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A note on Thomson’s characterizations of the uniform rule. (English) Zbl 0893.90007
Summary: W. Thomson [J. Econ. Theory 63, No. 2, 219-245 (1994; Zbl 0864.90008)] proved that the uniform rule of the fair division problem, where preferences are single-peaked, is the unique rule which is bilaterally consistent, continuous, Pareto optimal, and envy-free, in a setting of an infinite number of potential agents. We show that the uniqueness of the uniform rule is achieved without assuming continuity, even in a setting of a finite number of potential agents. A similar result is obtained by replacing envy- freeness with individual rationality from equal division.

91B14 Social choice
91B08 Individual preferences
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