Coalitionally strategy-proof rules in allotment economies with homogeneous indivisible goods

We 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. We would like to thank the associate editor and two anonymous referees whose comments and suggestions significantly improve this paper. We are also grateful to Masaki Aoyagi, Kazuhiko Hashimoto, Hervé Moulin, Hiroo Sasaki, Koji Takamiya, William Thomson, Takuma Wakayama as well as other participants at the Eighth International Meeting of the Society for Social Choice and Welfare in Istanbul, the 2006 Autumn Annual Meeting of the Japanese Economic Association in Osaka, and Yokohama National University Seminar of Economic Theory for their helpful comments. We acknowledge financial supports from the Japan Society for the Promotion of Science via the Research Fellowship for Young Scientist (Hatsumi) and the Grant-in-Aid for Scientific Research (Serizawa).