Which is the fairest (rent division) of them all?

Ya'Akov Gal, Moshe Mash, Ariel D. Procaccia, Yair Zick

Research output: Contribution to journalArticlepeer-review

37 Scopus citations

Abstract

What is a fair way to assign rooms to several housemates and divide the rent between them? This is not just a theoretical question: many people have used the Spliddit website to obtain envy-free solutions to rent division instances. But envy freeness, in and of itself, is insufficient to guarantee outcomes that people view as intuitive and acceptable. We therefore focus on solutions that optimize a criterion of social justice, subject to the envy-freeness constraint, in order to pinpoint the "fairest" solutions. We develop a general algorithmic framework that enables the computation of such solutions in polynomial time. We then study the relations between natural optimization objectives and identify the maximin solution, which maximizes the minimum utility subject to envy freeness, as the most attractive. We demonstrate, in theory and using experiments on real data from Spliddit, that the maximin solution gives rise to significant gains in terms of our optimization objectives. Finally, a user study with Spliddit users as subjects demonstrates that people find the maximin solution to be significantly fairer than arbitrary envy-free solutions; this user study is unprecedented in that it asks people about their real-world rent division instances. Based on these results, the maximin solution has been deployed on Spliddit since April 2015.

Original languageEnglish
Article number39
JournalJournal of the ACM
Volume64
Issue number6
DOIs
StatePublished - Nov 2017
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2017 Copyright is held by the owner/author(s). Publication rights licensed to ACM.

Keywords

  • Computational fair division

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