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# How the size of a coalition affects its chances to influence an election

Social Choice and Welfare
Vol. 26, No. 1 (January 2006), pp. 143-153
Stable URL: http://www.jstor.org/stable/41106725
Page Count: 11
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## Abstract

Since voting rules are prototypes for many aggregation procedures, they also illuminate problems faced by economics and decision sciences. In this paper we are trying to answer the question: How large should a coalition be to have a chance to influence an election? We answer this question for all scoring rules and multistage elimination rules, under the Impartial Anonymous Culture assumption. We show that, when the number of participating agents n tends to infinity, the ratio of voting situations that can be influenced by a coalition of voters to all voting situations is no greater than $D_m \frac{k}{n}$;, where Dm is a constant which depends only on the number m of alternatives but not on and n. Recent results on individual manipulability in three alternative elections show that this estimate is exact for k=1 and m=3.

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