Fairly dividing uncertain goods improves post-allocation satisfaction
Fair Division of Lotteries
Computer Science and Game Theory
Summary
The paper looks at how to share items whose values are not known until after they are divided. It studies fairness from two angles: before the values are known (ex-ante) and after they are revealed (ex-post). The authors find conditions where making a fair division beforehand also makes it likely to be considered fair after values are known. They also explore how difficult it is to measure fairness after values become clear and offer some algorithms for it.
What this means in practice
- •For resource allocation teams: Assign items with uncertain value fairly to increase the chance recipients feel treated just after outcomes are known.
- •For economics software developers: Create tools to compute allocation plans that balance fairness before and after randomness resolves in auctions or markets.
A theory result. No direct application yet.
Authors
Ayumi Igarashi, Yeeseok Oh
Abstract
We study fair division of uncertain items, where the utility of each item is a random variable whose realization is observed only after the allocation is determined. This uncertainty creates a distinction between ex-ante fairness, evaluated before utilities are realized, and ex-post fairness, evaluated after realization. We examine to what extent these two notions are compatible. We first identify conditions under which ex-ante envy-free allocations maximize ex-post envy-freeness probability. These include two-agent instances where utilities toward the same item follow the same distribution from a convolution-power family. For an arbitrary number of agents, we establish analogous optimality results when the common generator is non-atomic or log-concave. Beyond convolution-power families, we derive approximation guarantees for ex-ante envy-free allocations relative to the optimal ex-post envy-freeness probability under log-concave or symmetric utilities. We also study the computational complexity of evaluating ex-post envy-freeness probabilities, establishing hardness results as well as pseudo-polynomial-time algorithms.