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A law of large numbers for weighted plurality

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  • Joe Neeman

Abstract

Consider an election between $$k$$ candidates in which each voter votes randomly (but not necessarily independently) for a single candidate, and suppose that there is a single candidate that every voter prefers (in the sense that each voter is more likely to vote for this special candidate than any other candidate). Suppose we have a voting rule that takes all of the votes and produces a single outcome and suppose that each individual voter has little effect on the outcome of the voting rule. If the voting rule is a weighted plurality, then we show that with high probability, the preferred candidate will win the election. Conversely, we show that this statement fails for all other reasonable voting rules. This result is an extension of one by Häggström, Kalai and Mossel, who proved the above in the case $$k=2$$ . Copyright Springer-Verlag Berlin Heidelberg 2014

Suggested Citation

  • Joe Neeman, 2014. "A law of large numbers for weighted plurality," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 42(1), pages 99-109, January.
    • Handle: RePEc:spr:sochwe:v:42:y:2014:i:1:p:99-109
    DOI: 10.1007/s00355-013-0732-4
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    References listed on IDEAS

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    1. Milgrom, Paul R & Weber, Robert J, 1982. "A Theory of Auctions and Competitive Bidding," Econometrica, Econometric Society, vol. 50(5), pages 1089-1122, September.
    2. Gil Kalai, 2004. "Social Indeterminacy," Discussion Paper Series dp362, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
    3. Gibbard, Allan, 1973. "Manipulation of Voting Schemes: A General Result," Econometrica, Econometric Society, vol. 41(4), pages 587-601, July.
    4. Gil Kalai, 2004. "Social Indeterminacy," Econometrica, Econometric Society, vol. 72(5), pages 1565-1581, September.
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    Cited by:

    1. Maurice Koster & Sascha Kurz & Ines Lindner & Stefan Napel, 2017. "The prediction value," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 48(2), pages 433-460, February.

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