[EM] Defeat Strength Demystified
Richard, the VoteFair guy
electionmethods at votefair.org
Thu Sep 16 10:54:57 PDT 2021
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
Again, thanks for your forest-instead-of-the-trees perspective of
margins versus winning votes.
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
> 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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