Fair Division: From Cake-Cutting to Dispute Resolution.

TLDR

Fair division offers rigorous methods for allocating goods or resolving disputes in ubiquitous contexts such as cake cutting, estate division, and border delimitation. The authors analyze the classic “I cut, you choose” procedure and its extensions to multi‑party, multi‑good scenarios, emphasizing envy‑free allocations and evaluating fairness in auction and election mechanisms.

Abstract

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.