Asymptotic CollusionProofness of Voting Rules: The Case of Large Number of Candidates
Abstract
Classical results in voting theory show that strategic manipulation by voters is inevitable if a voting rule simultaneously satisfy certain desirable properties. Motivated by this, we study the relevant question of how often a voting rule is manipulable. It is well known that elections with a large number of voters are rarely manipulable under impartial culture (IC) assumption. However, the manipulability of voting rules when the number of candidates is large has hardly been addressed in the literature and our paper focuses on this problem. First, we propose two properties (1) asymptotic strategyproofness and (2) asymptotic collusionproofness, with respect to new voters, which makes the two notions more relevant from the perspective of computational problem of manipulation. In addition to IC, we explore a new culture of society where all score vectors of the candidates are equally likely. This new notion has its motivation in computational social choice and we call it impartial scores culture (ISC) assumption. We study asymptotic strategyproofness and asymptotic collusionproofness for plurality, veto, $k$approval, and Borda voting rules under IC as well as ISC assumptions. Specifically, we prove bounds for the fraction of manipulable profiles when the number of candidates is large. Our results show that the size of the coalition and the tiebreaking rule play a crucial role in determining whether or not a voting rule satisfies the above two properties.
 Publication:

arXiv eprints
 Pub Date:
 May 2013
 DOI:
 10.48550/arXiv.1305.5053
 arXiv:
 arXiv:1305.5053
 Bibcode:
 2013arXiv1305.5053D
 Keywords:

 Computer Science  Computer Science and Game Theory;
 I.2.11;
 J.4
 EPrint:
 Accepted as an extended abstract in AAMAS 2014