Manipulability and Tie-Breaking in Constrained School Choice

Decerf, Benoit; Linden, Martin Van der

doi:10.2139/ssrn.2809566

Cited by 7 publications

(4 citation statements)

References 37 publications

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“…Pathak and Sönmez (2013) were the first to observe these reforms and proposed a way to explain them using a notion of manipulability that compares mechanisms according to the inclusion of instances where they are not vulnerable to gaming. These results were further strengthened for other mechanisms and other vulnerability criteria (Chen and Kesten, 2017;Decerf and Van der Linden, 2018;Dur et al, 2018;Bonkoungou and Nesterov, 2020).…”

Section: Introductionmentioning

confidence: 72%

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Reforms meet fairness concerns in school and college admissions

Bonkoungou¹,

Nesterov²

2020

Preprint

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Recently, many matching systems around the world have been reformed. These reforms responded to objections that the matching mechanisms in use were unfair and manipulable. Surprisingly, the mechanisms remained unfair even after the reforms: the new mechanisms may induce an outcome with a blocking student who desires and deserves a school which she did not receive.However, as we show in this paper, the reforms introduced matching mechanisms which are more fair compared to the counterfactuals. First, most of the reforms introduced mechanisms that are more fair by stability: whenever the old mechanism does not have a blocking student, the new mechanism does not have a blocking student either. Second, some reforms introduced mechanisms that are more fair by counting: the old mechanism always has at least as many blocking students as the new mechanism.These findings give a novel rationale to the reforms and complement the recent literature showing that the same reforms have introduced less manipulable matching mechanisms. We further show that the fairness and manipulability of the mechanisms are strongly logically related.

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Section: Introductionmentioning

confidence: 72%

“…Related literature. Apart from the papers studying the reforms mentioned earlier (Pathak and Sönmez, 2013;Chen and Kesten, 2017;Decerf and Van der Linden, 2018;Bonkoungou and Nesterov, 2020) the recent literature has been interested in other ways to compare mechanism by fairness and stability.…”

Section: Introductionmentioning

confidence: 99%

Reforms meet fairness concerns in school and college admissions

Bonkoungou¹,

Nesterov²

2020

Preprint

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“…All strategy-proof mechanisms are alike, each vulnerable mechanism is vulnerable in its own way. Compared to another, a mechanism can be vulnerable at a larger set of profiles as in Pathak and Sönmez (2013), larger set of preference relations as in Decerf and Van der Linden (2018). A mechanism can also be manipulated by a larger set of agents, giving them stronger incentives to manipulate and causing worse consequences for others as measured by the range of outcomes that these manipulations induce.…”

Section: Discussionmentioning

confidence: 99%

“…Arribillaga and Massó (2016) ranked voting rules by inclusion of the vulnerable preference relations of each agent i, that is the relations for which there exist preferences of others such that i can manipulate. This notion was recently used by Decerf and Van der Linden (2018) to rank constrained Boston and GS mechanisms. Andersson et al (2014a) ranked budget balanced and fair rules by counting, for each preference profile, the number of agents who have profitable manipulations.…”

Section: Discussionmentioning

confidence: 99%

Comparing School Choice and College Admission Mechanisms By Their Immunity to Strategic Admissions

Alexander¹,

Bonkoungou²

2020

Preprint

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Recently dozens of school districts and college admissions systems around the world have reformed their admission rules. As a main motivation for these reforms the policymakers cited strategic flaws of the rules: students had strong incentives to game the system, which caused dramatic consequences for non-strategic students. However, almost none of the new rules were strategy-proof. We explain this puzzle. We show that after the reforms the rules became more immune to strategic admissions: each student received a smaller set of schools that he can get in using a strategy, weakening incentives to manipulate. Simultaneously, the admission to each school became strategy-proof to a larger set of students, making the schools more available for non-strategic students. We also show that the existing explanation of the puzzle due to Pathak and Sönmez ( 2013) is incomplete.

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Deferred acceptance is minimally manipulable

Linden

2018

Int J Game Theory

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This paper shows that the deferred acceptance mechanism (DA) cannot be improved upon in terms of manipulability in the sense of either Pathak and Sönmez (2013) or or Arribillaga and Massó (2015) without compromising with stability.A conflict between manipulability and fairness is also identified. It is shown that miniworst stable mechanisms that make the set of individuals who match with their worst achievable mate minimal are maximally manipulable among the stable mechanisms. Miniworst mechanisms are also more manipulable than DA in the sense of Arribillaga and Massó (2015). A similar conflict between fairness and manipulability is identified in the case of the median stable mechanism (Teo and Sethuraman, 1998).

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Manipulability and Tie-Breaking in Constrained School Choice

Cited by 7 publications

References 37 publications

Reforms meet fairness concerns in school and college admissions

Reforms meet fairness concerns in school and college admissions

Comparing School Choice and College Admission Mechanisms By Their Immunity to Strategic Admissions

Deferred acceptance is minimally manipulable

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