Downstream Effects of Affirmative Action

ABSTRACT

We study a two-stage model, in which students are 1) admitted to college on the basis of an entrance exam which is a noisy signal about their qualifications (type), and then 2) those students who were admitted to college can be hired by an employer as a function of their college grades, which are an independently drawn noisy signal of their type. Students are drawn from one of two populations, which might have different type distributions. We assume that the employer at the end of the pipeline is rational, in the sense that it computes a posterior distribution on student type conditional on all information that it has available (college admissions, grades, and group membership), and makes a decision based on posterior expectation. We then study what kinds of fairness goals can be achieved by the college by setting its admissions rule and grading policy. For example, the college might have the goal of guaranteeing equal opportunity across populations: that the probability of passing through the pipeline and being hired by the employer should be independent of group membership, conditioned on type. Alternately, the college might have the goal of incentivizing the employer to have a group blind hiring rule. We show that both goals can be achieved when the college does not report grades. On the other hand, we show that under reasonable conditions, these goals are impossible to achieve even in isolation when the college uses an (even minimally) informative grading policy.

References

1. Kenneth Arrow et al. 1973. The theory of discrimination. Discrimination in labor markets 3, 10 (1973), 3--33.
2. J Aislinn Bohren, Alex Imas, and Michael Rosenberg. 2017. The Dynamics of Discrimination: Theory and Evidence. (2017).
3. Alexandra Chouldechova. 2017. Fair prediction with disparate impact: A study of bias in recidivism prediction instruments. Big data 5, 2 (2017), 153--163.
4. Chuong. 2008. The Multivariate Gaussian Distribution.
5. Stephen Coate and Glenn C Loury. 1993. Will affirmative-action policies eliminate negative stereotypes? The American Economic Review (1993), 1220--1240.
6. Dean P Foster and Rakesh V Vohra. 1992. An economic argument for affirmative action. Rationality and Society 4, 2 (1992), 176--188.
7. Daniel Gottlieb and Kent Smetters. 2011. Grade non-disclosure. Technical Report. National Bureau of Economic Research.
8. Moritz Hardt, Eric Price, and Nati Srebro. 2016. Equality of opportunity in supervised learning. In Advances in neural information processing systems. 3315--3323.
9. Lily Hu and Yiling Chen. 2018. A Short-term Intervention for Long-term Fairness in the Labor Market. In Proceedings of the 2018 World Wide Web Conference on World Wide Web, WWW, Pierre-Antoine Champin, Fabien L. Gandon, Mounia Lalmas, and Panagiotis G. Ipeirotis (Eds.). ACM, 1389--1398.
10. Shahin Jabbari, Matthew Joseph, Michael Kearns, Jamie Morgenstern, and Aaron Roth. 2017. Fairness in Reinforcement Learning. In International Conference on Machine Learning. 1617--1626.
11. Sampath Kannan, Michael Kearns, Jamie Morgenstern, Mallesh Pai, Aaron Roth, Rakesh Vohra, and Zhiwei Steven Wu. 2017. Fairness Incentives for Myopic Agents. In Proceedings of the 2017 ACM Conference on Economics and Computation. ACM, 369--386.
12. Jon M. Kleinberg, Sendhil Mullainathan, and Manish Raghavan. 2017. Inherent Trade-Offs in the Fair Determination of Risk Scores. In 8th Innovations in Theoretical Computer Science Conference, ITCS.
13. Lydia T Liu, Sarah Dean, Esther Rolf, Max Simchowitz, and Moritz Hardt. 2018. Delayed Impact of Fair Machine Learning. In International Conference on Machine Learning.
14. Edmund S Phelps. 1972. The statistical theory of racism and sexism. The american economic review (1972), 659--661.
15. Andrew Michael Spence. 1974. Market signaling: Informational transfer in hiring and related screening processes. Vol. 143. Harvard Univ Press.

Index Terms

• Computing methodologies

  • Machine learning

• Mathematics of computing

  • Probability and statistics