A sufficient condition for voting rules to be frequently manipulable

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...

• Type: Journal
• Year: 2008
• Where: SIGECOM
• Authors: Lirong Xia, Vincent Conitzer
• Keywords: ECommerce, Neutral Voting Rule, Reasonable Voting Rule, SIGECOM 2008, Voting Rule