On societies choosing social outcomes, and their memberships: Strategy-proofness

We consider a society whose members have to choose not only an outcome from a given set of outcomes but also the subset of agents that will remain members of the society. We assume that each agent is indifferent between any two alternatives (pairs of final societies and outcomes) provided that the agent does not belong to any of the two final societies, regardless of the chosen outcome. Under this preference domain restriction we characterize the class of all strategy-proof, unanimous and outsider independent rules as the family of all serial dictator rules.