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.
Cite
@article{arxiv.2604.16973,
title = {Decomposition Envy-Freeness in Random Assignment},
author = {Yasushi Kawase and Warut Suksompong and Hanna Sumita and Yu Yokoi},
journal= {arXiv preprint arXiv:2604.16973},
year = {2026}
}