Coalitional Manipulations and Generalized Proportional Rules∗

In a unified framework of allocation problems with at least three entities (or agents), we show that “generalized proportional rules” are the only rules that are robust to coalitional manipulations. We characterize proportional rules imposing in addition efficiency, dummy, and nonnegativity. Coalitional manipulations are considered both in the environment without any restriction on coalition formation and in the restricted environment where coalitions of only pairs are possible. In the former case, non-manipulability is formalized by reallocation-proofness, saying that no coalition can benefit by a reallocation of characteristic vectors (or claims, in the context of bankruptcy) of its members. In the latter case, we consider pairwise reallocation-proofness. Several existing and new results in specialized models are obtained as corollaries. For example, axiomatizations of the proportional rule in the context of bankruptcy or surplus sharing; “utilitarian rules” in the context of social choice with transferable utilities; the Bayesian updating rule in the context of probability updating; “linear opinion pools” in the context of probability updating.