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Reallocation of an infinitely divisible good

Author

Listed:
  • Bettina Klaus

    (Department of Quantitative Economics, Maastricht University, P.O. Box 616, 6200 MD Maastricht, THE NETHERLANDS)

  • Hans Peters

    (Department of Quantitative Economics, Maastricht University, P.O. Box 616, 6200 MD Maastricht, THE NETHERLANDS)

  • Ton Storcken

    (Department of Quantitative Economics, Maastricht University, P.O. Box 616, 6200 MD Maastricht, THE NETHERLANDS)

Abstract

We consider the problem of reallocating the total initial endowments of an infinitely divisible commodity among agents with single-peaked preferences. With the uniform reallocation rule we propose a solution which satisfies many appealing properties, describing the effect of population and endowment variations on the outcome. The central properties which are studied in this context are population monotonicity, bilateral consistency, (endowment) monotonicity and (endowment) strategy-proofness. Furthermore, the uniform reallocation rule is Pareto optimal and satisfies several equity conditions, e.g., equal-treatment and envy-freeness. We study the trade-off between properties concerning variation and properties concerning equity. Furthermore, we provide several characterizations of the uniform reallocation rule based on these properties.

Suggested Citation

  • 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.
  • Handle: RePEc:spr:joecth:v:10:y:1997:i:2:p:305-333
    Note: Received: August 29, 1995; revised version June 26, 1996
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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. 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.
    3. 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.
    4. Dagan, Nir, 1996. "A Note on Thomson's Characterizations of the Uniform Rule," Journal of Economic Theory, Elsevier, vol. 69(1), pages 255-261, April.
    5. 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).
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    Citations

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    Cited by:

    1. Murat Atlamaz & Bettina Klaus, 2007. "Manipulation via Endowments in Exchange Markets with Indivisible Goods," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 28(1), pages 1-18, January.
    2. repec:spr:sochwe:v:49:y:2017:i:2:d:10.1007_s00355-017-1068-2 is not listed on IDEAS
    3. Erik Ansink & Hans-Peter Weikard, 2012. "Sequential sharing rules for river sharing problems," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 38(2), pages 187-210, February.
    4. Nir Dagan, 1995. "Consistent solutions in exchange economies: A characterization of the price mechanism," Economics Working Papers 141, Department of Economics and Business, Universitat Pompeu Fabra.
    5. Rahmi İlkılıç & Çağatay Kayı, 2014. "Allocation rules on networks," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 43(4), pages 877-892, December.
    6. Kibris, Ozgur & Kucuksenel, Serkan, 2005. "Trade rules for uncleared markets," Working Papers 1232, California Institute of Technology, Division of the Humanities and Social Sciences.
    7. 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.
    8. Ehlers, Lars, 2003. "Multiple public goods, lexicographic preferences, and single-plateaued preference rules," Games and Economic Behavior, Elsevier, vol. 43(1), pages 1-27, April.
    9. Rebelo, S., 1997. "On the Determinant of Economic Growth," RCER Working Papers 443, University of Rochester - Center for Economic Research (RCER).
    10. Erik Ansink & Carmen Marchiori, 2015. "Reallocating Water: An Application of Sequential Sharing Rules to Cyprus," Water Economics and Policy (WEP), World Scientific Publishing Co. Pte. Ltd., vol. 1(04), pages 1-22, December.
    11. William Thomson, 2010. "Implementation of solutions to the problem of fair division when preferences are single-peaked," Review of Economic Design, Springer;Society for Economic Design, vol. 14(1), pages 1-15, March.
    12. 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.
    13. 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.
    14. Moreno, Bernardo, 2002. "Single-peaked preferences, endowments and population-monotonicity," Economics Letters, Elsevier, vol. 75(1), pages 87-95, March.
    15. Özgür Kıbrıs & Serkan Küçükşenel, 2009. "Uniform trade rules for uncleared markets," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 32(1), pages 101-121, January.
    16. 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.

    More about this item

    JEL classification:

    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations

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