Advanced search
Publication Cover
The American Mathematical Monthly Volume 120, 2013 - Issue 1
Submit an article Journal homepage
93
Views
0
CrossRef citations to date
0
Altmetric
Original Articles

N-Person Cake-Cutting: There May Be No Perfect Division

Steven J. BramsDepartment of Politics, New York University, New York, [email protected]View further author information
,
Michael A. Jones Mathematical Reviews, 416 Fourth Street, Ann Arbor, [email protected]View further author information
&
Christian KlamlerInstitute of Public Economics, University of Graz, A-8010Graz, [email protected]View further author information
Pages 35-47 | Published online: 13 Dec 2017

REFERENCES

  • J.B. Barbanel, The Geometry of Efficient Fair Division, Cambridge University Press, New York, 2005.
  • J. B. Barbanel, 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, available at http://dx.doi.org/10.1016/j.mathsocsci.2004.03.006.
  • J. B. Barbanel, S. J. Brams, Two-person pie-cutting: The fairest cuts, College Math. J. 42 (2011a) 25–32, available at http://dx.doi.org/10.4169/college.math.j.42.1.025.
  • J. B. Barbanel, S. J. Brams, Two-person cake-cutting: The optimal number of cuts, Preprint, Department of Politics, New York University, 2011b.
  • J.B. Barbanel, S. J. Brams, W. Stromquist, Cutting a pie is not a piece of cake, Amer. Math. Monthly 116 (2009) 496–514, available at http://dx.doi.org/10.4169/193009709X470407.
  • S. J. Brams, Fair Division, in Oxford Handbook of Political Economy, Edited by B.R. Weingast and D. Wittman, Oxford University Press, Oxford, UK, 2006, 425–437.
  • S. J. Brams, Mathematics and Democracy: Designing Better Voting and Fair-Division Procedures, Princeton University Press, Princeton, NJ, 2008.
  • S. J. Brams, M. Feldman, J. K. Lai, J. Morgenstern, A. D. Procaccia, On naxsum cake divisions. Proceedings of the 26th AAAI Conference on Artificial Intelligence (2012) 1285–1291.
  • S. J. Brams, M. A. Jones, C. Klamler, Better ways to cut a cake, Notices of the AMS 53 (2006) 1314–1321.
  • S. J. Brams, M. A. Jones, C. Klamler, Proportional pie-cutting, Internat. J. Game Theory 26 (2008) 353–367, available at http://dx.doi.org/10.1007/s00182-007-0108-z.
  • S. J. Brams, M. A. Jones, C. Klamler, Divide and conquer: A proportional, minimal-envy cake-cutting algorithm, SIAM Rev. 53 (2011) 291–307, available at http://dx.doi.org/10.1137/080729475.
  • S. J. Brams, A. D. Taylor, Fair Division: From Cake-Cutting to Dispute Resolution, Cambridge University Press, Cambridge, UK, 1996.
  • I. Caragiannis, J. K. Lai, A. D. Procaccia, Towards more expressive cake cutting. Proceedings of the 22nd International Joint Conference on Artificial Intelligence, 2011, 127–132.
  • Y. Cohler, J. K. Lai, D. C. Parkes, A. D. Procaccia, Optimal envy-free cake cutting. Proceedings of the 25th AAAI Conference on Artificial Intelligence, 2011, 626–631.
  • D. Gale, Mathematical entertainments, Math. Intelligencer, 15 no. 1 (1993) 48–52, available at http://dx.doi.org/10.1007/BF03025257.
  • T. P. Hill, K. E. Morrison, Cutting cakes carefully. College Math. J. 41 no. 4 (2010) 281–288, available at http://dx.doi.org/10.4169/074683410X510272.
  • M. A. Jones, Equitable, envy-free, and efficient cake cutting for two people and its application to divisible goods, Math. Mag. 75 (2002) 275–283, available at http://dx.doi.org/10.2307/3219163.
  • C. Klamler, Fair Division, in Handbook of Group Decision and Negotiation, Edited by D. M. Kilgour and C. Eden, Springer, Heidelberg, 2010, 183–202.
  • A. Magid, Editor's note: More on cake cutting. Notices of the AMS 55 (2008) 1072.
  • J. Robertson, W. Webb, Cake-Cutting Algorithms: Be Fair If You Can, A K Peters, Natick, MA, 1998.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Order Reprints Request Corporate Permissions

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

Request Academic Permissions

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.

Related research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.