[EM] On which methods are good CDC methods

Kevin Venzke stepjak at yahoo.fr
Sat Sep 18 12:22:32 PDT 2021

 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.

    Le mercredi 15 septembre 2021, 23:09:57 UTC−5, Forest Simmons <forest.simmons21 at 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!

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