scholarly journals A Characterization of the Top Trading Cycles Mechanism for the School Choice Problem

Author(s):  
Umut Mert Dur
Author(s):  
Jacob D Leshno ◽  
Irene Lo

Abstract This paper develops a tractable theoretical framework for the Top Trading Cycles (TTC) mechanism for school choice that allows quantifying welfare and optimizing policy decisions. We compute welfare for TTC and Deferred Acceptance (DA) under different priority structures, and find that the choice of priorities can have larger welfare implications than the choice of mechanism. We solve for the welfare-maximizing distributions of school quality for parametrized economies, and find that optimal investment decisions can be very different under TTC and DA. Our framework relies on a novel characterization of the TTC assignment in terms of a cutoff for each pair of schools. These cutoffs parallel prices in competitive equilibrium, with students’ priorities serving the role of endowments. We show that these cutoffs can be computed directly from the distribution of preferences and priorities in a continuum model, and derive closed-form solutions and comparative statics for parameterized settings. The TTC cutoffs clarify the role of priorities in determining the TTC assignment, but also demonstrate that TTC is more complicated than DA.


2007 ◽  
Vol 97 (5) ◽  
pp. 1824-1839 ◽  
Author(s):  
Paola Manzini ◽  
Marco Mariotti

A sequentially rationalizable choice function is a choice function that can be retrieved by applying sequentially to each choice problem the same fixed set of asymmetric binary relations (rationales) to remove inferior alternatives. These concepts translate into economic language some human choice heuristics studied in psychology and explain cyclical patterns of choice observed in experiments. We study some properties of sequential rationalizability and provide a full characterization of choice functions rationalizable by two and three rationales. (JEL D01).


2015 ◽  
Vol 8 (5) ◽  
pp. 801-823
Author(s):  
Sinan Aksoy ◽  
Adam Azzam ◽  
Chaya Coppersmith ◽  
Julie Glass ◽  
Gizem Karaali ◽  
...  
Keyword(s):  

Author(s):  
Erel Segal-Halevi ◽  
Haris Aziz ◽  
Avinatan Hassidim

Ranking alternatives is a natural way for humans to explain their preferences. It is being used in many settings, such as school choice (NY, Boston), Course allocations, and the Israeli medical lottery. In some cases (such as the latter two), several ``items'' are given to each participant. Without having any information on the underlying cardinal utilities, arguing about fairness of allocation requires extending the ordinal item ranking to ordinal bundle ranking. The most commonly used such extension is stochastic dominance (SD), where a bundle X is preferred over a bundle Y if its score is better according to all additive score functions. SD is a very conservative extension, by which few allocations are necessarily fair while many allocations are possibly fair. We propose to make a natural assumption on the underlying cardinal utilities of the players, namely that the difference between two items at the top is larger than the difference between two items at the bottom. This assumption implies a preference extension which we call diminishing differences (DD), where a X is preferred over Y if its score is better according to all additive score functions satisfying the DD assumption. We give a full characterization of allocations that are necessarily-proportional or possibly-proportional according to this assumption. Based on this characterization, we present a polynomial-time algorithm for finding a necessarily-DD-proportional allocation if it exists. Using simulations, we show that with high probability, a necessarily-proportional allocation does not exist but a necessarily-DD-proportional allocation exists, and moreover, that allocation is proportional according to the underlying cardinal utilities.


2019 ◽  
Vol 35 (3) ◽  
pp. 361-381
Author(s):  
Conal Duddy

AbstractIn a school choice problem, each school has a priority ordering over the set of students. These orderings depend on criteria such as whether a student lives within walking distance or has a sibling at the school. A priority ordering provides a ranking of students but nothing more. I argue that this information is sufficient when priority is based on merit but not when priority is based on criteria such as walking distance. I propose an extended formulation of the problem wherein a ‘priority matrix’, indicating which criteria are satisfied by each student-school pair, replaces the usual priority orderings.


2018 ◽  
Vol 59 (4) ◽  
pp. 2219-2258 ◽  
Author(s):  
Rustamdjan Hakimov ◽  
Onur Kesten

Sign in / Sign up

Export Citation Format

Share Document