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The role of replication-invariance: two answers concerning the problem of fair division when preferences are single-peaked

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  • Klaus, B.E.

    (Microeconomics & Public Economics)

Abstract

We consider the problem of allocating an infinitely divisible commodity among a group of agents with single-peaked preferences. A rule that has played a central role in the previous analysis of the problem is the so-called uniform rule. Thomson (1995b) proved that the uniform rule is the only rule satisfying Pareto optimality, no-envy, one-sided population-monotonicity, and replication-invariance. Replacing one-sided population-monotonicity by one-sided replacement-domination yields another characterization of the uniform rule (Thomson, 1997a). Until now, the independence of replication-invariance from the other properties in these characterizations was an open problem. In this note we prove this independence by means of a single example.
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  • Klaus, B.E., 2007. "The role of replication-invariance: two answers concerning the problem of fair division when preferences are single-peaked," Research Memorandum 029, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    • Handle: RePEc:unm:umamet:2007029
    DOI: 10.26481/umamet.2007029
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    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. William Thomson, 1999. "Welfare-domination under preference-replacement: A survey and open questions," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 16(3), pages 373-394.
    4. Thomson, William, 1997. "The Replacement Principle in Economies with Single-Peaked Preferences," Journal of Economic Theory, Elsevier, vol. 76(1), pages 145-168, September.
    5. William Thomson, 1997. "The replacement principle in economies with indivisible goods," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 15(1), pages 57-66.
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    Cited by:

    1. Thomson, William, 2011. "Chapter Twenty-One - Fair Allocation Rules," Handbook of Social Choice and Welfare, in: K. J. Arrow & A. K. Sen & K. Suzumura (ed.), Handbook of Social Choice and Welfare, edition 1, volume 2, chapter 21, pages 393-506, Elsevier.
    2. Kazuhiko Hashimoto & Takuma Wakayama, 2021. "Fair reallocation in economies with single-peaked preferences," International Journal of Game Theory, Springer;Game Theory Society, vol. 50(3), pages 773-785, September.

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    More about this item

    JEL classification:

    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations

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