthermore the addition of approval into
the mix went against the Universal Domain purity ethos in the form of
ranked ballots only.
It was soon pointed out that margins automatically defends against chicken
ploys, and it was already well known that with minimal precaution wv
defends against burial, neither requiring any approval lever ... but nobody
quite managed to combine them into one holy grail ... because, as I
recently (last week) showed, the limitation to Universal Domain makes it
impossible. However, the method under Universal Domain requiring the least
vigilance to defend against both of these kinds of attacks is Fractional
Approval Sorted Margins. [Here the margins referred to are approval
differences, not pairwise defeat margins.] The defensive maneuvers required
are truncations or raising to equal top in the respective cases of Chicken
or Burial.
Now here is a suggestion for a minimal departure from Universal Domain
that makes both Burial and Chicken gambits too risky to be practical with
added benefit of potentially settling the wv versus margins debate once and
for all!
[But probably not before the debate about round or flat earth:-)]
To each ranked preference ballot append a check box labeled "symmetric
completion?"
Here we are making use of the equivalence of margins and wv under
symmetric completion of the ballots.
If more than half of the voters check the optional box, then defeat
strength will be according to margins ... otherwise wv is used.
Another more elegant way to finesse this thang is to symmetrically
complete those ballots having checked boxes, and then tally all of the
resulting ballots (checked or not) by wv rules.
The symmetric completion of a ballot takes place operationally at the
pairwise matrix stage ... if candidates i and j are ranked equally on a
ballot, then that ballot normally contributes nothing to row i or row j of
the pairwise matrix. But under symmetric completion it contributes 1/2 to
both the (i, j) and the (j, i) entries of the pairwise matrix.
I hope this has been interesting and stimulating to the imagination of
possibilities ... not the end of all debate... which would be more of a
tragedy than a triumph!
Election-Methods mailing list - see https://electorama.com/em for list
info
Your summary of that topic was indeed vey useful. I can't say I'm new to the list, but since I don't regularly read all the material on the list, I often have some trouble following the discussions due to missing some definitions, abbreviations and not understanding short references to earlier discussions. Getting the whole story (or one important part of it) in one package therefore really helps in getting some grip of what's going on in the list, and what I have missed. Not that I'd catch all of it at one go, but at least your message provided a good framework to build on. Electowiki is also a good source when trying to catch up, but this kind of short(ish) summaries make it easier not to lose touch totally :-) .
BR, Juho
On 17. Sep 2021, at 5.15, Forest Simmons forest.simmons21@gmail.com wrote:
Daniel,
I'm glad you liked it ... you must have a much greater attention span than average:-)
Forest
El jue., 16 de sep. de 2021 12:46 p. m., Daniel Carrera <dcarrera@gmail.com mailto:dcarrera@gmail.com> escribió:
As someone who is quite new to the list, I found this really interesting and I really learned a lot. Thanks.
On Wed, Sep 15, 2021 at 11:09 PM Forest Simmons <forest.simmons21@gmail.com mailto:forest.simmons21@gmail.com> wrote:
When I first joined the EM List twenty years ago the main topic of debate was margins vs winning votes for measuring defeat strength. It was all very mysterious to me ... to a mathematician the symmetry of margins was appealing ... and as a a sympathizer of underdog minorities to me it seemed callous to totally disregard the losing votes when they might help resolve a Condorcet cycle. On the other hand, there was the point of view that when there are competing majorities, the proposition supported by the greatest majority is the one most likely to be true. However a cynic might question this altruistic truth seeking assumption and assert that it's not so much a question of right or wrong but of who can get their way.
Which brings us to game theory, which looks at elections as multiplayer games with the players (voters or voter factions) strategically trying to optimize their expected personal or factional "utilities" given the rules of the game as well as the information they have about the preferences, desires, or "utilities" of the other players.
