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Best vs. All: Equity and Accuracy of Standardized Test Score Reporting

Author

Listed:
  • Sampath Kannan
  • Mingzi Niu
  • Aaron Roth
  • Rakesh Vohra

Abstract

We study a game theoretic model of standardized testing for college admissions. Students are of two types; High and Low. There is a college that would like to admit the High type students. Students take a potentially costly standardized exam which provides a noisy signal of their type. The students come from two populations, which are identical in talent (i.e. the type distribution is the same), but differ in their access to resources: the higher resourced population can at their option take the exam multiple times, whereas the lower resourced population can only take the exam once. We study two models of score reporting, which capture existing policies used by colleges. The first policy (sometimes known as "super-scoring") allows students to report the max of the scores they achieve. The other policy requires that all scores be reported. We find in our model that requiring that all scores be reported results in superior outcomes in equilibrium, both from the perspective of the college (the admissions rule is more accurate), and from the perspective of equity across populations: a student's probability of admission is independent of their population, conditional on their type. In particular, the false positive rates and false negative rates are identical in this setting, across the highly and poorly resourced student populations. This is the case despite the fact that the more highly resourced students can -- at their option -- either report a more accurate signal of their type, or pool with the lower resourced population under this policy.

Suggested Citation

  • Sampath Kannan & Mingzi Niu & Aaron Roth & Rakesh Vohra, 2021. "Best vs. All: Equity and Accuracy of Standardized Test Score Reporting," Papers 2102.07809, arXiv.org.
  • Handle: RePEc:arx:papers:2102.07809
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    References listed on IDEAS

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    1. Lily Hu & Yiling Chen, 2017. "A Short-term Intervention for Long-term Fairness in the Labor Market," Papers 1712.00064, arXiv.org, revised Feb 2018.
    2. Christopher Jung & Sampath Kannan & Changhwa Lee & Mallesh M. Pai & Aaron Roth & Rakesh Vohra, 2020. "Fair Prediction with Endogenous Behavior," Papers 2002.07147, arXiv.org.
    3. Lydia T. Liu & Ashia Wilson & Nika Haghtalab & Adam Tauman Kalai & Christian Borgs & Jennifer Chayes, 2019. "The Disparate Equilibria of Algorithmic Decision Making when Individuals Invest Rationally," Papers 1910.04123, arXiv.org.
    4. Coate, Stephen & Loury, Glenn C, 1993. "Will Affirmative-Action Policies Eliminate Negative Stereotypes?," American Economic Review, American Economic Association, vol. 83(5), pages 1220-1240, December.
    5. Dean P. Foster & Rakesh V. Vohra, 1992. "An Economic Argument for Affirmative Action," Rationality and Society, , vol. 4(2), pages 176-188, April.
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