Super arrovian domains with strict preferences

Peter C. Fishburn, Jerry S. Kelly

Research output: Contribution to journalArticle

8 Scopus citations

Abstract

Given m ≥ 3 alternatives and n ≥ 2 voters, let σ(m,n) be the least integer k for which there is a set of k strict preference profiles for the voters on the alternatives with the following property: Arrow's impossibility theorem holds for this profile set and for each of its strict preference profile supersets. We show that σ(3, 2) = 6 and that for each m, σ(m,n)/4n approaches 0 monotonically as n gets large. In addition, for each n and ε > 0, σ(m,n)/(log2 m)2+ε approaches 0 as m gets large. Hence for many alternatives or many voters, a robust version of Arrow's theorem is induced by a very small fraction of the set of all (m!)n strict preference profiles.

Original languageEnglish (US)
Pages (from-to)83-95
Number of pages13
JournalSIAM Journal on Discrete Mathematics
Volume10
Issue number1
DOIs
StatePublished - Feb 1997

Keywords

  • Arrow's impossibility theorem
  • Minimum profile sets
  • Voter preference profiles

ASJC Scopus subject areas

  • Mathematics(all)

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