Consistency and social choice: Possibilities and impossibilities

We study different notions of consistency in a model of preference aggregation where the feasible set of alternatives may vary. We show that there exists no social choice function (SCF) satisfying contraction consistency (CC), non-dictatorship, and Pareto efficiency (PE). We then characterize a class of priority-based SCFs, called Priority Rules (PRs), in two ways: first, using PE and efficient dominance, a WARP-type consistency condition with respect to PE; and second, using PE, weak contraction consistency, and invariant efficiency. We also characterize Decisive Individual Rules, in which the decisive individual may vary across profiles, using a top-selection condition, a weakening of CC, and an intersection condition on decisive individuals. Finally, in the social choice correspondence (SCC) setting, when the number of alternatives exceeds the number of voters, we characterize Voting by Minimal Committees SCCs using correspondence contraction consistency, top selection, unanimity, and committee intersection.