[EM] Example of participation/no-show paradox with Condorcet?
stepjak at yahoo.fr
Sat Nov 5 13:22:38 PST 2005
--- Allen Smith <easmith at beatrice.rutgers.edu> a écrit :
> >But as far as Participation is concerned, you don't obtain compliance by
> >specifying that no one wins when there's no CW. Suppose that nobody wants
> >a cycle, and everyone prefers any winner to no winner. Suppose X is the
> >CW. Then it's possible that adding ballots will change the winner from X to
> >nobody, unless these ballots don't rank X below anyone.
> I would not recommend a strict Condorcet requirement when any likelihood was
> present of nobody wanting a cycle.
I guess I should have said, "Suppose that the additional voters prefer
anybody at all to a cycle."
> >Suppose the additional voters *want* to create a cycle. Then it could be
> >that their sincere vote actually eliminates a cycle that already existed.
> Exactly how does one do a sincere vote in favor of a cycle?
You can't. All I'm saying is that these voters, voting as sincerely as the
method allows, could still worsen the result from their own perspective.
Basically, I can't see a way of amputating scenarios without a CW, and thereby
meaningfully obtain compliance with criteria that are normally incompatible with
> >> (I am currently contemplating a Schwartz/Approval combo.)
> >The most obvious ones are to eliminate the approval loser until one candidate
> >beats everyone left, or to explicitly reduce to Schwartz and take the approval
> >winner of those candidates.
> The latter is what I am considering, with a threshold being marked by the
> voter but subject to adjustment up/down the ranking so that the approval
> votes from the voter are not wasted (either by no approved-of candidates
> being among the Schwartz set or by all approved-of candidates being among
> the Schwartz set).
Unfortunately, I believe this will create a monotonicity problem.
> I am also contemplating the results of the following
> rules for deciding in _favor_ of there being a tie vote (partially to allow
> for more effectiveness of the Schwartz set as opposed to the Smith set),
> with X being votes for x, Y being votes for y, I being indifferent between X
> and Y, and M being a constant:
> A. abs(X - Y) <= min(I, M*(I+X+Y)); or
> B. (I/(I+X+Y)) > max(0.5, (max(X,Y)/(X+Y))).
> M is set high enough that outcomes that are so close as to be brought into
> rational dispute (e.g., Florida in 2000) are considered ties.
But this seems to create more opportunities to dispute ties rather than fewer,
unless I'm missing something.
> of candidates would put it in the middle of a tie. (I am contemplating
> whether an automated Approval strategy - automated initial placement of the
> threshold - based on (among the Schwartz set) initial first-place votes,
> ITV, or another mechanism might work better, but have concerns regarding
> strategic vulnerabilities and - depending on what mechanism was used - the
> amount of data that would need to be retained.)
Monotonicity, again. (But I don't mean to say that you need to value
monotonicity. It just seems to be a fairly easy criterion to satisfy, so
it's noticeable if you don't.)
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