[EM] Defeat Strength Demystified

Daniel Carrera dcarrera at gmail.com
Thu Sep 16 12:46:34 PDT 2021

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>

> 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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