We search for impartiality in the allocation of objects when monetary transfers are not possible. Our main focus is anonymity. The standard definition requires that if agents' names are permuted, their assignments should be permuted in the same way. Since no rule satisfies this definition in...

Arrow's "impossibility" and similar classical theorems are usually proved for an unrestricted domain of preference profiles. Recent work extends Arrow's theorem to various restricted but "saturating" domains of privately oriented, continuous, (strictly) convex, and (strictly) monotone "economic...