The undercut procedure: an algorithm for the envy-free division of indivisible items
AbstractWe 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 playerâs ranking. It ensures that each player receives a subset of items that it values more than the other playerâs complementary subset, given that such an envy-free division is possible. We show that the possibility of one playerâs undercutting the otherâs proposal, and implementing the reduced subset for himself or herself, makes the proposer âreasonableâ and generally leads to an envy-free division, even when the players rank items exactly the same. Although the undercut procedure is manipulable, each playerâs maximin strategy is to be truthful. Applications of the undercut procedure are briefly discussed.
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Bibliographic InfoArticle provided by Springer in its journal Social Choice and Welfare.
Volume (Year): 39 (2012)
Issue (Month): 2 (July)
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Web page: http://link.springer.de/link/service/journals/00355/index.htm
Other versions of this item:
- Brams, Steven J. & Kilgour, D. Marc & Klamler, Christian, 2009. "The undercut procedure: an algorithm for the envy-free division of indivisible items," MPRA Paper 12774, University Library of Munich, Germany.
- D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
- D74 - Microeconomics - - Analysis of Collective Decision-Making - - - Conflict; Conflict Resolution; Alliances
- C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
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- 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.
- Brams, S.J. & Kaplan, T.R., 2002.
"Dividing the Indivisible: Procedures for Allocating Cabinet Ministries to Political Parties in a Parliamentary System,"
02-06, C.V. Starr Center for Applied Economics, New York University.
- 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.
- 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.
- Weingast, Barry R. & Wittman, Donald, 2008. "The Oxford Handbook of Political Economy," OUP Catalogue, Oxford University Press, number 9780199548477.
- 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.
- 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.
- Brams, S.J. & Fishburn, P.C., 1998. "Fair Division of Indivisible Items between Two People with Identical Preferences: Envy-Freeness, Pareto-Optimality, and Equity," Working Papers 98-20, C.V. Starr Center for Applied Economics, New York University.
- 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.
- 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,Steven J. & Taylor,Alan D., 1996. "Fair Division," Cambridge Books, Cambridge University Press, number 9780521556446.
- RAMAEKERS, Eve, .
"Fair allocation of indivisible goods: the two-agent case,"
CORE Discussion Papers RP
-2483, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Eve Ramaekers, 2013. "Fair allocation of indivisible goods: the two-agent case," Social Choice and Welfare, Springer, vol. 41(2), pages 359-380, July.
- 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.
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