Once I became aware of this point of view, I saw the futility of Borda's assumption of honest voters, and the irrelevance of Saari's appeal to geometric symmetry in Borda's defense. Also it made it more obvious why the standard use of Cardinal Ratings/Score/Range/Grade ballots might just as well be replaced by simple Approval, since they all have the same optimal strategy ... only the naive voter would vote strictly between the extremes.
[Of course there are some extremely sophisticated voters who might factor in an externality that we could call the "ultimate utility of supporting eternal truth" ... not part of the limited scope of the voting game proper ... perhaps something more along the lines of Pascal's wager.]
After this point of view soaked in ... the defeat strength debate started to make more sense. In fact, a paramount ranked voting strategy problem is the insincere "burial" of a second choice to give added support to a first choice. This problem is especially evident in pairwise methods like Borda and Condorcet. But this kind of attack against a sincere Condorcet candidate is easier to defend against when defeat strength is measured by winning votes.
Once this fact soaked in to my newbie psyche, I saw the wisdom of the Ossipoff camp with its impressive array of defense criteria based on winning votes.
Eventually Mike O. went on to bigger and better things but a few years ago he made a brief, but passionate, return to the EM List when the Possibilities of Hope seemed to include a real possibility of election reform. As we weighed the merits of various methods it suddenly became apparent that we didn't have a Condorcet method that was immune to both burial abd "Chicken," a ploy that had not concerned us much in the past but now loomed larger.
O course IRV came up as a method that was immune to both Burial and Chicken, but at the expense of the Condorcet Criterion. A flurry of activity on the EM list searched for a hybrid between IRV and Condorcet similar to what we have seen since the resurrection of IRV as RCV.
BTR-IRV and Benham were the leading contenders, but neither of these inspired the fire in anybody from the glory days of the List. A few of us toyed with a hybrid between Condorcet and Approval called Approval Sorted Margins (ASM) that gave a way of defending against both Burial and Chicken, but nobody took it seriously because unlike the automatic defense under IRV it required awareness of the problem to know when to lower the approval of a potential chicken defector ... furthermore the addition of approval into the mix went against the Universal Domain purity ethos in the form of ranked ballots only.
It was soon pointed out that margins automatically defends against chicken ploys, and it was already well known that with minimal precaution wv defends against burial, neither requiring any approval lever ... but nobody quite managed to combine them into one holy grail ... because, as I recently (last week) showed, the limitation to Universal Domain makes it impossible. However, the method under Universal Domain requiring the least vigilance to defend against both of these kinds of attacks is Fractional Approval Sorted Margins. [Here the margins referred to are approval differences, not pairwise defeat margins.] The defensive maneuvers required are truncations or raising to equal top in the respective cases of Chicken or Burial.
Now here is a suggestion for a minimal departure from Universal Domain that makes both Burial and Chicken gambits too risky to be practical with added benefit of potentially settling the wv versus margins debate once and for all!
[But probably not before the debate about round or flat earth:-)]
To each ranked preference ballot append a check box labeled "symmetric completion?"
Here we are making use of the equivalence of margins and wv under symmetric completion of the ballots.
If more than half of the voters check the optional box, then defeat strength will be according to margins ... otherwise wv is used.
Another more elegant way to finesse this thang is to symmetrically complete those ballots having checked boxes, and then tally all of the resulting ballots (checked or not) by wv rules.
The symmetric completion of a ballot takes place operationally at the pairwise matrix stage ... if candidates i and j are ranked equally on a ballot, then that ballot normally contributes nothing to row i or row j of the pairwise matrix. But under symmetric completion it contributes 1/2 to both the (i, j) and the (j, i) entries of the pairwise matrix.
I hope this has been interesting and stimulating to the imagination of possibilities ... not the end of all debate... which would be more of a tragedy than a triumph!
Election-Methods mailing list - see https://electorama.com/em https://electorama.com/em for list info
--
Dr. Daniel Carrera
Postdoctoral Research Associate
Iowa State University
Election-Methods mailing list - see https://electorama.com/em for list info