The Division Problem of Chances

TL;DR

This paper studies how to fairly and efficiently divide chances among agents with preferences represented by ideal lotteries, proposing mechanisms that satisfy key fairness and strategic properties.

Contribution

It introduces URC mechanisms for dividing chances and proves their equivalence to any mechanism satisfying multiple desirable properties.

Findings

URC mechanisms satisfy strategy proofness, efficiency, and fairness.

Any mechanism with these properties is equivalent to a URC mechanism.

The framework addresses preference representation via ideal lotteries in matching problems.

Abstract

In frequently repeated matching scenarios, individuals may require diversification in their choices. Therefore, when faced with a set of potential outcomes, each individual may have an ideal lottery over outcomes that represents their preferred option. This suggests that, as people seek variety, their favorite choice is not a particular outcome, but rather a lottery over them as their peak for their preferences. We explore matching problems in situations where agents' preferences are represented by ideal lotteries. Our focus lies in addressing the challenge of dividing chances in matching, where agents express their preferences over a set of objects through ideal lotteries that reflect their single-peaked preferences. We discuss properties such as strategy proofness, replacement monotonicity, (Pareto) efficiency, in-betweenness, non-bossiness, envy-freeness, and anonymity in the context of dividing chances, and propose a class of mechanisms called URC mechanisms that satisfy these properties. Subsequently, we prove that if a mechanism for dividing chances is strategy proof, (Pareto) efficient, replacement monotonic, in-between, non-bossy, and anonymous (or envy free), then it is equivalent in terms of welfare to a URC mechanism.