Guaranteed shares of benefits and costs

2024-06-20

arXiv.org

AI Summary

This paper addresses fairness guarantees in public resource allocation, focusing on bounding individual agents’ benefits and costs under a common-pool resource regime. Methodologically, it introduces a symmetric tight-bound guarantee framework grounded in the self-ownership axiom: (i) it characterizes existence conditions for unique upper/lower guarantees via supermodularity/submodularity; (ii) in the bimodular case, it identifies infinitely many tight guarantees, each reflecting distinct normative positions. Theoretically, it establishes precise existence criteria and a structured taxonomy of upper and lower guarantees. Practically, it designs interpretable, implementable guarantee-based allocation rules for canonical settings—including indivisible goods allocation, joint production, and facility location—thereby unifying fairness constraints with mechanism feasibility.

Technology Category

Game Theory and Economic Paradigms: Fair DivisionMultiagent Systems: Mechanism DesignConstraint Satisfaction and Optimization: Satisfiability Modulo Theories

Application Category

Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environmentsUser Modeling, Personalization and Recommendation: Fairness-aware retrieval and rankingSecurity and Privacy: Data transparency and provenance

Abstract

We revisit the self-ownership viewpoint to regulate the utilisation of common property resources. Allocating to each agent"the fruit of their own labor"is typically ill-depned, so we look for tight approximations of this decentralised ideal. For each agent i two guarantees limit, from above and below, the impact of other agents on i's allocation. They limit the range of unscripted negotiations, or the choice of a full sharing rule. Our context-free model of the commons is a mapping W from profiles of"types"to a freely transferable amount of benefit or cost. If W is super (resp. sub) modular there is a single tight upper (resp. lower) guarantee, and an infinite menu of tight lower (resp. upper) guarantees, each one conveying a precise normative viewpoint. We describe the menu for essentially all modular two person problems, and familiar examples like the allocation of an indivisible item, cooperative production, and facility location.

Problem

• Fair division of surplus in common property regimes
• Establishing tight share guarantees for different agent types
• Exploring fair sharing rules in economic contexts

Innovation

• Fair Division context-free problem solution
• Tight guarantees for benefit-cost shares
• New fair sharing rules from economic types