Improving the Chilean College Admissions System

Ríos, Ignacio; Larroucau, Tomás; Parra, Giorgiogiulio; Cominetti, Roberto

doi:10.1287/opre.2021.2116

Cited by 6 publications

(3 citation statements)

References 25 publications

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“…There is a robust and growing body of practical work on designing real world matching markets, especially in the contexts of school and college admissions (e.g., Rios et al 2019, Abdulkadiroglu et al 2005, Dur et al 2018, and various labor markets (e.g., Peranson 1999, Hassidim et al 2017b). Stability, namely, that no pair of agents should prefer to match with each other, has been found to be crucial in the design of centralized clearinghouses (Roth 1991) and predictive of outcomes in decentralized matching markets (Kagel andRoth 2000, Hitsch et al 2010).…”

Section: Related Workmentioning

confidence: 99%

“…Meanwhile, over the past two decades, a large number of real world matching market datasets from deferred acceptance (DA) based clearinghouses have become available to different researchers in the field, e.g., from centralized labor markets like the National Residency Matching Program (NRMP) (Roth and Peranson 1999) and the Israel Psychology Masters Match (Hassidim et al 2017b), college admissions (e.g., Rios et al 2019), and school choice (e.g., Abdulkadiroglu et al 2005). Since these (and other) clearinghouses run the incentive-compatible deferred acceptance (DA) algorithm, the preference rankings collected may be assumed to reflect the true underlying preferences.…”

Section: Introductionmentioning

confidence: 99%

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Which Random Matching Markets Exhibit a Stark Effect of Competition?

Kanoria¹,

Min²,

Qian³

2020

Preprint

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We revisit the popular random matching market model introduced by Knuth (1976) and Pittel (1989), and shown by Ashlagi, Kanoria and Leshno (2013) to exhibit a "stark effect of competition", i.e., with any difference in the number of agents on the two sides, the short side agents obtain substantially better outcomes. We generalize the model to allow "partially connected" markets with each agent having an average degree d in a random (undirected) graph. Each agent has a (uniformly random) preference ranking over only their neighbors in the graph. We characterize stable matchings in large markets and find that the short side enjoys a significant advantage only for d exceeding log 2 n where n is the number of agents on one side:For moderately connected markets with d = o(log 2 n), we find that there is no stark effect of competition, with agents on both sides getting a √ d-ranked partner on average. Notably, this regime extends far beyond the connectivity threshold of d = Θ(log n). In contrast, for densely connected markets with d = ω(log 2 n), we find that the short side agents get log n-ranked partner on average, while the long side agents get a partner of (much larger) rank d/ log n on average. Numerical simulations of our model confirm and sharpen our theoretical predictions.Since preference list lengths in most real-world matching markets are much below log 2 n, our findings may help explain why available datasets do not exhibit a strong effect of competition.

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Section: Related Workmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Which Random Matching Markets Exhibit a Stark Effect of Competition?

Kanoria¹,

Min²,

Qian³

2020

Preprint

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show abstract

“…Mechanisms based on Gale and Shapley's deferred acceptance (DA) algorithm [5] are widely used to compute matchings in real-world applications: the National Residency Matching Program (NRMP), which matches future residents to hospital programs [25]; university admissions programs which match students to programs, e.g. in Chile [24], school choice programs, e.g. for placement in New York City's high schools [1], the Israeli psychology Masters match [9], and no doubt many others (e.g.…”

Section: Introductionmentioning

confidence: 99%

Stable Matching: Choosing Which Proposals to Make

Agarwal¹,

Cole²

2022

Preprint

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Why does stable matching work well in practice despite agents only providing short preference lists? Perhaps the most compelling explanation is due to Lee [17]. He considered a model with preferences based on correlated cardinal utilities. Specifically, the utilities were based on common public values for each agent and individual private values. He showed that for suitable utility functions, in large markets, for most agents, all stable matches yield similar valued utilities.By means of a new analysis, we strengthen this result, showing that in large markets, with high probability, for all but the bottommost agents, all stable matches yield similar valued utilities. We can then deduce that for all but the bottommost agents, relatively short preference lists suffice.Our analysis shows that the key distinction is between models in which the derivatives of the utility function are bounded, and those in which they can be unbounded. An important instance of the first model is the linear separable model, in which the utility function is a sum of public and private values. For the bounded derivative model, we show that for any given constant c ≥ 1, with n agents on each side of the market, with probability 1 − n −c , for each agent its possible utilities in all stable matches vary by at most O((c ln n/n) 1/3 ) for all but the bottommost O((c ln n/n) 1/3 ) fraction of the agents. This result is tight, even for the linear model. When the derivatives can be unbounded, we obtain the following bound on the utility range and the bottommost fraction: for any constant > 0, for large enough n, the bound is . This bound too cannot be improved in general. These bounds continue to hold when the two sides have unequal numbers of agents. Thus, in this model, the "stark effect of competition", meaning that the agents on the short side fare much better, which is observed in the standard random preferences model, is limited to a lower portion of the agents on the longer side.We extend the study to many-to-one settings, e.g. employers and workers, where each employer has the same fixed number d of positions. Qualitatively, the results are unchanged. However, the outcomes are no longer symmetric. The range of utilities for employers is unchanged for small d, while the range for workers is increased, compared to the one-to-one setting. We completely characterize these outcomes as a function of employer size.In the bounded derivative model, we also show the existence of an -Bayes-Nash equilibrium in which agents make relatively few proposals. Specifically, there is an equilibrium in which no agent proposes more than O(ln 2 n) times, and all but the bottommost O((ln n/n) 1/3 ) fraction of the agents make only O(ln n) proposals, and = O(ln n/n 1/3 ).These results all rely on a new technique for sidestepping the conditioning between the matching events that occur over the course of a run of the Deferred Acceptance algorithm.We complement these theoretical results with a variety of simulation experiments.

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