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Fair Reallocation in Economies with Single-Peaked Preferences

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  • Kazuhiko Hashimoto
  • Takuma Wakayama

Abstract

We consider the problem of fairly reallocating the individual endowments of a perfectly divisible good among agents with single-peaked preferences. We provide a new concept of fairness, called position-wise envy-freeness, that is compatible with individual rationality. This new concept requires that each demander (i.e., agent whose most preferred amount is strictly greater than his endowment) should not envy another demander who does not receive his endowment and that each supplier (i.e., agent whose most preferred amount is strictly less than his endowment) should not envy another supplier who does not receive his endowment. We establish that a rule is efficient, individually rational, strategy-proof, and position-wise envy-free if and only if it is the gradual uniform rule, which is an extension of the well-known uniform rule.

Suggested Citation

  • Kazuhiko Hashimoto & Takuma Wakayama, 2015. "Fair Reallocation in Economies with Single-Peaked Preferences," ISER Discussion Paper 0947, Institute of Social and Economic Research, Osaka University.
  • Handle: RePEc:dpr:wpaper:0947
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    File URL: https://www.iser.osaka-u.ac.jp/library/dp/2015/DP0947.pdf
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. Hideyuki Mizobuchi & Shigehiro Serizawa, 2006. "Maximal Domain for Strategy-proof Rules in Allotment Economies," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 27(1), pages 195-210, August.
    4. 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.
    5. Shigehiro Serizawa, 2006. "Pairwise Strategy-Proofness and Self-Enforcing Manipulation," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 26(2), pages 305-331, April.
    6. Moreno, Bernardo, 2002. "Single-peaked preferences, endowments and population-monotonicity," Economics Letters, Elsevier, vol. 75(1), pages 87-95, March.
    7. Thomson, William, 1997. "The Replacement Principle in Economies with Single-Peaked Preferences," Journal of Economic Theory, Elsevier, vol. 76(1), pages 145-168, September.
    8. Bettina Klaus & Hans Peters & Ton Storcken, 1998. "Strategy-proof division with single-peaked preferences and individual endowments," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 15(2), pages 297-311.
    9. Agustín Bonifacio, 2015. "Bribe-proof reallocation with single-peaked preferences," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 44(3), pages 617-638, March.
    10. 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.
    11. Youngsub Chun, 2006. "The Separability Principle in Economies with Single-Peaked Preferences," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 26(2), pages 239-253, April.
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