Committee formation under constraints through randomized voting rules on separable domains

Abstract

We consider the problem of choosing a committee from a set of available candidates through a randomized social choice function when there are restrictions on the committee to be formed and agents have separable preferences over the committees. We show that when the set of feasible committees is non-vacuously restricted, that is, cannot be seen as the set of all committees with a subset of members, a random social choice function is onto and strategy-proof if and only if it is random dictatorial.