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Paradoxes of Fair Division

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Author Info
Brams, S. J.
Eldelman, P. H.
Fishburn, P. C.

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Abstract

Two or more players are required to divide up a set of indivisible items that they can rank from best to worst. They may, as well, be able to indicate preferences over subsets, or packages, of items. The main criteria used to assess the fairness of a division are efficiency (Pareto-optimality) and envy-freeness. Other criteria are also suggested, including a Rawlsian criterion that the worst-off player be made as well off as possible and a scoring procedure, based on the Borda count, that helps to render allocations as equal as possible. Eight paradoxes, all of which involve unexpected conflicts among the criteria, are described and classified into three categories, reflecting (1) incompatibilities between efficiency and envy-freeness, (2) the failure of a unique efficient and envy-free division to satisfy other criteria, and (3) the desirability, on occasion, of dividing up items unequally. While troublesome, the paradoxes also indicate opportunities for achieving fair division, which will depend on the fairness criteria one deems important and the trade-offs one considers acceptable.

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File URL: http://www.econ.nyu.edu/cvstarr/working/2000/RR00-13.PDF
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Paper provided by C.V. Starr Center for Applied Economics, New York University in its series Working Papers with number 00-13.

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Length: 23pages
Date of creation: 2000
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Handle: RePEc:cvs:starer:00-13

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Postal: C.V. Starr Center, Department of Economics, New York University, 269 Mercer Street 7th Floor, New York, NY 10003
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Postal: C.V. Starr Center, Department of Economics, New York University, 269 Mercer Street 7th Floor, New York, NY 10003
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Related research
Keywords: FAIR DIVISION ALLOCATION OF INDIVISIBLE ITEMS ENVY-FREENESS PARETO- OPTIMALITY RAWLSIAN JUSTICE BORDA COUNT.

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Find related papers by JEL classification:
D61 - Microeconomics - - Welfare Economics - - - Allocative Efficiency; Cost-Benefit Analysis
D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement

References listed on IDEAS
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  1. Claus-Jochen Haake & Matthias G. Raith & Francis Edward Su, 2002. "Bidding for envy-freeness: A procedural approach to n-player fair-division problems," Social Choice and Welfare, Springer, vol. 19(4), pages 723-749. [Downloadable!] (restricted)
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  2. Steven J. Brams & D. Marc Kilgour, 2001. "Competitive Fair Division," Journal of Political Economy, University of Chicago Press, vol. 109(2), pages 418-443, April. [Downloadable!] (restricted)
    Other versions:
  3. Steven J. Brams & Paul H. Edelman & Peter C. Fishburn, 2003. "Fair Division Of Indivisible Items," Theory and Decision, Springer, vol. 55(2), pages 147-180, 09. [Downloadable!]
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  4. Dorothea Herreiner & Clemens Puppe, 2002. "A simple procedure for finding equitable allocations of indivisible goods," Social Choice and Welfare, Springer, vol. 19(2), pages 415-430. [Downloadable!] (restricted)
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Brams,S.L. & Kaplan,T.R., 2002. "Dividing the indivisible : procedures for allocating cabinet ministries to political parties in a parliamentary system," Working papers 340, University of Bielefeld, Insitute of Mathematical Economics. [Downloadable!]
    Other versions:
  2. Somdeb Lahiri, 2003. "Equitable and Decentralized Solution for the Allocation of Indivisible Objects," Grand Coalition 18, Grand Coalition Web Site. [Downloadable!]
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