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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)


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.

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Bibliographic Info

Article provided by Springer in its journal Social Choice and Welfare.

Volume (Year): 15 (1997)
Issue (Month): 1 ()
Pages: 57-66

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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. Juan Perote Peña, 2003. "Solidarity in Terms of Reciprocity," Economic Working Papers at Centro de Estudios Andaluces E2003/16, Centro de Estudios Andaluces.
  2. Youngsub Chun, 2001. "The Replacement Principle in Bargaining," Working Paper Series no42, Institute of Economic Research, Seoul National University.
  3. 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.
  4. Ichiishi, Tatsuro & Idzik, Adam, 1999. "Market allocation of indivisible goods," Journal of Mathematical Economics, Elsevier, vol. 32(4), pages 457-466, December.


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