[EM] A thought about manipulability

[Forest Simmons]

It seems to me that impartial culture is a very tenuous assumption for
public elections ... even less realistic than Yee diagram culture which is
generically cycle free ... not just free of a top cycle.

The Yee diagram is based on  multivariate normal distributions, perhaps not
too realistic ... but the Central Limit Theorem would seem to make it more
(not less) realistic as the size of the election increases.

Remember the governor recall election in California that Arnold won ...
there were several dozens of candidates. Since the ballots were "vote one"
style there could be no ballot cycle.

But who could plausibly argue that a top cycle would have been likely ...
if only complete preferences had been elicited, and there had been even
more candidates?

Yes, inconsequential ties among lower popularity candidates might become
more common with more candidates, just as tied lower candidates in a Yee
diagram might become more common.

In that context all candidates at the same distance from the center of the
distribution are tied with each other ... but not likely for first place.
There is only one point at the precise center... but infinitely many points
at any positive radius r from the center ... the bigger the radius, the
more room for tied candidates ... for what that's worth (if anything).



On Sun, Jun 25, 2023, 4:07 PM Kristofer Munsterhjelm <km_elmet at t-online.de>
wrote:

> As the Condorcification proof shows, if you elect someone else than the
> (absolute) CW, there will exist at least one majority who all prefer
> someone else to the winner, and (if majorities can force outcomes) they
> can compromise to get that candidate elected.
>
> But one subtlety that I missed: this means that if the honest election
> is a cycle, there's always a strategy. There may be a "cycle to cycle"
> strategy, but there is definitely a "cycle to CW" (or rather, cycle to
> majority winner) strategy.
>
> I think it's been proven (though I don't remember who did it) that with
> impartial culture, as the number of voters goes to infinity, the
> fraction of elections that are a Condorcet cycle approaches one. If so,
> then a consequence of the above is that *every* method with the majority
> forcing property is manipulable in almost every case, under impartial
> culture with enough voters.
>
> That's surprising. Though again, maybe not?
>
> It suggests that impartial culture is too strong, at least with lots of
> voters -- it's too close to a tie to be realistic.
>
> (But then again, we usually don't consider this sort of "forced
> compromise" in a cycle to be a type of strategy that anyone can reliably
> pull off. Intuitively, a method electing a non-CW seems to be open to
> strategy to get the CW elected, but with a honest cycle it feels more
> like the electorate is too divided to pull a cycle to non-cycle strategy
> off.)
>
> -km
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