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Lotteries in student assignment: An equivalence result

2011; Econometric Society; Volume: 6; Issue: 1 Linguagem: Inglês

10.3982/te816

1933-6837

Parag A. Pathak, Jay Sethuraman,

Smart Parking Systems Research

Theoretical EconomicsVolume 6, Issue 1 p. 1-17 Open Access Lotteries in student assignment: An equivalence result Parag A. Pathak, Parag A. Pathak Department of Economics, Massachusetts Institute of Technology; [email protected]Search for more papers by this authorJay Sethuraman, Jay Sethuraman Department of Industrial Engineering and Operations Research, Columbia University; [email protected] This paper is a combination of working papers by Pathak (2008) and Sethuraman (2009). We are grateful to Debraj Ray for encouraging us to collaborate. We are grateful to various seminar participants and anonymous referees for comments. Pathak is indebted to Susan Athey, Drew Fudenberg, Alvin E. Roth, and Tayfun Sönmez. Sethuraman is grateful to Thiam Lee and Hervé Moulin for many insightful discussions during the course of this research: It was an early conversation with Thiam Lee that led to a formulation of the PRP mechanism and Hervé Moulin suggested thinking about the PRE mechanism. We thank Stergios Athanassoglou and Yeon-Koo Che for detailed comments on an earlier draft of the paper. Pathak's research was supported by the National Science Foundation under Grant SES-0924555 and Sethuraman's research was supported by the National Science Foundation under Grant CMMI-0916453.Search for more papers by this author Parag A. Pathak, Parag A. Pathak Department of Economics, Massachusetts Institute of Technology; [email protected]Search for more papers by this authorJay Sethuraman, Jay Sethuraman Department of Industrial Engineering and Operations Research, Columbia University; [email protected] This paper is a combination of working papers by Pathak (2008) and Sethuraman (2009). We are grateful to Debraj Ray for encouraging us to collaborate. We are grateful to various seminar participants and anonymous referees for comments. Pathak is indebted to Susan Athey, Drew Fudenberg, Alvin E. Roth, and Tayfun Sönmez. Sethuraman is grateful to Thiam Lee and Hervé Moulin for many insightful discussions during the course of this research: It was an early conversation with Thiam Lee that led to a formulation of the PRP mechanism and Hervé Moulin suggested thinking about the PRE mechanism. We thank Stergios Athanassoglou and Yeon-Koo Che for detailed comments on an earlier draft of the paper. Pathak's research was supported by the National Science Foundation under Grant SES-0924555 and Sethuraman's research was supported by the National Science Foundation under Grant CMMI-0916453.Search for more papers by this author First published: 14 January 2011 https://doi.org/10.3982/TE816Citations: 53 AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Abstract This paper formally examines two competing methods of conducting a lottery to assign students to schools, motivated by the design of the centralized high school student assignment system in New York City. The main result of the paper is that single and multiple lottery mechanisms are equivalent for the problem of allocating students to schools in which students have strict preferences and the schools are indifferent. In proving this result, a new approach is introduced that simplifies and unifies all the known equivalence results in the house allocation literature. Along the way, two new mechanisms—Partitioned Random Priority and Partitioned Random Endowment—are introduced for the house allocation problem. These mechanisms generalize widely studied mechanisms for the house allocation problem and may be appropriate for the many-to-one setting such as the school choice problem. References Abdulkadiroğlu, Atila, Parag A. Pathak, and Alvin E. Roth (2005a), "The New York City high school match. American Economic Review (Papers and Proceedings), 95, 364– 367. DOI: 10.1257/000282805774670167 Abdulkadiroğlu, Atila, Parag A. Pathak, and Alvin E. Roth (2009), "Strategy-proofness versus efficiency in matching with indifferences: Redesigning the NYC high school match. American Economic Review, 99, 1954– 1978. DOI: 10.1257/aer.99.5.1954 Abdulkadiroğlu, Atila, Parag A. Pathak, Alvin E. Roth, and Tayfun Sönmez (2005b), "The Boston public school match. American Economic Review (Papers and Proceedings), 95, 368– 371. DOI: 10.1257/000282805774669637 Abdulkadiroğlu, Atila and Tayfun Sönmez (1998), "Random serial dictatorship and the core from random endowments in house allocation problems. Econometrica, 66, 689– 701. DOI: 10.2307/2998580 Abdulkadiroğlu, Atila and Tayfun Sönmez (2003), "School choice: A mechanism design approach. American Economic Review, 93, 729– 747. DOI: 10.1257/000282803322157061 Balinski, Michel and Tayfun Sönmez (1999), "A tale of two mechanisms: Student placement. Journal of Economic Theory, 84, 73– 94. 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Unpublished paper, Department of Economics, MIT . Pathak, Parag A. and Tayfun Sönmez (2008), "Leveling the playing field: Sincere and sophisticated players in the Boston mechanism. American Economic Review, 98, 1636– 1652. DOI: 10.1257/aer.98.4.1636 Roth, Alvin E. and Marilda A. Sotomayor (1990), Two-Sided Matching. Cambridge University Press, Cambridge . Sethuraman, Jay (2009), " An equivalence result in school choice." Unpublished paper, Department of Industrial Engineering and Operations Research, Columbia University . Shapley, Lloyd S. and Herbert E. Scarf (1974), "On cores and indivisibility. Journal of Mathematical Economics, 1, 23– 37. DOI: 10.1016/0304-4068(74)90033-0 Sönmez, Tayfun and M. Utku Ünver (2005), "House allocation with existing tenants: An equivalence. Games and Economic Behavior, 52, 153– 185. DOI: 10.1016/j.geb.2004.04.008 Stanley, Richard P. (1997), Enumerative Combinatorics, Volume 1. Cambridge University Press, Cambridge . Svensson, Lars-Gunnar and Bo Larsen (2005), "Strategy-proofness, core, and sequential trade. Review of Economic Design, 9, 167– 190. DOI: 10.1007/s10058-005-0126-x Citing Literature Volume6, Issue1January 2011Pages 1-17 ReferencesRelatedInformation