Possible Fairness for Allocating Indivisible Resources
Abstract: Fair division of indivisible resources has attracted significant attention from multi-agent systems and computational social choice. Two popular solution concepts are envy-freeness up to any item (EFX) and maximin share (MMS) fairness which are defined using agents' cardinal preferences. On one hand, accurate cardinal values are hard to express in real-life applications, and on the other hand, with cardinal values, MMS and EFX may not be easy to satisfy. In this work, we study a new setting where agents have arbitrary ordinal preferences for the items (possibly with indifferences), and an allocation is called possible EFX (p-EFX) or possible MMS (p-MMS) if there exist cardinal preferences that are consistent with the ordinal ones so that the allocation is EFX or MMS.We first design a polynomial-time algorithm to compute an allocation that is p-EFX and p-MMS under lexicographic preferences. This result also strengthens a result of Hosseini et al.(AAAI 2021) who proved the existence of EFX and MMS allocations under strict lexicographic preferences (i.e., the items do not have ties). Although it has been well justified that lexicographic preferences are natural and common, there are situations where they do not fit appropriately, especially when the items have similar types. Therefore, on top of p-EFX and p-MMS, we want the allocation to be balanced (i.e., the numbers of items allocated to the agents differ by at most one). We then design another algorithm that satisfies p-EFX, p-MMS, and balanced simultaneously.
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