Lecture Notes on Fair Division

Fair division is the problem of dividing one or several goods amongst two or more agents in a way that satisfies a suitable fairness criterion. That is, fair division may be considered part of the larger research area of multiagent resource allocation (Chevaleyre et al., 2006). What is special about fair division is the explicit focus on fairness concerns. These notes give a succinct introduction to the field, focusing on formal and computational aspects that are particularly relevant to research in Computational Social Choice (Chevaleyre et al., 2007b) and Multiagent Systems (Wooldridge, 2009). We begin by briefly outlining how fair division fits into (and relates to) these two disciplines. Like voting, the archetypical instance of a social choice problem, fair division amounts to selecting an outcome from a set of possible collective agreements, given the individual preferences of a group of agents. There are however two main differences when compared to voting. The first difference is that, typically, voting theory assumes that agents (voters) have ordinal preferences (that is, they rank the available candidates and can say for any two candidates which one they like more), while in the context of fair division we usually assume that agents have cardinal preferences (that is, each agent has got a utility function mapping possible outcomes to appropriate numerical values). The second difference is that a fair division problem comes with a certain internal "structure" that is typically absent from problems in voting: