Guarantees in Fair Division: general or monotone preferences

TL;DR

This paper explores fairness guarantees in dividing private items among agents with non-atomic, continuous utilities, proposing methods to ensure minimum welfare levels under various preference assumptions.

Contribution

It introduces a framework for guaranteeing minMax utility in fair division with non-monotone preferences and proposes Bid & Choose rules for approximate guarantees.

Findings

Guarantee of minMax utility in non-atomic, continuous utility settings.

Impossibility of guaranteeing Maxmin utility in general.

Bid & Choose rules interpolate between minMax and Maxmin guarantees.

Abstract

To divide a "manna" {\Omega} of private items (commodities, workloads, land, time intervals) between n agents, the worst case measure of fairness is the welfare guaranteed to each agent, irrespective of others' preferences. If the manna is non atomic and utilities are continuous (not necessarily monotone or convex), we can guarantee the minMax utility: that of our agent's best share in her worst partition of the manna; and implement it by Kuhn's generalisation of Divide and Choose. The larger Maxmin utility -- of her worst share in her best partition -- cannot be guaranteed, even for two agents. If for all agents more manna is better than less (or less is better than more), our Bid & Choose rules implement guarantees between minMax and Maxmin by letting agents bid for the smallest (or largest) size of a share they find acceptable.