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 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.
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Paper provided by Northwestern University, Center for Mathematical Studies in Economics and Management Science in its series Discussion Papers with number
1246.
Length: Date of creation: Jul 1998 Date of revision: Handle: RePEc:nwu:cmsems:1246
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