Decomposition Envy-Freeness in Random Assignment

Yasushi Kawase, Warut Suksompong, Hanna Sumita and Yu Yokoi

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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.

Date: 2026-04
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Published in Mathematical Social Sciences, 141:102532 (2026)

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