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

2012 ◽  
Author(s):  
Umut Mert Dur
Keyword(s):  
School Choice ◽  
Choice Problem ◽  
Top Trading Cycles

The Cutoff Structure of Top Trading Cycles in School Choice

2020 ◽  
Author(s):  
Jacob D Leshno ◽  
Irene Lo
Keyword(s):  
School Choice ◽  
School Quality ◽  
Competitive Equilibrium ◽  
Optimal Investment ◽  
Comparative Statics ◽  
Closed Form Solutions ◽  
Top Trading Cycles ◽  
Deferred Acceptance

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.

scholarly journals Sequentially Rationalizable Choice

2007 ◽  
Vol 97 (5) ◽  
pp. 1824-1839 ◽  
Author(s):  
Paola Manzini ◽  
Marco Mariotti
Keyword(s):  
Choice Function ◽  
Binary Relations ◽  
Choice Functions ◽  
Choice Problem ◽  
Full Characterization ◽  
Human Choice ◽  
Fixed Set ◽  
Rationalizable Choice

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).

scholarly journals Coalitions and cliques in the school choice problem

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

scholarly journals Fair Allocation based on Diminishing Differences

2017 ◽  
Author(s):  
Erel Segal-Halevi ◽  
Haris Aziz ◽  
Avinatan Hassidim
Keyword(s):  
School Choice ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Conservative Extension ◽  
Score Functions ◽  
Full Characterization ◽  
Proportional Allocation ◽  
The Difference ◽  
Natural Way

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.

scholarly journals The structure of priority in the school choice problem

2019 ◽  
Vol 35 (3) ◽  
pp. 361-381
Author(s):  
Conal Duddy
Keyword(s):  
School Choice ◽  
Walking Distance ◽  
Extended Formulation ◽  
Choice Problem ◽  
A Priority ◽  
Priority Ordering

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.

scholarly journals THE EQUITABLE TOP TRADING CYCLES MECHANISM FOR SCHOOL CHOICE

2018 ◽  
Vol 59 (4) ◽  
pp. 2219-2258 ◽  
Author(s):  
Rustamdjan Hakimov ◽  
Onur Kesten
Keyword(s):  
School Choice ◽  
Top Trading Cycles
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