(Il)legal Assignments in School Choice

We introduce a general class of simplicity standards that vary the foresight abilities required of agents in extensive-form games. Rather than planning for the entire future of a game, agents are presumed to be able to plan only for those histories they view as simple from their current perspective. Agents may update their so-called strategic plan as the game progresses, and, at any point, for the called-for action to be simply dominant, it must lead to unambiguously better outcomes, no matter what occurs at non-simple histories. We use our gradated approach to simplicity to provide characterizations of simple mechanisms. While more demanding simplicity standards may reduce the flexibility of the designer in some cases, this is not always true, and many well-known mechanisms are simple, including ascending auctions, posted prices, and serial dictatorship-style mechanisms. In particular, we explain the widespread popularity of the well-known Random Priority mechanism by characterizing it as the unique mechanism that is efficient, fair, and simple to play.

Section: Introductionmentioning

confidence: 99%

A Theory of Simplicity in Games and Mechanism Design

Pycia

Troyan

2021

“…Ehlers and Morrill (2020) provide a thorough analysis of legal assignments in school choice.3 This result is also proven inTang and Zhang (2020). We present our proof which is independent and different.4 Not all conclusions have to be sensitive, however.…”

mentioning

confidence: 60%

“…6 See Section 4 for a definition of an improvement cycle 7 Dogan and Yenmez (2020), Dur et al (2019), Ehlers and Morrill (2020), Kwon and Shorrer (2019), Tang and Zhang (2020), and Troyan et al (2020) provide different other justifications for EADA. school choice mechanisms are compared in terms of their manipulability by comparing the sets of problems, in the set inclusion sense, at which they are manipulable.…”

Section: Introductionmentioning

confidence: 99%

Blocking Pairs Versus Blocking Students: Stability Comparisons in School Choice

Doğan

Ehlers

2020

Self Cite

It is known that there are school choice problems without an efficient and stable assignment. We consider comparing assignments in terms of their stability by comparing their sets of blocking (student-school) pairs or comparing their sets of blocking students who are involved in at least one blocking pair. Although there always exists a Pareto improvement over the student-optimal stable (DA) assignment which is minimally unstable among efficient assignments when the stability comparison is based on comparing the sets of blocking pairs in the set-inclusion sense, we show that this is not necessarily true when the stability comparison is based on comparing the sets of blocking pairs in the cardinal sense, or when it is based on comparing sets of blocking students (in the set-inclusion or cardinal sense). Given the latter impossibilities, we characterize the priority profiles where there exists a Pareto improvement over the DA mechanism which is cardinally minimally stable among efficient assignments when counting blocking pairs or counting blocking students. The resulting domain restrictions suggest to take with caution school choice analysis which relies on a particular stability comparison method.

“…Since no pair of a student and a school has an incentive to deviate from the existing matching, stability is usually assumed to eliminate the threat of appeals and lawsuits (Abdulkadiro §lu, Pathak, and . Specically, the existence of blocking pairs may be conceptualized as an infringement upon equal protection rights, depending on the legal requirements for the right to bring an action to court (locus standi ) and the burden imposed on plaintis to prove an injury resulting from an assignment procedure (Ehlers and Morrill 2018). On the other hand, strategy-proofness makes sure that the outcome generated by the mechanism does not depend on the strategic sophistication of students.…”

Section: Theorymentioning

confidence: 99%

Transparency and Fairness in School Choice Mechanisms

Hermstrüwer

2019

This article explores the impact of procedural information on the behavior of applicants under two of the most commonly used school admissions procedures: the Gale-Shapley mechanism and the Boston mechanism. In a lab experiment, I compare the impact of information about the mechanism, information about individually optimal application strategies, and information about both. I nd that strategic and full information increase truth-telling and stability under the Gale-Shapley mechanism. Under the Boston mechanism, however, the adoption of equilibrium strategies remains unaected. Contrary to prevailing assumptions in matching theory, I show that the Boston mechanism improves perceived fairness. These results underscore the importance of procedural information and suggest that eliminating justied envy may not be a sucient condition of fairness.