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Two derivations of the uniform rule and an application to bankruptcy

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  • Schummer, James
  • Thomson, William

Abstract

We consider the problem of allocating a single infinitely divisible commodity to agents with single-peaked preferences, and establish two properties of the rule that has played the central role in the analysis of this problem, the uniform role. Among the efficient allocations, it selects (1) the one at which the difference between the largest amount received by any agent and the smallest sush amount is minimal, and (2) the one at which the variance of the amounts received by the agents is minimal.
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Suggested Citation

  • Schummer, James & Thomson, William, 1997. "Two derivations of the uniform rule and an application to bankruptcy," Economics Letters, Elsevier, vol. 55(3), pages 333-337, September.
  • Handle: RePEc:eee:ecolet:v:55:y:1997:i:3:p:333-337
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    1. Hans Peters & Gert-Jan Otten & Oscar Volij, 1996. "Two characterizations of the uniform rule for division problems with single-peaked preferences (*)," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 7(2), pages 291-306.
    2. Dutta, Bhaskar & Ray, Debraj, 1989. "A Concept of Egalitarianism under Participation Constraints," Econometrica, Econometric Society, vol. 57(3), pages 615-635, May.
    3. Ching, Stephen, 1992. "A simple characterization of the uniform rule," Economics Letters, Elsevier, vol. 40(1), pages 57-60, September.
    4. Thomson, William, 1995. "Population-Monotonic Solutions to the Problem of Fair Division When Preferences Are Single-Peaked," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 5(2), pages 229-246, March.
    5. Barbera, Salvador & Jackson, Matthew O. & Neme, Alejandro, 1997. "Strategy-Proof Allotment Rules," Games and Economic Behavior, Elsevier, vol. 18(1), pages 1-21, January.
    6. Bettina Klaus & Hans Peters & Ton Storcken, 1997. "Reallocation of an infinitely divisible good," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 10(2), pages 305-333.
    7. Nir Dagan, 1996. "Consistency and the Walrasian allocations correspondence," Economics Working Papers 151, Department of Economics and Business, Universitat Pompeu Fabra.
    8. Sprumont, Yves, 1991. "The Division Problem with Single-Peaked Preferences: A Characterization of the Uniform Allocation Rule," Econometrica, Econometric Society, vol. 59(2), pages 509-519, March.
    9. Thomson William, 1994. "Consistent Solutions to the Problem of Fair Division When Preferences Are Single-Peaked," Journal of Economic Theory, Elsevier, vol. 63(2), pages 219-245, August.
    10. Klaus Bettina & Peters Hans & Storcken Ton, 1995. "Strategy-proof division with single-peaked preferences and initial endowments," Research Memorandum 001, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    11. O'Neill, Barry, 1982. "A problem of rights arbitration from the Talmud," Mathematical Social Sciences, Elsevier, vol. 2(4), pages 345-371, June.
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    More about this item

    JEL classification:

    • D51 - Microeconomics - - General Equilibrium and Disequilibrium - - - Exchange and Production Economies
    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
    • D70 - Microeconomics - - Analysis of Collective Decision-Making - - - General

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