An extension rule assigns to each fractional tournament x (specifying, for every pair of social alternatives a and b, the proportion xab of voters who prefer a to b) a random choice function y (specifying a collective choice probability distribution for each subset of alternatives), which...

We propose a class of decisive collective choice rules that rely on a linear ordering to partition the majority relation into two acyclic relations. The first of these relations is used to pare down the set of the feasible alternatives into a shortlist while the second is used to make a final...

Ranking by rating consists in evaluating the performances of items using exoge- nous rating functions and ranking these items according to their performance rat- ings. Any such method is separable: the ordering of two items does not depend on the performances of the remaining items. When...