[EM] Defeat Strength Demystified

[Forest Simmons]

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 at 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 at 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
>
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