Strategy-proof group selection under single-peaked preferences over group size

One group has to be selected among a set of agents. Agents have preferences over the size of the group if they are selected, and preferences over size as well as the “stand-outside” option are single-peaked. Two classes of efficient, individually rational and strategy-proof rules, are presented. The proposingrules allow agents to either maintain or shrink the group size following a fixed priority and are characterized by group strategy-proofness. The voting rules enlarge the group size in each voting round and achieve at least half of the maximal group size compatible with individual rationality.