ISER discussion paperMarch 2007 Revised July 2008 Revised February 2009We consider the allotment problem of homogeneous indivisible goods among agents with single-peaked and risk-averse von Neumann- Morgenstern expected utility functions. We establish that a 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, this statement does not hold even with the additional requirements of no-envy, anonymity, at most binary, peaks-onlyness and continuity
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