Allocation of an Indivisible Object on the Full Preference Domain: Axiomatic Characterizations

We study the problem of allocating an indivisible object to one of several agents on the full preference domain when monetary transfers are not allowed. Our main requirement is strategy-proofness. The other properties we seek are Pareto optimality, non-dictatorship, and non-bossiness. We provide characterizations of strategy-proof rules that satisfy Pareto optimality and non-bossiness, non-dictatorship and non-bossiness, and Pareto optimality and non-dictatorship. As a consequence of these characterizations, we show that a strategy-proof rule cannot satisfy Pareto optimality, non-dictatorship, and non-bossiness simultaneously.