Two-person pie-cutting: The fairest cuts
AbstractBarbanel, Brams, and Stromquist (2009) asked whether there exists a two-person moving-knife procedure that yields an envy-free, undominated, and equitable allocation of a pie. We present two procedures: One yields an envy-free, almost undominated, and almost equitable allocation, whereas the second yields an allocation with the two “almosts” removed. The latter, however, requires broadening the definition of a “procedure," which raises philosophical, as opposed to mathematical, issues. An analogous approach for cakes fails because of problems in eliciting truthful preferences.
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Bibliographic InfoPaper provided by University Library of Munich, Germany in its series MPRA Paper with number 22703.
Date of creation: Mar 2010
Date of revision:
mechanism design; fair division; divisible good; cake-cutting; pie-cutting;
Find related papers by JEL classification:
- D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
- D74 - Microeconomics - - Analysis of Collective Decision-Making - - - Conflict; Conflict Resolution; Alliances
- C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
This paper has been announced in the following NEP Reports:
- NEP-ALL-2010-05-29 (All new papers)
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- 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.
- Brams,Steven J. & Taylor,Alan D., 1996. "Fair Division," Cambridge Books, Cambridge University Press, Cambridge University Press, number 9780521556446.
- Steven J. Brams & D. Marc Kilgour, 2001.
"Competitive Fair Division,"
Journal of Political Economy, University of Chicago Press,
University of Chicago Press, vol. 109(2), pages 418-443, April.
- Brams, S.J. & Kilgour, D.M., 1999. "Competitive Fair Division," Working Papers, C.V. Starr Center for Applied Economics, New York University 99-05, C.V. Starr Center for Applied Economics, New York University.
- Brams, Steven J. & Jones, Michael A. & Klamler, Christian, 2010. "Divide-and-conquer: A proportional, minimal-envy cake-cutting algorithm," MPRA Paper 22704, University Library of Munich, Germany.
- Barbanel, Julius B. & Brams, Steven J., 2011. "Two-person cake-cutting: the optimal number of cuts," MPRA Paper 34263, University Library of Munich, Germany.
- Brams, Steven J. & Jones, Michael A. & Klamler, Christian, 2011. "N-Person cake-cutting: there may be no perfect division," MPRA Paper 34264, University Library of Munich, Germany.
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