Cycling of simple rules in the spatial model

David Austen-Smith*, Jeffrey S. Banks

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


McKelvey [4] proved that for strong simple preference aggregation rules applied to multidimensional sets of alternatives, the typical situation is that either the core is nonempty or the top-cycle set includes all available alternatives. But the requirement that the rule be strong excludes, inter alia, all supermajority rules. In this note, we show that McKelvey's theorem further implies that the typical situation for any simple rule is that either the core is nonempty or the weak top-cycle set (equivalently, the core of the transitive closure of the rule) includes all available alternatives. Moreover, it is often the case that both of these statements obtain.

Original languageEnglish (US)
Pages (from-to)663-672
Number of pages10
JournalSocial Choice and Welfare
Issue number4
StatePublished - 1999

ASJC Scopus subject areas

  • Social Sciences (miscellaneous)
  • Economics and Econometrics


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