Decomposition Envy-Freeness in Random Assignment
Yasushi Kawase, Warut Suksompong, Hanna Sumita, Yu Yokoi
TLDR
Introduces Decomposition Envy-Freeness (Dec-EF) to address envy in random assignment decompositions, showing its existence for specific cases.
Key contributions
- Identifies that Stochastic-Dominance Envy-Freeness (SD-EF) can still lead to high-probability envy in decompositions.
- Proposes Decomposition Envy-Freeness (Dec-EF) as a new fairness property for assignment decompositions.
- Clarifies Dec-EF as a property of the decomposition itself, distinct from the assignment matrix.
- Proves SD-EF assignments always admit a Dec-EF decomposition for <=3 agents or <=2 distinct preferences.
Why it matters
This paper addresses a critical flaw in the widely used SD-EF fairness concept for random assignments, showing it can fail in practice. By introducing Dec-EF, it provides a stronger, more robust fairness guarantee. This advances the design of fair allocation mechanisms by offering a refined criterion.
Original 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.
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