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Published September 1999 | public
Journal Article

Cycling of simple rules in the spatial model


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.

Additional Information

© 1999 Springer-Verlag. Received: 13 October 1997. Accepted: 24 August 1998. We are grateful to John Duggan, Michel Le Breton and an anonymous referee for useful comments on an earlier version of the paper.

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