Fair Division Without Disparate Impact

TL;DR

This paper explores modifying the competitive equilibrium from equal incomes (CEEI) mechanism to ensure fair division without disparate impact, analyzing the tradeoffs between fairness, efficiency, and other desirable properties.

Contribution

It introduces two modified algorithms, equitable equilibrium and competitive equilibrium from equitable incomes, to address disparate impact in fair division, and analyzes their theoretical and experimental properties.

Findings

Removing disparate impact in outcomes breaks key properties like envy and Pareto optimality.

Removing disparate impact in utility levels preserves these properties.

Experimental results highlight tradeoffs between fairness, efficiency, and impact.

Abstract

We consider the problem of dividing items between individuals in a way that is fair both in the sense of distributional fairness and in the sense of not having disparate impact across protected classes. An important existing mechanism for distributionally fair division is competitive equilibrium from equal incomes (CEEI). Unfortunately, CEEI will not, in general, respect disparate impact constraints. We consider two types of disparate impact measures: requiring that allocations be similar across protected classes and requiring that average utility levels be similar across protected classes. We modify the standard CEEI algorithm in two ways: equitable equilibrium from equal incomes, which removes disparate impact in allocations, and competitive equilibrium from equitable incomes which removes disparate impact in attained utility levels. We show analytically that removing disparate impact in outcomes breaks several of CEEI's desirable properties such as envy, regret, Pareto optimality, and incentive compatibility. By contrast, we can remove disparate impact in attained utility levels without affecting these properties. Finally, we experimentally evaluate the tradeoffs between efficiency, equity, and disparate impact in a recommender-system based market.