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Two desirable fairness concepts for allocation of indivisible objects under ordinal preferences

Two desirable fairness concepts for allocation of indivisible objects under ordinal preferences Two Desirable Fairness Concepts for Allocation of Indivisible Objects under Ordinal Preferences HARIS AZIZ and SERGE GASPERS and SIMON MACKENZIE and TOBY WALSH Data61 and UNSW Fair allocation of indivisible objects under ordinal preferences is an important problem. Unfortunately, a fairness notion like envy- freeness is both incompatible with Pareto optimality and is also NP-complete to achieve. To tackle this predicament, we consider a different notion of fairness, namely proportionality. We frame allocation of indivisible objects as randomized assignment but with integrality requirements. We then use the stochastic dominance relation to define two natural notions of proportionality. Since an assignment may not exist even for the weaker notion of proportionality, we propose relaxations of the concepts -- optimal weak proportionality and optimal proportionality. For both concepts, we propose algorithms to compute fair assignments under ordinal preferences. Both new fairness concepts appear to be desirable in view of the following: they are compatible with Pareto optimality, admit efficient algorithms to compute them, are based on proportionality, and are guaranteed to exist. Categories and Subject Descriptors: F.2.2 [Analysis of Algorithms and Problem Complexity]: Nonnumerical Algorithms and Problems; I.2.11 [Distributed Artificial Intelligence]: Multiagent Systems; J.4 [Computer Applications]: Social and Behavioral Sciences--Economics http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png ACM SIGecom Exchanges Association for Computing Machinery

Two desirable fairness concepts for allocation of indivisible objects under ordinal preferences

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Publisher
Association for Computing Machinery
Copyright
Copyright © 2016 by ACM Inc.
ISSN
1551-9031
DOI
10.1145/2904104.2904106
Publisher site
See Article on Publisher Site

Abstract

Two Desirable Fairness Concepts for Allocation of Indivisible Objects under Ordinal Preferences HARIS AZIZ and SERGE GASPERS and SIMON MACKENZIE and TOBY WALSH Data61 and UNSW Fair allocation of indivisible objects under ordinal preferences is an important problem. Unfortunately, a fairness notion like envy- freeness is both incompatible with Pareto optimality and is also NP-complete to achieve. To tackle this predicament, we consider a different notion of fairness, namely proportionality. We frame allocation of indivisible objects as randomized assignment but with integrality requirements. We then use the stochastic dominance relation to define two natural notions of proportionality. Since an assignment may not exist even for the weaker notion of proportionality, we propose relaxations of the concepts -- optimal weak proportionality and optimal proportionality. For both concepts, we propose algorithms to compute fair assignments under ordinal preferences. Both new fairness concepts appear to be desirable in view of the following: they are compatible with Pareto optimality, admit efficient algorithms to compute them, are based on proportionality, and are guaranteed to exist. Categories and Subject Descriptors: F.2.2 [Analysis of Algorithms and Problem Complexity]: Nonnumerical Algorithms and Problems; I.2.11 [Distributed Artificial Intelligence]: Multiagent Systems; J.4 [Computer Applications]: Social and Behavioral Sciences--Economics

Journal

ACM SIGecom ExchangesAssociation for Computing Machinery

Published: Mar 16, 2016

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