Efficiency and converse reduction-consistency in collective choice

We consider the problem of selecting a subset of a feasible set over which each agent has a strict preference. We propose an invariance property, converse reduction-consistency, which is the converse of reduction-consistency introduced by Yeh (2006), and study its implications. Our results are two characterizations of the Pareto rule: (1) it is the only rule satisfying efficiency and converse reduction-consistency and (2) it is the only rule satisfying one-agent efficiency, converse reduction-consistency, and reduction-consistency.