The undercut procedure: an algorithm for the envy-free division of indivisible items
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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Volume (Year): 39 (2012)
Issue (Month): 2 (July)
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References listed on IDEAS
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- Brams, S. J. & Eldelman, P. H. & Fishburn, P. C., 2000.
"Fair Division of Indivisible Items,"
00-15, C.V. Starr Center for Applied Economics, New York University.
- Steven J. Brams & Todd R. Kaplan, 2002.
"Dividing the Indivisible: Procedures for Allocating Cabinet Ministries to Political Parties in a Parliamentary System,"
0202, Exeter University, Department of Economics.
- 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, Bielefeld University, Center for Mathematical Economics.
- Brams, S.J. & Kaplan, T.R., 2002. "Dividing the Indivisible: Procedures for Allocating Cabinet Ministries to Political Parties in a Parliamentary System," Working Papers 02-06, C.V. Starr Center for Applied Economics, New York University.
- 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.
- Brams, S.J. & Fishburn, P.C., 1998.
"Fair Division of Indivisible Items between Two People with Identical Preferences: Envy-Freeness, Pareto-Optimality, and Equity,"
98-20, C.V. Starr Center for Applied Economics, New York University.
- 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.
- 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.
- repec:cup:cbooks:9780521556446 is not listed on IDEAS
- 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.
- Weingast, Barry R. & Wittman, Donald, 2008. "The Oxford Handbook of Political Economy," OUP Catalogue, Oxford University Press, number 9780199548477, March.
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