We consider private good economies with single-plateaued preferences. We show that the uniform rule is the only allocation rule satisfying indifference (in terms of welfare), strategy-proofness and no-envy. Indifference (in terms of welfare) means that if one allocation is recommended, then another allocation is recommended if and only if all agents are indifferent between these allocations.  ...

We provide a generalization of Harsanyi (1955)’s aggregation theorem to the case of incomplete preferences at the individual and social level. Individuals and society have possibly incomplete expected utility preferences that are represented by sets of expected utility functions. Under Pareto indifference, social preferences are represented through a set of aggregation rules that are utilitaria...