On two competing mechanisms for priority-based allocation problems

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. The prevalent affirmative action policy in school choice limits the number of admitted majority students to give minority students higher chances to attend their desired schools. There have been numerous efforts to reconcile affirmative action policies with celebrated matching mechanisms such as the deferred acceptance and top trading cycles algorithms. Nevertheless, it is theoretically shown that under these algorithms, the policy based on majority quotas may be detrimental to minorities. Using simulations, we find that this is a more common phenomenon rather than a peculiarity. To circumvent the inefficiency caused by majority quotas, we offer a different interpretation of the affirmative action policies based on minority reserves. With minority reserves, schools give higher priority to minority students up to the point that the minorities fill the reserves. We compare the welfare effects of these policies. The deferred acceptance algorithm with minority reserves Pareto dominates the one with majority quotas. Our simulations, which allow for correlations between student preferences and school priorities, indicate that minorities are, on average, better off with minority reserves while adverse effects on majorities are mitigated. Terms of use: Documents in

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“…6 Kesten (2006) shows that these two mechanisms are the same if and only if school priorities are acyclic.…”

Section: Related Literaturementioning

confidence: 99%

Effective Affirmative Action in School Choice

2011

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“…Sasaki and Toda (1992) show that the core correspondence for marriage markets satisfies converse consistency and that this property is part of a core 1 Sometimes it is also assumed that exactly one position of each type is available. Some recent articles on house allocation problems are Ergin (2000), Ehlers (2002), Ehlers et al (2002), and Ehlers and Klaus (2003, 2006, 2007.…”

Section: Introductionmentioning

confidence: 99%

“…2 See, for instance, Balinski and Sönmez (1999), Ergin (2002), and Kesten (2006). 3 For instance, Thomson's (2009, page 16) "Fundamental Definition" of consistency deals with a variable population setup and imposes the consistency requirement on all subpopulations as well.…”

Section: Introductionmentioning

confidence: 99%

Local and global consistency properties for student placement

Klaus

Klijn

2013

Journal of Mathematical Economics

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In the context of resource allocation on the basis of priorities, Ergin (2002) identifies a necessary and sufficient condition on the priority structure such that the student-optimal stable mechanism satisfies a consistency principle. Ergin (2002) formulates consistency as a local property based on a fixed population of agents and fixed resources -we refer to this condition as local consistency and to his condition on the priority structure as local acyclicity. We identify a related but stronger necessary and sufficient condition (unit acyclicity) on the priority structure such that the student-optimal stable mechanism satisfies a more standard global consistency property.Next, we provide necessary and sufficient conditions for the student-optimal stable mechanism to satisfy converse consistency principles. We identify a necessary and sufficient condition (local shift-freeness) on the priority structure such that the student-optimal stable mechanism satisfies local converse consistency. Interestingly, local acyclicity implies local shift-freeness and hence the student-optimal stable mechanism more frequently satisfies local converse consistency than local consistency. Finally, in order for the student-optimal stable mechanism to be globally conversely consistent, one again has to impose unit acyclicity on the priority structure. Hence, unit acyclicity is a necessary and sufficient condition on the priority structure for the student-optimal stable mechanism to satisfy global consistency or global converse consistency. JEL classification: D63, C78.

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“…Some recent articles on house allocation problems are Ehlers (2002), Ehlers et al (2002), and Ehlers andKlaus (2003, 2006a,b). 2 See, for instance, Balinski and Sönmez (1999), Ergin (2002), and Kesten (2006). "close enough together" in the priority ranking of all position types.…”

Section: Introductionmentioning

confidence: 99%

Fair and efficient student placement with couples

Klaus

Klijn

2007

Int J Game Theory

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We study situations of allocating positions to students based on priorities. An example is the assignment of medical students to hospital residencies on the basis of entrance exams. For markets without couples, e.g., for undergraduate student placement, acyclicity is a necessary and sufficient condition for the existence of a fair and efficient placement mechanism (Ergin in Econometrica 70: [2489][2490][2491][2492][2493][2494][2495][2496][2497] 2002). We show that in the presence of couples acyclicity is still necessary, but not sufficient. A second necessary condition is priority-togetherness of couples. A priority structure that satisfies both necessary conditions is called pt-acyclic.For student placement problems where all quotas are equal to one we characterize pt-acyclicity and show that it is a sufficient condition for the existence of a fair and efficient placement mechanism. If in addition to pt-acyclicity we require reallocation-and vacancy-fairness for couples, the so-called dictatorbidictator placement mechanism is the unique fair and efficient placement mechanism.Finally, for general student placement problems, we show that pt-acyclicity may not be sufficient for the existence of a fair and efficient placement mechanism. We identify a sufficient condition such that the so-called sequential placement mechanism produces a fair and efficient allocation.

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On two competing mechanisms for priority-based allocation problems

Cited by 139 publications

References 16 publications

Effective Affirmative Action in School Choice

Effective Affirmative Action in School Choice

Local and global consistency properties for student placement

Fair and efficient student placement with couples

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