Decomposition Envy-Freeness in Random Assignment
For researchers in fair division and random assignment, this work addresses a subtle but important flaw in existing fairness notions.
The paper identifies that stochastic-dominance envy-free (SD-EF) random assignments can have decompositions where agents envy each other with high probability. To fix this, they introduce decomposition envy-freeness (Dec-EF) and prove that SD-EF assignments always admit a Dec-EF decomposition for up to three agents or two distinct preference types.
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.