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Permutation cycles and manipulation of choice functions

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Abstract

Let σ be a social preference function, and let v(σ) be the Nakamura number of σ. If W is a finite set of cardinality at least v(σ) then it is shown that there exists an acyclic profile P on W such that σ(P) is cyclic. Any choice function which is compatible with σ can then be manipulated. A similar result holds if W is a manifold (or a subset of Euclidean space) with dimension at least v(σ)-1.

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Authors and Affiliations

  1. University of California at Irvine, Irvine, USA

    N. Schofield

  2. Department of Economics, University of Essex, Wivenhoe Park, CO4 3SQ, Colchester, Essex, England

    N. Schofield

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  1. N. Schofield
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Schofield, N. Permutation cycles and manipulation of choice functions. Soc Choice Welfare 3, 107–117 (1986). https://doi.org/10.1007/BF00435661

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  • DOI: https://doi.org/10.1007/BF00435661

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