Fair Division
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Article Outline Glossary Introduction Cutting Cakes Conclusion Future Directions Bibliography
Glossary Efficiency An allocation is efficient if there is no other allocation that is strictly preferred by at least one agent and not worse for any other agent. Envy-freeness An allocation is envy-free if no agent strictly prefers any of the other agents’ portions. Equitability An allocation is equitable if every agent values his or her portion the same. Maximinality An allocation is maximin if the worst ranked item received by any of the agents is as highly ranked as possible. Proportionality An allocation is proportional if each of the n agents gets at least 1/n of the good or goods in his or her valuation.
Introduction Over the last decades, fairness has become a major issue in many different research areas such as economics and computer science. Various books (e.g., Brams and Taylor 1996; Robertson and Webb 1998; Moulin 2003) and surveys (e.g., Thomson 2016; Bouveret et al. 2016; Procaccia
2016) have given many results. The goal in this survey is to single out certain issues of fairness and discuss some contributions. In particular, we focus on (i) cake-cutting, i.e., the division of a single heterogeneous divisible good, and (ii) the allocation of indivisible items. Issues of fairness come up in many different situations, be it a divorce settlement, the division of land, the sharing of a common resource, the allocation of costs, or simply the division of a birthday cake. From a philosophical point of view, fairness concepts have been widely studied (see, e.g., Rawls 1971; Roemer 1996; Ryan 2006; Young 1994). But how can we transform this work into concepts useful in disciplines such as economics or computer science? The goal of this review is to address certain specific situations in which fairness considerations might play a role and how normative and/or algorithmic concepts can help in finding acceptable fair-division rules and/or solutions. The above situations and most other fairdivision problems do have certain aspects in common. First, there are at least two agents. These might be human beings, but they could also be states, firms, or other entities. Second, there is a resource that is going to be divided. Such a resource can be a heterogeneous good (such as a cake with different toppings), a set of indivisible items, costs or benefits of a joint project, or anything else that might have to be divided or allocated in a division process. Third, there is information about the agents’ preferences over the object(s) to be divided. Such preferences could be in the form of value functions (as in cake-cutting), an ordinal ranking over sets of objects (such as in the division of indivisible items), or simply the idea that a smaller cost share is preferred to a larger cost share. Many other aspects of an allocation problem might, of course, be of importance in different situations. For an overview, see Thomson (2016). In general, the fairness of a division procedure is determined by the properties it satisfies, i.e., a nor
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