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 \(k=2\).
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Acknowledgments
The author would like to thank Elchanan Mossel for suggesting this problem and providing fruitful discussions. He also thanks the Managing Editor and the two anonymous referees for helping him to substantially improve the presentation.
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Neeman, J. A law of large numbers for weighted plurality. Soc Choice Welf 42, 99–109 (2014). https://doi.org/10.1007/s00355-013-0732-4
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DOI: https://doi.org/10.1007/s00355-013-0732-4