Fair Division: From Cake-Cutting to Dispute Resolution

Cutting a cake, dividing up the property in an estate, determining the borders in an international dispute - such problems of fair division are ubiquitous. Fair Division treats all these problems and many more through a rigorous analysis of a variety of procedures for allocating goods (or 'bads' like chores), or deciding who wins on what issues, when there are disputes. Starting with an analysis of the well-known cake-cutting procedure, 'I cut, you choose', the authors show how it has been adapted in a number of fields and then analyze fair-division procedures applicable to situations in which there are more than two parties, or there is more than one good to be divided. In particular they focus on procedures which provide 'envy-free' allocations, in which everybody thinks he or she has received the largest portion and hence does not envy anybody else. They also discuss the fairness of different auction and election procedures.

Steven Brams is Professor of Politics at New York University. He is a Fellow of the American Association for the Advancement of Science, a Guggenheim Fellow and a past president of the Peace Science Society International. Alan Taylor is Marie Louise Bailey Professor of Mathematics at Union College, where he is Chair of the Science Division. He works on logic and set theory, finite and infinitary combinatorics, simple games, and social choice theory.