Decomposition Envy-Freeness in Random Assignment

TL;DR

This paper introduces decomposition envy-freeness (Dec-EF), a new fairness concept in random assignment that addresses limitations of stochastic-dominance envy-freeness (SD-EF) by focusing on decompositions rather than assignments.

Contribution

It proposes Dec-EF as a novel fairness criterion and proves that SD-EF assignments always admit Dec-EF decompositions under certain conditions.

Findings

SD-EF assignments admit Dec-EF decompositions for up to three agents.

Dec-EF focuses on decompositions, not just assignment matrices.

Addresses limitations of SD-EF in random assignment fairness.

Abstract

In random assignment, fairness is often captured by stochastic-dominance envy-freeness (SD-EF). We observe that assignments satisfying SD-EF may admit decompositions that result in each agent envying another agent with high probability. To address this, we introduce decomposition envy-freeness (Dec-EF), which is a property of a decomposition rather than of an assignment matrix. We show that an SD-EF assignment matrix always admits a Dec-EF decomposition when there are at most three agents or the agents have at most two distinct preferences.