Beyond Truth-Telling: Preference Estimation with Centralized School Choice and College Admissions

Abstract

CpSq ¡ CpS ¡ 1q. For such students, σ ST T is a dominated strategy, dominated by dropping r S i and submitting pr 1 i , . . . , r S i q. In other words, σ ST T is not an equilibrium strategy for these students.In fact, σ ST T is not an equilibrium strategy for more student types, given others playing σ ST T . If a student drops an arbitrary school s and submits a partial true preference order L i of length pS ¡ 1q, the saved cost of is CpSq ¡ CpS ¡ 1q, while the associated foregone benefit is at most u i,s ³ a s L i , e i ; σ ST T ¡i pθ ¡i q, e ¡i¨d Gpθ ¡i q. The saved cost can exceed the forgone benefit because the latter can be close to zero when s tends to have cutoff much higher than e i,s or when i can be almost certainly accepted by more desirable schools, given that everyone else plays STT. When it is the case, i deviates from STT.The above arguments can be extended to any non-zero application cost.Proof of Lemma 1.The sufficiency of the first statement is implied by the strategy-proofness of DA and by DA producing a stable matching when everyone is STT. That is, STT is a dominant strategy

Self-selection in school choice

“…Moreover, they are based on experimental evidence, and then the presence of these strategies in the field remains as an open question. In a recent paper, Fack, Grenet, and He (2015) propose a method to estimate students' preferences under deferred acceptance mechanism without assuming truth-telling. Different from our approach, application cost of submitting preferences is their main concern for non-truth-telling behavior.…”

A Pseudo-Market Approach to Allocation with Priorities

“…For example, Rees-Jones (2016) uses survey data and reports that 5.38 percent of the agents do not report true ordinal preferences under the DA mechanism, which is a strategy-proof ordinal mechanism; Hassidim, Romm, and Shorrer (2016) report an even higher rate, 19 percent, using data on agents' behavior. However, misreporting behavior may not affect the outcome or the assignment, because agents tend to omit objects that are unlikely to be obtained by them (Fack, Grenet, and He 2015;Artemov, Che, and He 2017). Indeed, as documented in Hassidim, Romm, and Shorrer (2016), at most 1.4 percent of the agents misreport and end up with suboptimal outcomes; even lower rates are reported in Artemov, Che, and He (2017).…”

The role of strategic reports and subjective admission beliefs in explaining the ‘ethnic admissions gap’ in English secondary schools

“…This work is also related to a growing literature combining structural empirical modelling of strategic school choice with topics from market design (Calsamiglia et al, 2010;Klijn et al, 2013;Abdulkadiroğlu et al, 2017;Cantillon, 2017;Chen and Pereyra, 2017;Calsamiglia and Güell, 2018). Within this recent body of work, a handful of papers investigate non-strategyproof markets by explicitly estimating joint models of strategic choice and the probability of admission (Ajayi, 2013;Calsamiglia et al, 2014;Fack et al, 2015;Ajayi and Sidibé, 2016;Agarwal and Somaini, 2018;Luflade, 2018).…”

“…Of these papers, Fack et al (2015) avoids modelling strategic choice, but instead posits methods for recovering the distribution of preferences that are robust to strategy. Calsamiglia et al (2014) and Agarwal and Somaini (2018) model decision-makers divided into strategic and sincere types, and estimate the proportion of each type in the population.…”