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The Mathematical Intelligencer

, Volume 36, Issue 3, pp 23–35 | Cite as

Two-Person Cake Cutting: The Optimal Number of Cuts

  • Julius B. BarbanelEmail author
  • Steven J. Brams
Article

Keywords

Mathematical Intelligencer Fair Division Changeover Point Linear Piece Total Valuation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Notes

Acknowledgment

We thank the referee for valuable comments on an earlier version of this article.

References

  1. Barbanel, Julius B. (2000). “On the Structure of Pareto Optimal Cake Partitions.” Journal of Mathematical Economics 33: 401–424.Google Scholar
  2. Barbanel, Julius B. (2005). The Geometry of Efficient Fair Division. New York: Cambridge University Press.Google Scholar
  3. Barbanel, Julius B., and Steven J. Brams (2004). “Cake Division with Minimal Cuts: Envy-Free Procedures for 3 Person, 4 Persons, and Beyond.” Mathematical Social Sciences 48, no. 4 (November): 251–269.Google Scholar
  4. Barbanel, Julius B., and Steven J. Brams (2011). “Two-Person Pie-Cutting: The Fairest Cuts.” College Mathematics Journal 42, no. 1 (January): 25–32.Google Scholar
  5. Barbanel, Julius B., Steven J. Brams, and Walter Stromquist (2009). “Cutting a Pie Is Not a Piece of Cake.” American Mathematical Monthly 116, no. 6 (June-July): 496–514.Google Scholar
  6. Brams, Steven J. (2008). Mathematics and Democracy: Designing Better Voting and Fair-Division Procedures. Princeton, NJ: Princeton University Press.Google Scholar
  7. Brams, Steven J., Michal Feldman, John K. Lai, Jamie Morgenstern, and Ariel D. Procaccia (2012). “On Maxsum Fair Cake Divisions.” Proceedings of the 26 th AAAI Conference on Artificial Intelligence, pp. 1285–1291.Google Scholar
  8. Brams, Steven J., Michael A. Jones, and Christian Klamler (2005). “Proportional Pie-Cutting.” International Journal of Game Theory 36, nos. 3–4 (March): 353–367.Google Scholar
  9. Brams, Steven J., Michael A. Jones, and Christian Klamler (2006). “Better Ways to Cut a Cake.” Notices of the AMS 35, no. 11 (December): 1314–1321.Google Scholar
  10. Brams, Steven J., Michael A. Jones, and Christian Klamler (2011). “Divide-and-Conquer: A Proportional, Minimal-Envy Cake-Cutting Algorithm.” SIAM Review 53, no. 2 (June): 291–307.Google Scholar
  11. Brams, Steven J., Michael A. Jones, and Christian Klamler (2013). “N-Player Cake-Cutting: There May Be No Perfect Division.” American Mathematical Monthly 120, no. 1 (January): 35–47.Google Scholar
  12. Brams, Steven J., and Alan D. Taylor (1996). Fair Division: From Cake-Cutting to Dispute Resolution. Cambridge, UK: Cambridge University Press.Google Scholar
  13. Brams, Steven J., and Alan D. Taylor (1999). The Win-Win Solution: Guaranteeing Fair Shares to Everybody. New York: W.W. Norton.Google Scholar
  14. Caragiannis, Ioannis, John K. Lai, and Ariel D. Procaccia (2011). “Towards More Expressive Cake Cutting.” Proceedings of the 22nd International Joint Conference on Artificial Intelligence, pp. 127–132.Google Scholar
  15. Cohler, Yuga, John K. Lai, David C. Parkes, and Ariel D. Procaccia (2011). “Optimal Envy-Free Cake Cutting.” Proceedings of the 25th AAAI Conference on Artificial Intelligence, pp. 626–631.Google Scholar
  16. Jones, Michael A. (2002). “Equitable, Envy-Free, and Efficient Cake Cutting for Two People and Its Application to Divisible Goods.” Mathematics Magazine 75, no. 4 (October): 275–283.Google Scholar
  17. Klamler, Christian (2010). "Fair Division." In Handbook of Group Decision and Negotiation, edited by D. Marc Kilgour and Colin Eden. Heidelberg, Germany: Springer, pp. 183–202.Google Scholar
  18. Robertson, Jack, and William Webb (1998). Cake-Cutting Algorithms: Be Fair If You Can. Natick, MA: A.K. Peters.Google Scholar
  19. Weller, D. (1985). “Fair Division of a Measurable Space.” Journal of Mathematical Economics 14: 5–17.Google Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Department of MathematicsUnion CollegeSchenectadyUSA
  2. 2.Department of PoliticsNew York UniversityNew YorkUSA

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