Ratings are present in many areas of assessment including peer review of research proposals and journal articles, teacher observations, university admissions and selection of new hires. One feature present in any rating process with multiple raters is that different raters often assign different scores to the same assessee, with the potential for bias and inconsistencies related to rater or assessee covariates. This paper analyzes disparities in ratings of internal and external applicants to teaching positions using applicant data from Spokane Public Schools. We first test for biases in rating while accounting for measures of teacher applicant qualifications and quality. Then, we develop model-based inter-rater reliability (IRR) estimates that allow us to account for various sources of measurement error, the hierarchical structure of the data, and to test whether covariates, such as applicant status, moderate IRR. We find that applicants external to the district receive lower ratings for job applications compared to internal applicants. This gap in ratings remains significant even after including measures of qualifications and quality such as experience, state licensure scores, or estimated teacher value added. With model-based IRR, we further show that consistency between raters is significantly lower when rating external applicants. We conclude the paper by discussing policy implications and possible applications of our model-based IRR estimate for hiring and selection practices in and out of the teacher labor market.
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On Hiring Secretaries with Stochastic Departures
We study a generalization of the secretary problem, where decisions do not have to be made immediately upon applicants’ arrivals. After arriving, each applicant stays in the system for some (random) amount of time and then leaves, whereupon the algorithm has to decide irrevocably whether to select this applicant or not. The arrival and waiting times are drawn from known distributions, and the decision maker’s goal is to maximize the probability of selecting the best applicant overall. Our first main result is a characterization of the optimal policy for this setting. We show that when deciding whether to select an applicant, it suffices to know only the time and the number of applicants that have arrived so far. Furthermore, the policy is monotone nondecreasing in the number of applicants seen so far, and, under certain natural conditions, monotone nonincreasing in time. Our second main result is that when the number of applicants is large, a single threshold policy is almost optimal. Funding: A. Psomas is supported in part by the National Science Foundation [Grant CCF-2144208], a Google Research Scholar Award, and by the Algorand Centres of Excellence program managed by Algorand Foundation. Supplemental Material: The online appendix is available at https://doi.org/10.1287/opre.2023.2476 .
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- Award ID(s):
- 2144208
- PAR ID:
- 10421983
- Publisher / Repository:
- Operations Research
- Date Published:
- Journal Name:
- Operations Research
- ISSN:
- 0030-364X
- Subject(s) / Keyword(s):
- Optimization online algorithms secretary problem stopping problems
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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