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What happens when majority rule breaks down?

Some probability calculations

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Abstract

Computational results of Niemi and Weisberg are extended to investigate the number of alternatives in the top cycle set (possible winning alternatives in a sequence of pairwise votes) when there is no Condorcet winner. With n alternatives we assume a large number of voters each equally likely to select any of the n! preference orderings. If no Condorcet winner exists, the number of members of the top cycle set is always more likely to be n or n−1 than between 3 and n−2 inclusive. As n grows the probability that all alternatives are in the top cycle set approaches 1.

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Authors
  1. Colin E. Bell
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Additional information

Assistant Professor, Management Science, University of Tennessee. The author is grateful to Richard Rosenthal for his insight and programming assistance critical to this revised paper. John Plotnicki's computer programming was very helpful at the first draft stage.

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Bell, C.E. What happens when majority rule breaks down?. Public Choice 33, 121–126 (1978). https://doi.org/10.1007/BF00118362

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  • DOI: https://doi.org/10.1007/BF00118362

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