Center for Complex Systems and Enterprises
Distinguished Lecture Series
Fair Division: From Cake Cutting to Dispute Resolution
Steven J. Brams
Department of Politics, New York University
ABSTRACT: I begin with an overview of the literature on the fair division of divisible goods--starting with the use of "I cut, you choose" in the Hebrew Bible--and then survey both 2-person and n-person more modern procedures, including Last Diminisher, Divide and Conquer, and Adjusted Winner. I then turn to a new algorithm for the fair division of indivisible goods between two players, who strictly rank the goods from best to worst. Its allocations are Pareto-optimal, envy-free, and maximal. As the number of goods increases, the probability that all the goods are allocated approaches 1 if all possible rankings are equiprobable. The algorithm seems eminently applicable to real-world disputes, such as dividing the marital property in a divorce.
BIO: Steven J. Brams is Professor of Politics at New York University and the author, co-author, or co-editor of 18 books and more than 250 articles. His books include Theory of Moves (Cambridge, 1994) and, co-authored with Alan D. Taylor, Fair Division: From Cake-Cutting to Dispute Resolution (Cambridge, 1996) and The Win-Win Solution: Guaranteeing Fair Shares to Everybody (Norton, 1999). His newest books are Mathematics and Democracy: Designing Better Voting and Fair-Division Procedures (Princeton, 2008) and Game Theory and the Humanities: Bridging Two Worlds (MIT, 2011). He holds two patents for fair-division algorithms and is chairman of the advisory board of Fair Outcomes, Inc. Brams has applied game theory and social-choice theory to voting and elections, bargaining and fairness, international relations, and the Bible, theology, and literature. He is a former president of the Peace Science Society (1990-91) and of the Public Choice Society (2004-2006). He is a Fellow of the American Association for the Advancement of Science (1986), a Guggenheim Fellow (1986-87), and was a Visiting Scholar at the Russell Sage Foundation (1998-99).