A note on Thomson's characterizations of the uniform rule

Nir Dagan

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Thomson (Consistent solutions to the problem of fair division when preferences are single-peaked, J. Econ. Theory 63 (1994), 219-245) proved that the uniform rule of 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.

JEL: D63, C71.

Journal of Economic Theory 69:255-261 (1996)

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