scholarly journals The Review of Methods for Assignment of Elective Courses at Universities

2019 ◽  
Vol 57 (4) ◽  
pp. 511-526
Author(s):  
Dejan Trifunović
Keyword(s):  
Business School ◽  
Competitive Equilibrium ◽  
Price Mechanism ◽  
Ex Post ◽  
Elective Courses ◽  
Deferred Acceptance Algorithm ◽  
Deferred Acceptance ◽  
Strategy Proof ◽  
Pareto Efficient ◽  
Serial Dictatorship

AbstractIn this paper we present a review of matching algorithms that are used for matching students with elective courses at universities. This is an example of a market where price mechanism cannot be used to determine the equilibrium allocation. In the Random Serial Dictatorship students select courses based on their position in a random queue. This mechanism is not ex post Pareto-efficient and its drawback is overcome in the Probabilistic Serial Assignment, although this mechanism is not strategy-proof. In the auction mechanism, students’ bids for courses do not represent their true preferences, since bids depend on their beliefs about the popularity of courses. The efficient allocation is obtained when Deferred Acceptance Algorithm is used - where the priority of students is determined based on their bids. Harvard draft mechanism is based on changing the order of students in the random queue from one round to another and this mechanism is not strategy-proof; however, it is, by all means, better for students than Random Serial Dictatorship. The Wharton Business School mechanism is based on the calculation of approximate competitive equilibrium.

scholarly journals Beyond Truth-Telling: Preference Estimation with Centralized School Choice and College Admissions

2019 ◽  
Vol 109 (4) ◽  
pp. 1486-1529 ◽  
Author(s):  
Gabrielle Fack ◽  
Julien Grenet ◽  
Yinghua He
Keyword(s):  
School Choice ◽  
Test Scores ◽  
Real Life ◽  
Truth Telling ◽  
Student Preferences ◽  
Ex Post ◽  
Is Strategy ◽  
Deferred Acceptance ◽  
Strategy Proof ◽  
Novel Approaches

We propose novel approaches to estimating student preferences with data from matching mechanisms, especially the Gale-Shapley deferred acceptance. Even if the mechanism is strategy-proof, assuming that students truthfully rank schools in applications may be restrictive. We show that when students are ranked strictly by some ex ante known priority index (e.g., test scores), stability is a plausible and weaker assumption, implying that every student is matched with her favorite school/college among those she qualifies for ex post. The methods are illustrated in simulations and applied to school choice in Paris. We discuss when each approach is more appropriate in real-life settings. (JEL D11, D12, D82, I23)

scholarly journals Heterogeneous Beliefs and School Choice Mechanisms

2020 ◽  
Vol 110 (5) ◽  
pp. 1274-1315 ◽  
Author(s):  
Adam J. Kapor ◽  
Christopher A. Neilson ◽  
Seth D. Zimmerman
Keyword(s):  
School Choice ◽  
Rational Expectations ◽  
Choice Behavior ◽  
Heterogeneous Beliefs ◽  
Welfare Costs ◽  
Subjective Beliefs ◽  
Opposite Conclusion ◽  
Deferred Acceptance Algorithm ◽  
Deferred Acceptance ◽  
Strategy Proof

This paper studies how welfare outcomes in centralized school choice depend on the assignment mechanism when participants are not fully informed. Using a survey of school choice participants in a strategic setting, we show that beliefs about admissions chances differ from rational expectations values and predict choice behavior. To quantify the welfare costs of belief errors, we estimate a model of school choice that incorporates subjective beliefs. We evaluate the equilibrium effects of switching to a strategy-proof deferred acceptance algorithm, and of improving households’ belief accuracy. We find that a switch to truthful reporting in the DA mechanism offers welfare improvements over the baseline given the belief errors we observe in the data, but that an analyst who assumed families had accurate beliefs would have reached the opposite conclusion. (JEL D83, H75, I21, I28)

Mistaken Play in the Deferred Acceptance Algorithm: Implications for Positive Assortative Matching

2017 ◽  
Vol 107 (5) ◽  
pp. 225-229 ◽  
Author(s):  
Alex Rees-Jones
Keyword(s):  
Recent Literature ◽  
Welfare Effects ◽  
Assortative Matching ◽  
Welfare Evaluation ◽  
Deferred Acceptance Algorithm ◽  
Deferred Acceptance ◽  
Strategy Proof

Recent literature has documented failures of truthful preference reporting in the strategy-proof deferred acceptance algorithm. I consider the implications of these strategic mistakes for a common welfare consideration: the ability of the mechanism to sort the best students to the best schools. I find that these mistakes have the potential to significantly help or significantly hinder sorting. Through this channel, the presence of mistaken play may have widely varying welfare effects. I discuss related considerations in the welfare evaluation of mistaken play in the deferred acceptance algorithm and the implications for “nudges” that correct these mistakes.

