Swap Bounded Envy

TL;DR

This paper explores a new fairness concept called swap bounded envy in discrete goods allocation, proposing an algorithm to achieve this fairness under certain preference restrictions.

Contribution

It introduces the notion of swap bounded envy and provides an algorithm to attain this fairness criterion in discrete allocations.

Findings

Proposes swap bounded envy as a new fairness measure.

Develops an algorithm achieving swap bounded envy under preference restrictions.

Advances fairness in discrete allocations where envy-free solutions are impossible.

Abstract

We study fairness in the allocation of discrete goods. Exactly fair (envy-free) allocations are impossible, so we discuss notions of approximate fairness. In particular, we focus on allocations in which the swap of two items serves to eliminate any envy, either for the allocated bundles or with respect to a reference bundle. We propose an algorithm that, under some restrictions on agents' preferences, achieves an allocation with ``swap bounded envy.''