Efficient lottery design

Abstract

Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in Onur Kesten Carnegie Mellon University Morimitsu Kurino University of Tsukuba Alexander Nesterov WZB Copyright remains with the author(s).Discussion papers of the WZB serve to disseminate the research results of work in progress prior to publication to encourage the exchange of ideas and academic debate. Inclusion of a paper in the discussion paper series does not constitute publication and should not limit publication in any other venue. The discussion papers published by the WZB represent the views of the respective author(s) and not of the institute as a whole. There has been a surge of interest in stochastic assignment mechanisms which proved to be theoretically compelling thanks to their prominent welfare properties. Contrary to stochastic mechanisms, however, lottery mechanisms are commonly used for indivisible good allocation in real-life. To help facilitate the design of practical lottery mechanisms, we provide new tools for obtaining stochastic improvements in lotteries. As applications, we propose lottery mechanisms that improve upon the widely-used random serial dictatorship mechanism and a lottery representation of its competitor, the probabilistic serial mechanism. The tools we provide here can be useful in developing welfare-enhanced new lottery mechanisms for practical applications such as school choice.

A pessimist’s approach to one-sided matching

“…As such, our column generation framework can be readily adapted to alternative assignment settings where ties have to be broken, or where probabilistic solution concepts are preferred. Next to RSD and PS, interesting probabilistic assignments to be decomposed are proposed by Ashlagi & Shi (2016), Ashlagi et al (2020), Kavitha et al (2011), Kesten et al (2017), andShi (2022).…”

“…Nevertheless, their method is not capable of imposing certain desirable criteria, such as ex-post efficiency, upon the matchings in the decomposition. Second, Kesten et al (2017) require the matchings to be ex-post efficient, but their algorithm does not allow the decision-maker to choose among the possibly many decompositions based on some worst-case measure or on alternative ex-post properties. The frameworks that we propose overcome both limitations.…”

Simultaneously Achieving Ex-ante and Ex-post Fairness

“…In order to ensure polynomial-time computability, they resort to a result by Grötschel et al [14] about convex polytopes and separation oracles. Kesten et al [19] also look at lottery implementation of the PS rule. However, their focus is on allocations with single-unit demand, in which case, any deterministic allocation in the support is trivially EF1.…”

Fair solutions to the random assignment problem

“…While the design of such lotteries has received a lot of attention in recent years, most of the work concentrates on their efficiency and incentive properties (i.e. what are the incentives for participants to reveal their true preferences) -see for example Erdil and Ergin [2008], Pathak and Sethuraman [2011], Abdulkadiroğlu et al [2015], Kesten et al [2017]. In this paper, we try to complement the literature by taking a closer look at the original motivation for applying a lottery and ask "when is a lottery fair?".…”