Two-person pie-cutting: The fairest cuts

Barbanel, Julius B. and Brams, Steven J. (2010): Two-person pie-cutting: The fairest cuts. Forthcoming in: College Mathematics Journal (2011)

Abstract

Barbanel, 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.

• Item Type: MPRA Paper
• Language: English
• Keywords: mechanism design; fair division; divisible good; cake-cutting; pie-cutting
• Subjects: D - Microeconomics > D6 - Welfare Economics > D63 - Equity, Justice, Inequality, and Other Normative Criteria and Measurement; D - Microeconomics > D7 - Analysis of Collective Decision-Making > D74 - Conflict ; Conflict Resolution ; Alliances ; Revolutions; C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C70 - General

References

1. J. B. Barbanel, The Geometry of Efficient Fair Division, Cambridge University Press, Cambridge, 2005.

2. J. B. Barbanel and S. J. Brams, Cake division with minimal cuts: envy-free procedures for 3 persons, 4 persons, and beyond, Math. Social Sci. 48 (2004) 251-269.

3. J. B. Barbanel, S. J. Brams, and W. Stromquist, Cutting a pie is not a piece of cake, Amer. Math. Monthly 116 (2009) 496-514.

4. S. J. Brams, Mathematics and Democracy: Designing Better Voting and Fair-Division Procedures, Princeton University Press, Princeton, 2008.

5. S. J. Brams, M. A. Jones, and C. Klamler, Better ways to cut a cake, Notices Amer. Math. Soc. 35 (2006)1314-1321.

6. ——, Proportional pie-cutting, Internat. J. Game Theory 36 (2008) 353-367.

7. S. J. Brams and D. M. Kilgour, Competitive fair division, Journal of Political Economy 109 (2001) 418-443.

8. S.J. Brams and A. D. Taylor, Fair Division: From Cake-Cutting to Dispute Resolution, Cambridge University Press, Cambridge, 1996.

9. S. J. Brams, A. D. Taylor, and W. S. Zwicker, Old and new moving-knife schemes, Mathematical Intelligencer 17 (1995) 547-554.

10. D. Gale, Mathematical entertainments, Math. Intelligencer 15 (1993), 48-52.

11. J. Robertson and W. Webb, Cake-Cutting Algorithms: Be Fair If You Can, A K Peters, Natick MA, 1998.