Nonexistence of voting rules that are usually hard to manipulate

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Nonexistence of voting rules that are usually hard to manipulate (2006)

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by Vincent Conitzer , Tuomas Sandholm

Venue:	IN AAAI
Citations:	85 - 8 self

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@INPROCEEDINGS{Conitzer06nonexistenceof,
    author = {Vincent Conitzer and Tuomas Sandholm},
    title = {Nonexistence of voting rules that are usually hard to manipulate},
    booktitle = {IN AAAI},
    year = {2006},
    publisher = {}
}

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Abstract

Aggregating the preferences of self-interested agents is a key problem for multiagent systems, and one general method for doing so is to vote over the alternatives (candidates). Unfor-tunately, the Gibbard-Satterthwaite theorem shows that when there are three or more candidates, all reasonable voting rules are manipulable (in the sense that there exist situations in which a voter would benefit from reporting its preferences insincerely). To circumvent this impossibility result, recent research has investigated whether it is possible to make find-ing a beneficial manipulation computationally hard. This ap-proach has had some limited success, exhibiting rules under which the problem of finding a beneficial manipulation is NP-hard, #P-hard, or even PSPACE-hard. Thus, under these rules, it is unlikely that a computationally efficient algorithm can be constructed that always finds a beneficial manipulation (when it exists). However, this still does not preclude the ex-istence of an efficient algorithm that often finds a successful manipulation (when it exists). There have been attempts to design a rule under which finding a beneficial manipulation is usually hard, but they have failed. To explain this failure, in this paper, we show that it is in fact impossible to design such a rule, if the rule is also required to satisfy another prop-erty: a large fraction of the manipulable instances are both weakly monotone, and allow the manipulators to make either of exactly two candidates win. We argue why one should expect voting rules to have this property, and show experi-mentally that common voting rules clearly satisfy it. We also discuss approaches for potentially circumventing this impos-sibility result.

Keyphrases

beneficial manipulation voting rule efficient algorithm recent research general method impossibility result manipulable instance common voting rule large fraction multiagent system self-interested agent reasonable voting rule gibbard-satterthwaite theorem show weakly monotone limited success key problem impos-sibility result successful manipulation

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