Claims-based Fair Division

In a fair division problem a scarce good, also called the estate, has to be divided amongst some agents and the problem is to do so in a fair way. The claims-based and preference-based approach to fair division take, respectively claims and preferences of the agents into account for realizing fair divisions. This chapter provides an introduction to the claims-based approach to fair division. In particular, we will present an overview of various models that are within the scope of the claims-based approach: in a bankruptcy problem, agents have claims with different amounts, whereas in a weighted bankruptcy problem, claims may not only vary in their amount, but also in their strength. First we discuss (weighted) bankruptcy problems for which the estate is continuous, such as an amount of money. Then we discuss versions of these problems for which the estate is discrete, such as a number of parliamentary seats. Finally, we discuss cooperative game theory, which can be used to model problems in which claims belong, first and foremost, to groups of agents. The presented overview of claims-based models and corresponding allocation rules is, deliberately, biased. For, models and rules are presented with an eye towards the extent to which they can elaborate on and make precise the idea that ‘fairness requires that claims are satisfied in proportion to their strength’. This idea has been advocated for, in the philosophical literature, by a.o. Nicholas Rescher and John Broome. This chapter sketches the philosophical underpinning of ‘proportional claims-based fairness’ and briefly introduces the aforementioned claims-based models. In subsequent chapters, the various claims-based models, their allocation rules, and ‘results on proportionality’ will be discussed in more detail.