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The undercut procedure: an algorithm for the envy-free division of indivisible items

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  • Brams, Steven J.
  • Kilgour, D. Marc
  • Klamler, Christian

Abstract

We propose a procedure for dividing indivisible items between two players in which each player ranks the items from best to worst and has no information about the other player’s ranking. It ensures that each player receives a subset of items that it values more than the other player’s complementary subset, given that such an envy-free division is possible. We show that the possibility of one player’s undercutting the other’s proposal, and implementing the reduced subset for himself or herself, makes the proposer “reasonable” and generally leads to an envy-free division, even when the players rank items exactly the same. Although the undercut procedure is manipulable, each player’s maximin strategy is to be truthful. Applications of the undercut procedure are briefly discussed.

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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 12774.

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Date of creation: Jan 2009
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Handle: RePEc:pra:mprapa:12774

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Keywords: Fair division; allocation of indivisible items; envy-freeness; ultimatum game;

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References

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  1. Weingast, Barry R. & Wittman, Donald, 2008. "The Oxford Handbook of Political Economy," OUP Catalogue, Oxford University Press, number 9780199548477.
  2. Edelman, Paul & Fishburn, Peter, 2001. "Fair division of indivisible items among people with similar preferences," Mathematical Social Sciences, Elsevier, vol. 41(3), pages 327-347, May.
  3. 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.
  4. Brams,Steven J. & Taylor,Alan D., 1996. "Fair Division," Cambridge Books, Cambridge University Press, number 9780521556446, October.
  5. Steven J. Brams & Todd R. Kaplan, 2002. "Dividing the Indivisible: Procedures for Allocating Cabinet Ministries to Political Parties in a Parliamentary System," Discussion Papers 0202, Exeter University, Department of Economics.
  6. I. D. Hill, 2008. "Mathematics and Democracy: Designing Better Voting and Fair-division Procedures," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 171(4), pages 1032-1033.
  7. 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.
  8. Steven J. Brams & Peter C. Fishburn, 2000. "Fair division of indivisible items between two people with identical preferences: Envy-freeness, Pareto-optimality, and equity," Social Choice and Welfare, Springer, vol. 17(2), pages 247-267.
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Cited by:
  1. Eve Ramaekers, 2013. "Fair allocation of indivisible goods: the two-agent case," Social Choice and Welfare, Springer, vol. 41(2), pages 359-380, July.
  2. Brams, Steven J. & Kilgour, D. Marc & Klamler, Christian, 2013. "Two-Person Fair Division of Indivisible Items: An Efficient, Envy-Free Algorithm," MPRA Paper 47400, University Library of Munich, Germany.
  3. Brams, Steven J. & Kilgour, D. Marc & Klamler, Christian, 2014. "An algorithm for the proportional division of indivisible items," MPRA Paper 56587, University Library of Munich, Germany.

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