What majority decisions are possible

Saharon Shelah*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

Abstract

Suppose we are given a family of choice functions on pairs from a given finite set (with at least three elements) closed under permutations of the given set. The set is considered the set of alternatives (say candidates for an office). The question is, what are the choice functions c on pairs of this set of the following form: for some (finite) family of "voters", each having a preference, i.e. a choice from each pair from the given family, c {x, y} is chosen by the preference of the majority of voters. We give full characterization.

Original languageEnglish
Pages (from-to)2349-2364
Number of pages16
JournalDiscrete Mathematics
Volume309
Issue number8
DOIs
StatePublished - 28 Apr 2009

Keywords

  • Choice function
  • Condorcet's paradox
  • Majority decision
  • Tournament

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