TY - GEN

T1 - Fair Division via Quantile Shares

AU - Babichenko, Yakov

AU - Feldman, Michal

AU - Holzman, Ron

AU - Narayan, Vishnu V.

N1 - Publisher Copyright:
© 2024 Copyright held by the owner/author(s).

PY - 2024/6/10

Y1 - 2024/6/10

N2 - We consider the problem of fair division, where a set of indivisible goods should be distributed fairly among a set of agents with combinatorial valuations. To capture fairness, we adopt the notion of shares, where each agent is entitled to a fair share, based on some fairness criterion, and an allocation is considered fair if the value of every agent (weakly) exceeds her fair share. A share-based notion is considered universally feasible if it admits a fair allocation for every profile of monotone valuations. A major question arises: is there a non-trivial share-based notion that is universally feasible? The most well-known share-based notions, namely the proportional share and the maximin share, are not universally feasible, nor are any constant approximations of them. We propose a novel share notion, where an agent assesses the fairness of a bundle by comparing it to her valuation in a random allocation. In this framework, a bundle is considered q-quantile fair, for q∈[0,1], if it is at least as good as a bundle obtained in a uniformly random allocation with probability at least q. Our main question is whether there exists a constant value of q for which the q-quantile share is universally feasible. Our main result establishes a strong connection between the feasibility of quantile shares and the classical Erdos Matching Conjecture. Specifically, we show that if a version of this conjecture is true, then the 1/2e-quantile share is universally feasible. Furthermore, we provide unconditional feasibility results for additive, unit-demand and matroid-rank valuations for constant values of q. Finally, we discuss the implications of our results for other share notions.

AB - We consider the problem of fair division, where a set of indivisible goods should be distributed fairly among a set of agents with combinatorial valuations. To capture fairness, we adopt the notion of shares, where each agent is entitled to a fair share, based on some fairness criterion, and an allocation is considered fair if the value of every agent (weakly) exceeds her fair share. A share-based notion is considered universally feasible if it admits a fair allocation for every profile of monotone valuations. A major question arises: is there a non-trivial share-based notion that is universally feasible? The most well-known share-based notions, namely the proportional share and the maximin share, are not universally feasible, nor are any constant approximations of them. We propose a novel share notion, where an agent assesses the fairness of a bundle by comparing it to her valuation in a random allocation. In this framework, a bundle is considered q-quantile fair, for q∈[0,1], if it is at least as good as a bundle obtained in a uniformly random allocation with probability at least q. Our main question is whether there exists a constant value of q for which the q-quantile share is universally feasible. Our main result establishes a strong connection between the feasibility of quantile shares and the classical Erdos Matching Conjecture. Specifically, we show that if a version of this conjecture is true, then the 1/2e-quantile share is universally feasible. Furthermore, we provide unconditional feasibility results for additive, unit-demand and matroid-rank valuations for constant values of q. Finally, we discuss the implications of our results for other share notions.

KW - Erdos Matching Conjecture

KW - Fair Division

KW - Quantile Share

UR - http://www.scopus.com/inward/record.url?scp=85196612656&partnerID=8YFLogxK

U2 - 10.1145/3618260.3649728

DO - 10.1145/3618260.3649728

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AN - SCOPUS:85196612656

T3 - Proceedings of the Annual ACM Symposium on Theory of Computing

SP - 1235

EP - 1246

BT - STOC 2024 - Proceedings of the 56th Annual ACM Symposium on Theory of Computing

A2 - Mohar, Bojan

A2 - Shinkar, Igor

A2 - O�Donnell, Ryan

T2 - 56th Annual ACM Symposium on Theory of Computing, STOC 2024

Y2 - 24 June 2024 through 28 June 2024

ER -