Two Birds With One Stone: Fairness and Welfare via Transfers

06/01/2021
by   Vishnu V. Narayan, et al.
0

We study the question of dividing a collection of indivisible goods amongst a set of agents. The main objective of research in the area is to achieve one of two goals: fairness or efficiency. On the fairness side, envy-freeness is the central fairness criterion in economics, but envy-free allocations typically do not exist when the goods are indivisible. A recent line of research shows that envy-freeness can be achieved if a small quantity of a homogeneous divisible good (money) is introduced into the system, or equivalently, if transfer payments are allowed between the agents. A natural question to explore, then, is whether transfer payments can be used to provide high welfare in addition to envy-freeness, and if so, how much money is needed to be transferred. We show that for general monotone valuations, there always exists an allocation with transfers that is envy-free and whose Nash social welfare (NSW) is at least an e^-1/e-fraction of the optimal Nash social welfare. Additionally, when the agents have additive valuations, an envy-free allocation with negligible transfers and whose NSW is within a constant factor of optimal can be found in polynomial time. Consequently, we demonstrate that the seemingly incompatible objectives of fairness and high welfare can be achieved simultaneously via transfer payments, even for general valuations, when the welfare objective is NSW. On the other hand, we show that a similar result is impossible for utilitarian social welfare: any envy-freeable allocation that achieves a constant fraction of the optimal welfare requires non-negligible transfers. To complement this result we present algorithms that compute an envy-free allocation with a given target welfare and with bounded transfers.

READ FULL TEXT
POST COMMENT

Comments

There are no comments yet.

Authors

page 1

page 2

page 3

page 4

07/14/2020

Almost Envy-freeness, Envy-rank, and Nash Social Welfare Matchings

Envy-free up to one good (EF1) and envy-free up to any good (EFX) are tw...
02/28/2022

Setting Fair Incentives to Maximize Improvement

We consider the problem of helping agents improve by setting short-term ...
06/04/2021

Approximating Nash Social Welfare under Binary XOS and Binary Subadditive Valuations

We study the problem of allocating indivisible goods among agents in a f...
04/13/2022

Fair Algorithm Design: Fair and Efficacious Machine Scheduling

Motivated by a plethora of practical examples where bias is induced by a...
02/16/2020

Pipeline Interventions

We introduce the pipeline intervention problem, defined by a layered dir...
05/26/2019

Justifications of Welfare Guarantees under Normalized Utilities

It is standard in computational social choice to analyse welfare conside...
01/27/2020

The Empirical Core of the Multicommodity Flow Game Without Side Payments

Policy makers focus on stable strategies as the ones adopted by rational...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.