The Multi-unit Assignment Problem: Theory and Evidence from Course Allocation at Harvard

Budish, Eric; Cantillon, Estelle

doi:10.1257/aer.102.5.2237

Cited by 227 publications

(193 citation statements)

References 43 publications

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“…An approach based on estimated preferences complements survey data for comparing mechanisms. For instance, Budish and Cantillon (2012) use survey data on a multi-unit course allocation mechanism and find that more students are assigned to preferable choices in a strategy-proof mechanism than in the draft mechanism used at the Harvard Business School. Finally, our work relates to comparisons of decentralized and centralized medical labor markets by Niederle and Roth (2003).…”

mentioning

confidence: 99%

The Welfare Effects of Coordinated Assignment: Evidence from the New York City High School Match

Abdulkadiroğlu

Agarwal²,

Pathak³

2017

American Economic Review

115

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In recent years, market design theory has inspired dramatic changes in how children are assigned to public schools across numerous American cities and around the world. The first new system adopted was for placing eighth graders into high schools in New York City (NYC). NYC's new system has not only received widespread scientific and popular acclaim (Economic Sciences Prize Committee 2012; Tullis 2014; Roth 2015), but also became a template for reforms in other cities. 1 Despite widespread adoption of and apparent consensus on the value of market-design-inspired

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mentioning

confidence: 99%

The Welfare Effects of Coordinated Assignment: Evidence from the New York City High School Match

Abdulkadiroğlu

Agarwal²,

Pathak³

2017

American Economic Review

115

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“…Multi-unit assignment with exogenous quotas, commonly known as the Course Allocation Problem (CAP), described by Brams and Kilgour (2001); Budish (2011);Budish and Cantillon (2012); Kominers et al (2010);Krishna andÜnver (2008);and Sönmez and Unver (2010), with an important difference. In CAP the number of seats available for each course (in this case game slots per day) is fixed and given exogenously, whereas in GTPs the number of seats is determined endogenously by players' preferences, representing the real possibility that the number of courses is not fully fixed in practice.…”

Section: Related Literaturementioning

confidence: 99%

Random Multi-Unit Assignment with Endogenous Quotas

Ortega

2017

SSRN Journal

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We study the random multi-unit assignment problem in which the number of goods to be distributed depends on players' preferences.In this setup, the egalitarian solution is more appealing than the competitive equilibrium with equal incomes because it is Lorenz dominant, unique in utilities, and impossible to manipulate by groups when agents have dichotomous preferences.Moreover, it can be adapted to satisfy a new fairness axiom that arises naturally in this context. Both solutions are disjoint.Two standard results disappear. The competitive solution can no longer be computed with the Eisenberg-Gale program maximizing the Nash product, and the competitive equilibrium with equal incomes is no longer unique in its corresponding utility profile.

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“…Other works that use continuum matching models include Abdulkadiroglu et al (2008), Miralles (2008), and Budish and Cantillon (2012).…”

Section: Large Market Modelmentioning

confidence: 99%

Improving Community Cohesion in School Choice via Correlated-Lottery Implementation

Ashlagi

Shi

2014

Operations Research

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In school choice, children submit a preference ranking over schools to a centralized assignment algorithm, which takes into account schools' priorities over children and uses randomization to break ties. One criticism of existing school choice mechanisms is that they tend to disperse communities so children do not go to school with others from their neighborhood.We suggest to improve community cohesion by implementing a correlated lottery in a given school choice mechanism:we find a convex combination of deterministic assignments that maintains the original assignment probabilities, thus maintaining choice, but improving community cohesion.To analyze the gain in cohesion for a wide class of mechanisms, we first prove the following characterization which may be of independent interest: any mechanism which, in the large market limit, is non-atomic, Bayesian incentive compatible, symmetric and efficient within each priority class, is a "lottery-plus-cutoff" mechanism. This means that the large market limit can be described as follows: given the distribution of preferences, every student receives an identically distributed lottery number, every school sets a lottery cutoff for each priority class, and a student is assigned her most preferred school for which she meets the cutoff. This generalizes Liu and Pycia (2012) to allow arbitrary priorities. Using this, we derive analytic expressions for maximum cohesion under a large market approximation. We show that the benefit of lottery-correlation is greater when students' preferences are more correlated.In practice, although the correlated-lottery implementation problem is NP-hard, we present a heuristic that does well.We apply this to real data from Boston elementary school choice 2012 and find that we can increase cohesion by 79% for K1 and 37% for K2 new families. Greater cohesion gain is possible (tripling cohesion for K1 and doubling for K2) if we reduce the choice menus on top of applying lottery-correlation.

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The Multi-unit Assignment Problem: Theory and Evidence from Course Allocation at Harvard

Cited by 227 publications

References 43 publications

The Welfare Effects of Coordinated Assignment: Evidence from the New York City High School Match

The Welfare Effects of Coordinated Assignment: Evidence from the New York City High School Match

Random Multi-Unit Assignment with Endogenous Quotas

Improving Community Cohesion in School Choice via Correlated-Lottery Implementation

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