A sufficient condition for voting rules to be frequently manipulable

13 years 4 months ago

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The Gibbard-Satterthwaite Theorem states that (in unrestricted settings) any reasonable voting rule is manipulable. Recently, a quantitative version of this theorem was proved by Ehud Friedgut, Gil Kalai, and Noam Nisan: when the number of alternatives is three, for any neutral voting rule that is far from any dictatorship, there exists a voter such that a random manipulation--that is, the true preferences and the strategic vote are all drawn i.i.d., uniformly at random--will succeed with a probability of ( 1 n ), where n is the number of voters. However, it seems that the techniques used to prove this theorem can not be fully extended to more than three alternatives. In this paper, we give a more limited result that does apply to four or more alternatives. We give a sufficient condition for a voting rule to be randomly manipulable with a probability of ( 1 n ) for at least one voter, when the number of alternatives is held fixed. Specifically, our theorem states that if a voting rule...

Lirong Xia, Vincent Conitzer

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