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Classification theorem for smooth social choice on a manifold

Abstract

A classification theorem for voting rules on a smooth choice space W of dimension w is presented. It is shown that, for any non-collegial voting rule, σ, there exist integers v *(σ), w *(σ) (with v *(σ)<w *(σ)) such that

  1. (i)

    structurally stable σ-voting cycles may always be constructed when wv *(σ) + 1

  2. (ii)

    a structurally stable σ-core (or voting equilibrium) may be constructed when wv *(σ) − 1

Finally, it is shown that for an anonymous q-rule, a structurally stable core exists in dimension \(\frac{{n - 2}}{{n - q}}\), where n is the cardinality of the society.

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Schofield, N. Classification theorem for smooth social choice on a manifold. Soc Choice Welfare 1, 187–210 (1984). https://doi.org/10.1007/BF00433516

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Keywords

  • Economic Theory
  • Social Choice
  • Vote Rule
  • Stable Core
  • Classification Theorem