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A note on Thomson's characterizations of the uniform rule

Nir Dagan

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Abstract

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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  2. Carmen Herrero and Antonio Villar, The equal-distance rule in allocation problems with single-peaked preferences, in Ahmet Alkan, Charalambos D Aliprantis, and Nicholas C Yannelis (Eds), Current Trends in Economics: Theory and Applications, pp. 215-223, Springer (1999)
  3. William Thomson, On the axiomatic method and its recent applications to game theory and resource allocation, Social Choice and Welfare 18:327-386 (2001)
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  5. Carmen Herrero, General allocation problems with single-peaked preferences: path-independence and related topics, Spanish Economic Review 4:19-40 (2002)
  6. Joe Malkevitch, Resolving bankruptcy claims, Feature Column, Monthly Essays on Mathematical Topics, AMS website (March 2005)
  7. Youngsub Chun, The Separability Principle in Economies with Single-Peaked Preferences, Social Choice and Welfare 26:239-253 (2006)
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