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The replacement principle in economies with indivisible goods

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  • William Thomson

    (Department of Economics, University of Rochester, Rochester, NY 14627, USA)

Abstract

We consider the problem of allocating a list of indivisible goods and some amount of an infinitely divisible good among agents with equal rights on these resources, and investigate the implications of the following requirement on allocation rules: when the preferences of some of the agents change, all agents whose preferences are fixed should (weakly) gain, or they should all (weakly) lose. This condition is an application of a general principle of solidarity discussed in Thomson (1990b) under the name "replacement principle". We look for selections from the no-envy solution satisfying this property. We show that in the general case, when the number of objects is arbitrary, there is no such selection. However, in the one-object case (a single prize), up to Pareto-indifference, there is only one selection from the no-envy solution satisfying the property. Such a solution always selects an envy-free allocation at which the winner of the prize is indifferent between his bundle and the losers' common bundle.

Suggested Citation

  • 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.
  • Handle: RePEc:spr:sochwe:v:15:y:1997:i:1:p:57-66
    Note: Received: 15 May 1995 / Accepted: 5 June 1996
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    Cited by:

    1. Bergantiños, Gustavo & Massó, Jordi & Neme, Alejandro, 2015. "The division problem under constraints," Games and Economic Behavior, Elsevier, vol. 89(C), pages 56-77.
    2. Javier Perote Peña & Juan Perote Peña, 2003. "A Social Choice Trade-off Between Alternative Fairness Concepts: Solidarity versus Flexibility," Economic Working Papers at Centro de Estudios Andaluces E2003/10, Centro de Estudios Andaluces.
    3. repec:spr:sochwe:v:49:y:2017:i:2:d:10.1007_s00355-017-1068-2 is not listed on IDEAS
    4. Ichiishi, Tatsuro & Idzik, Adam, 1999. "Market allocation of indivisible goods," Journal of Mathematical Economics, Elsevier, vol. 32(4), pages 457-466, December.
    5. Gustavo Bergantiños & Jordi Massó & Inés Moreno de Barreda & Alejandro Neme, 2015. "Stable partitions in many division problems: the proportional and the sequential dictator solutions," Theory and Decision, Springer, vol. 79(2), pages 227-250, September.
    6. Juan Perote Peña, 2003. "Solidarity in Terms of Reciprocity," Economic Working Papers at Centro de Estudios Andaluces E2003/16, Centro de Estudios Andaluces.
    7. Kim, Sunyoung & Bergantiños, Gustavo & Chun, Youngsub, 2015. "The separability principle in single-peaked economies with participation constraints," Mathematical Social Sciences, Elsevier, vol. 78(C), pages 69-75.
    8. Rebelo, S., 1997. "On the Determinant of Economic Growth," RCER Working Papers 443, University of Rochester - Center for Economic Research (RCER).
    9. Karol Flores-Szwagrzak, 2017. "Efficient, fair, and strategy-proof (re)allocation under network constraints," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 48(1), pages 109-131, January.
    10. Abizada, Azar & Chen, Siwei, 2014. "A characterization of the uniform rule based on new robustness properties," Mathematical Social Sciences, Elsevier, vol. 71(C), pages 80-85.
    11. Erlanson, Albin & Flores-Szwagrzak, Karol, 2015. "Strategy-proof assignment of multiple resources," Journal of Economic Theory, Elsevier, vol. 159(PA), pages 137-162.
    12. Youngsub Chun & Inkee Jang & Biung-Ghi Ju, 2014. "Priority, solidarity and egalitarianism," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 43(3), pages 577-589, October.
    13. Moulin, Hervé, 2017. "One dimensional mechanism design," Theoretical Economics, Econometric Society, vol. 12(2), May.
    14. Klaus Bettina, 2010. "The Role of Replication-Invariance: Two Answers Concerning the Problem of Fair Division When Preferences Are Single-Peaked," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 10(1), pages 1-14, April.
    15. 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.
    16. Karol Flores-Szwagrzak, 2016. "The replacement principle in networked economies with single-peaked preferences," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 47(4), pages 763-789, December.
    17. Harless, Patrick, 2016. "Solidarity in preference aggregation: Improving on a status quo," Games and Economic Behavior, Elsevier, vol. 95(C), pages 73-87.
    18. Youngsub Chun, 2001. "The Replacement Principle in Bargaining," Working Paper Series no42, Institute of Economic Research, Seoul National University.
    19. 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.
    20. Patrick Harless, 2015. "Reaching consensus: solidarity and strategic properties in binary social choice," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 45(1), pages 97-121, June.
    21. Balazs Sziklai & Erel Segal-Halevi, 2015. "Resource-monotonicity and Population-monotonicity in Cake-cutting," IEHAS Discussion Papers 1552, Institute of Economics, Centre for Economic and Regional Studies, Hungarian Academy of Sciences.

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    JEL classification:

    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation

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