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Decomposition Envy-Freeness in Random Assignment

Author

Listed:
  • Yasushi Kawase
  • Warut Suksompong
  • Hanna Sumita
  • Yu Yokoi

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.

Suggested Citation

  • Yasushi Kawase & Warut Suksompong & Hanna Sumita & Yu Yokoi, 2026. "Decomposition Envy-Freeness in Random Assignment," Papers 2604.16973, arXiv.org.
    • Handle: RePEc:arx:papers:2604.16973
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    File URL: http://arxiv.org/pdf/2604.16973
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