Power Structure and Cardinality Restrictions for Paretian Social Choice Rules

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, 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|≤[(n-1)/(n-q)]. Other n-q inequalities are obtained if strong equilibria are present for every preference profile.