Envy-freeness up to one item: Shall we add or remove resources?
This work addresses fair resource allocation problems in computational economics and social choice, but appears incremental as it modifies existing fairness concepts.
The paper tackles fair division of indivisible items by proposing two new axiomatic properties (EF1+- and EFX+-) and comparing them with existing ones (EF1 and EFX). It shows that EFX+- allocations exist in cases where EFX allocations do not, while also proving new impossibility results.
We consider a fair division model in which agents have general valuations for bundles of indivisible items. We propose two new axiomatic properties for allocations in this model: EF1+- and EFX+-. We compare these with the existing EF1 and EFX. Although EF1 and EF1+- allocations often exist, our results assert eloquently that EFX+- and PO allocations exist in each case where EFX and PO allocations do not exist. Additionally, we prove several new impossibility and incompatibility results.