Rejoinder to Shubik's “Comment”

1971 ◽  
Vol 65 (4) ◽  
pp. 1146-1146
Author(s):  
Peter C. Ordeshook
Keyword(s):  
Competitive Equilibrium ◽  
Pure Strategy ◽  
Majority Voting ◽  
Noncooperative Game ◽  
Simple Majority ◽  
Ex Post ◽  
Social Decisions ◽  
Electoral Strategies ◽  
Ex Ante ◽  
Pareto Efficient

First, Shubik's comment distinguishes between ex ante and ex post judgments about markets and elections. He claims that given his assumptions, both markets and elections are efficient ex post, though elections may not be efficient ex ante. I agree insofar as in my last paragraph I state, “If … we ask … ‘For some forthcoming sequence of one or more social decisions, do citizens prefer elections to markets?’ our answer is ‘Possibly no.’”But Shubik's essay contains no distinction between ex ante and ex post judgments. Shubik begins, “it is demonstrated that if all the conditions for the existence of a competitive equilibrium are satisfied, then simple majority voting to determine the distribution of goods may be less efficient than a price system” (page 179). Shubik notes later, “if they [voters] are riskneutral or risk-averse, then, whenever the ‘political noncooperative game’ has no pure strategy solution, the result will not be Pareto optimal” (page 180). These two statements indicate that Shubik's judgment is ex post and not ex ante, and ex post he is wrong.Second, to complicate matters further, Shubik fails to distinguish correctly between mixed and risky strategies by the dictates of these concepts' theoretical definitions. I show that if these concepts are correctly interpreted, then a Pareto efficient allocation occurs no matter what form the candidates' electoral strategies take. Manifestly, an ex ante comparison of markets and elections by the Pareto efficient criterion is meaningless, as ex post they are both Pareto efficient.

Efficiency, Justified Envy, and Incentives in Priority-Based Matching

2020 ◽  
Vol 2 (4) ◽  
pp. 425-442 ◽  
Author(s):  
Atila Abdulkadiroǧlu ◽  
Yeon-Koo Che ◽  
Parag A. Pathak ◽  
Alvin E. Roth ◽  
Olivier Tercieux
Keyword(s):  
Public Schools ◽  
New Orleans ◽  
Empirical Evidence ◽  
Boston Public Schools ◽  
Top Trading Cycles ◽  
Strategy Proof ◽  
Pareto Efficient ◽  
One To One ◽  
Serial Dictatorship

Top trading cycles (TTC) is Pareto efficient and strategy-proof in priority-based matching, but so are other mechanisms including serial dictatorship. We show that TTC minimizes justified envy among all Pareto-efficient and strategy-proof mechanisms in one-to-one matching. In many-to-one matching, TTC admits less justified envy than serial dictatorship in an average sense. Empirical evidence from New Orleans OneApp and Boston Public Schools shows that TTC has significantly less justified envy than serial dictatorship. (JEL C78, D61)

Approximate Random Allocation Mechanisms

2020 ◽  
Vol 87 (6) ◽  
pp. 2473-2510
Author(s):  
Mohammad Akbarpour ◽  
Afshin Nikzad
Keyword(s):  
Competitive Equilibrium ◽  
Previous Literature ◽  
Random Allocation ◽  
Hard Constraints ◽  
Ex Post ◽  
Feasibility Constraints ◽  
Serial Dictatorship

Abstract We generalize the scope of random allocation mechanisms, in which the mechanism first identifies a feasible “expected allocation” and then implements it by randomizing over nearby feasible integer allocations. The previous literature has shown that the cases in which this is possible are sharply limited. We show that if some of the feasibility constraints can be treated as goals rather than hard constraints, then, subject to weak conditions that we identify, any expected allocation that satisfies all the constraints and goals can be implemented by randomizing among nearby integer allocations that satisfy all the hard constraints exactly and the goals approximately. By defining ex post utilities as goals, we are able to improve the ex post properties of several classic assignment mechanisms, such as the random serial dictatorship. We use the same approach to prove the existence of $\epsilon$-competitive equilibrium in large markets with indivisible items and feasibility constraints.

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