Coalitionally strategy-proof rules in allotment economies of homogeneous indivisible objects

We consider the allotment problems of homogeneous indivisible objects among agents with single-peaked and risk-averse von Neumann-Morgenstern expected utility functions. We establish that the rule satisfies coalitional strategy-proofness, same-sideness, and strong symmetry if and only if it is the uniform probabilistic rule. By constructing an example, we show that if same-sideness is replaced by respect for unanimity, the statement does not hold even with additional requirements of peaks-onlyness and continuity.