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 language | English |
|---|---|
| Article number | 39 |
| Journal | Journal of the ACM |
| Volume | 64 |
| Issue number | 6 |
| DOIs | |
| State | Published - Nov 2017 |
| Externally published | Yes |
Bibliographical note
Funding Information:This work was supported by the EU FP7 FET project, grant agreement n.600854; by the National Science Foundation under grants IIS-1350598, CCF-1215883, and CCF-1525932; and by a Sloan Research Fellowship. A preliminary version of this article was presented at the 17th ACM Conference on Economics and Computation (EC’16). Authors’ addresses: Y. Gal and M. Mash, Dept. of Information Systems Engineering; Ben-Gurion University, Israel, Beer-Sheva; email: kobig@bgu.ac.il, mashm@post.bgu.ac.il. A. Procaccia and Y. Zick, Computer Science Department, Carnegie Mellon University, USA, Pittburgh, PA; email: {arielpro,yairzick}@cs.cmu.edu. Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than the author(s) must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from permissions@acm.org. 2017 Copyright is held by the owner/author(s). Publication rights licensed to ACM. ACM 0004-5411/2017/11-ART39 $15.00 https://doi.org/10.1145/3131361
Funding Information:
This work was supported by the EU FP7 FET project, grant agreement n.600854; by the National Science Foundation under grants IIS-1350598, CCF-1215883, and CCF-1525932; and by a Sloan Research Fellowship.
Publisher Copyright:
© 2017 Copyright is held by the owner/author(s). Publication rights licensed to ACM.
Keywords
- Computational fair division