Design of Lotteries and Waitlists for Affordable Housing Allocation

64 Pages Posted: 4 May 2017 Last revised: 27 Jul 2018

Nick Arnosti

Columbia Business School - Decisions, Risk, and Operations Division

Peng Shi

University of Southern California - Marshall School of Business

Date Written: February 13, 2017

Abstract

We study a setting in which dynamically arriving items are assigned to waiting agents, who have heterogeneous values for distinct items and heterogeneous outside options. An ideal match would both target items to agents with the worst outside options, and match them to items for which they have high value.

Our first finding is that two common approaches -- using independent lotteries for each item, and using a waitlist in which agents lose priority when they reject an offer -- lead to identical outcomes in equilibrium. Both approaches encourage agents to accept items that are marginal fits. We show that the quality of the match can be improved by using a common lottery for all items. If participation costs are negligible, a common lottery is equivalent to several other mechanisms, such as limiting participants to a single lottery, using a waitlist in which offers can be rejected without punishment, or using artificial currency.

However, when there are many agents with low need, there is an unavoidable tradeoff between matching and targeting. In this case, utilitarian welfare may be maximized by focusing on good matching (if the outside option distribution is light-tailed) or good targeting (if it is heavy-tailed). Using a common lottery achieves near-optimal matching, while introducing participation costs achieves near-optimal targeting.

JEL Classification: C78, D82, D44

Suggested Citation

Arnosti, Nick and Shi, Peng, Design of Lotteries and Waitlists for Affordable Housing Allocation (February 13, 2017). Columbia Business School Research Paper No. 17-52. Available at SSRN: https://ssrn.com/abstract=2963178 or http://dx.doi.org/10.2139/ssrn.2963178

Nick Arnosti (Contact Author)

Columbia Business School - Decisions, Risk, and Operations Division ( email )

3022 Broadway
New York, NY 10027
United States

Peng Shi

University of Southern California - Marshall School of Business ( email )

701 Exposition Blvd
Los Angeles, CA 90089
United States

Register to save articles to
your library

Register

Paper statistics

Downloads
342
rank
80,817
Abstract Views
1,318
PlumX