On the Difficulty of Budget Allocation in Claims Problems with Indivisible Items and Prices

In this paper we study the class of claims problems where the amount to be divided is perfectly divisible and claims are made on indivisible units of several items. Each item has a price, and the available amount falls short to be able to cover all the claims at the given prices. We propose several properties that may be of interest in this particular framework. These properties represent the common principles of fairness, efficiency, and non-manipulability by merging or splitting. Efficiency is our focal principle, which is formalized by means of two axioms: non-wastefulness and Pareto efficiency. We show that some combinations of the properties we consider are compatible, others are not.

Book Reviews

Alexander Nesterov of Higher School of Economics reviews “How to Divide When There Isn't Enough: From Aristotle, the Talmud, and Maimonides to the Axiomatics of Resource Allocation,” by William Thomson. The Econlit abstract of this book begins: “Explores the resolution of claims problems using division rules, focusing on an axiomatic approach.”

Fairness Concepts

Issues of fairness arise in many different situations that involve a certain distribution of resources, an allocation of costs or objects, or any other algorithmic division process. This chapter discusses these issues of fairness. It starts with an introduction to certain general aspects of fairness for the models at stake, dealing especially with the concept of responsibility. In the following sections, the focus lies in particular on some specific fair division settings, such as claims problems, cost sharing, and the division of indivisible items. We introduce various well-known fair division procedures and discuss their normative foundations in terms of widely used axioms in the literature. Several numerical examples are provided.