[Election-Methods] RE : Re: RE : Re: Is the Condorcet winner always the best?
Kevin Venzke
stepjak at yahoo.fr
Fri Dec 14 06:22:09 PST 2007
Jonathan,
--- Jonathan Lundell <jlundell at pobox.com> a écrit :
> Alternatively, consider the A & C voters if they know in advance,
> let's say from polling, the approximate shape of the profile.
>
> If they bury B, they figure a tossup between A & C; expected utility:
> 50.
> If they don't, B is a shoo-in; expected utility: 10.
>
> Even one chance in five for an A (or C) voter beats a B sure thing.
>
> So why rank (or approve) B?
In Condorcet WV methods you should rank B.
Let's say that we're determining strategy for the A faction. The B faction
is the smallest and no faction is a majority. The A faction's utilities are
100, 10, 0.
Let's say that the C faction votes C>B and the A faction votes A. If
pairwise A beats C, WV elects B. If C beats A, then C is the CW. A voters'
expected utility is 5.
If the A faction votes A>B, then B wins. Expected utility 10.
Let's say that the C faction votes C and the A faction votes A. Then either
A or C wins. Expected utility is 50.
If the A faction instead votes A>B, then the winner is either A (if the CW)
or B (if C beats A pairwise). Expected utility is 55.
So voting A>B adds half of B's value to A voters' expectation no matter
what the C voters do.
It's sort of a prisoner's dilemma, since the A and C factions are both
happier on average if they agree to an AC coin flip.
Kevin Venzke
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