Power structure and cardinality restrictions for Paretian social choice rules (Q800196)

Let f be a multiple-valued Paretian social choice rule for n voters and an outcome set X. The preventing sets for f are shown to form an acyclic majority when \(| X| <n\), a prefilter when \(| X|\geq n\), and a filter when f also satisfies a binary independence condition. These results are then shown to yield inequalities relating \(| X|\), n, and certain preventing sets. In particular, if every coalition of q voters constitutes a preventing set, then \(| X|\leq [n-1/n-q]\). Other inequalities are obtained if strong equilibria are present for every preference profile.