Pipeline Interventions

Authors Eshwar Ram Arunachaleswaran, Sampath Kannan, Aaron Roth, Juba Ziani

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Eshwar Ram Arunachaleswaran
  • University of Pennsylvania, Philadelphia, PA, USA
Sampath Kannan
  • University of Pennsylvania, Philadelphia, PA, USA
Aaron Roth
  • University of Pennsylvania, Philadelphia, PA, USA
Juba Ziani
  • University of Pennsylvania, Philadelphia, PA, USA

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Eshwar Ram Arunachaleswaran, Sampath Kannan, Aaron Roth, and Juba Ziani. Pipeline Interventions. In 12th Innovations in Theoretical Computer Science Conference (ITCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 185, pp. 8:1-8:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


We introduce the pipeline intervention problem, defined by a layered directed acyclic graph and a set of stochastic matrices governing transitions between successive layers. The graph is a stylized model for how people from different populations are presented opportunities, eventually leading to some reward. In our model, individuals are born into an initial position (i.e. some node in the first layer of the graph) according to a fixed probability distribution, and then stochastically progress through the graph according to the transition matrices, until they reach a node in the final layer of the graph; each node in the final layer has a reward associated with it. The pipeline intervention problem asks how to best make costly changes to the transition matrices governing people’s stochastic transitions through the graph, subject to a budget constraint. We consider two objectives: social welfare maximization, and a fairness-motivated maximin objective that seeks to maximize the value to the population (starting node) with the least expected value. We consider two variants of the maximin objective that turn out to be distinct, depending on whether we demand a deterministic solution or allow randomization. For each objective, we give an efficient approximation algorithm (an additive FPTAS) for constant width networks. We also tightly characterize the "price of fairness" in our setting: the ratio between the highest achievable social welfare and the social welfare consistent with a maximin optimal solution. Finally we show that for polynomial width networks, even approximating the maximin objective to any constant factor is NP hard, even for networks with constant depth. This shows that the restriction on the width in our positive results is essential.

Subject Classification

ACM Subject Classification
  • Theory of computation → Algorithmic game theory
  • Interventions for fairness
  • fairness in navigating life paths
  • social welfare
  • maximin welfare
  • budget-constrained optimization
  • hardness of approximation


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  1. Eshwar Ram Arunachaleswaran, Sampath Kannan, Aaron Roth, and Juba Ziani. Pipeline interventions, 2020. URL: http://arxiv.org/abs/2002.06592.
  2. Siddharth Barman and Sanath Kumar Krishnamurthy. Approximation algorithms for maximin fair division. In Proceedings of the 2017 ACM Conference on Economics and Computation, pages 647-664, 2017. Google Scholar
  3. Matt Barnum. A new study questions whether Head Start still produces long-run gains seen in past research, 2019. URL: https://www.chalkbeat.org/2019/8/8/21108602/a-new-study-questions-whether-head-start-still-produces-long-run-gains-seen-in-past-research.
  4. Amanda Bower, Sarah N Kitchen, Laura Niss, Martin J Strauss, Alexander Vargas, and Suresh Venkatasubramanian. Fair pipelines. arXiv preprint, 2017. URL: http://arxiv.org/abs/1707.00391.
  5. Eric Budish. The combinatorial assignment problem: Approximate competitive equilibrium from equal incomes. Journal of Political Economy, 119(6):1061-1103, 2011. Google Scholar
  6. Alexandra Chouldechova and Aaron Roth. The frontiers of fairness in machine learning. arXiv preprint, 2018. URL: http://arxiv.org/abs/1810.08810.
  7. Stephen Coate and Glenn C Loury. Will affirmative-action policies eliminate negative stereotypes? The American Economic Review, pages 1220-1240, 1993. Google Scholar
  8. Irit Dinur and Samuel Safra. On the hardness of approximating minimum vertex cover. Annals of mathematics, pages 439-485, 2005. Google Scholar
  9. Cynthia Dwork and Christina Ilvento. Fairness under composition. In 10th Innovations in Theoretical Computer Science Conference (ITCS 2019). Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik, 2018. Google Scholar
  10. Dean P Foster and Rakesh V Vohra. An economic argument for affirmative action. Rationality and Society, 4(2):176-188, 1992. Google Scholar
  11. Yoav Freund and Robert E Schapire. Game theory, on-line prediction and boosting. In Proceedings of the ninth annual conference on Computational learning theory, pages 325-332, 1996. Google Scholar
  12. Lily Hu and Yiling Chen. A short-term intervention for long-term fairness in the labor market. In Proceedings of the 2018 World Wide Web Conference, pages 1389-1398, 2018. Google Scholar
  13. Christopher Jung, Sampath Kannan, Changwa Lee, Mallesh M. Pai, Aaron Roth, and Rakesh Vohra. Fair prediction with endogenous behavior. Manuscript, 2020. Google Scholar
  14. Sampath Kannan, Aaron Roth, and Juba Ziani. Downstream effects of affirmative action. In Proceedings of the Conference on Fairness, Accountability, and Transparency, pages 240-248, 2019. Google Scholar
  15. Lydia T Liu, Sarah Dean, Esther Rolf, Max Simchowitz, and Moritz Hardt. Delayed impact of fair machine learning. In Proceedings of the 28th International Joint Conference on Artificial Intelligence, pages 6196-6200. AAAI Press, 2019. Google Scholar
  16. Lydia T Liu, Ashia Wilson, Nika Haghtalab, Adam Tauman Kalai, Christian Borgs, and Jennifer Chayes. The disparate equilibria of algorithmic decision making when individuals invest rationally. arXiv preprint, 2019. URL: http://arxiv.org/abs/1910.04123.
  17. Hussein Mouzannar, Mesrob I Ohannessian, and Nathan Srebro. From fair decision making to social equality. In Proceedings of the Conference on Fairness, Accountability, and Transparency, pages 359-368, 2019. Google Scholar
  18. Niche. Best Public Elementary Schools in America, 2020. URL: https://www.niche.com/k12/search/best-public-elementary-schools/.
  19. Ariel D Procaccia and Junxing Wang. Fair enough: Guaranteeing approximate maximin shares. In Proceedings of the fifteenth ACM conference on Economics and computation, pages 675-692, 2014. Google Scholar
  20. U.S. News. Best High Schools Rankings, 2020. URL: https://www.usnews.com/education/best-high-schools.
  21. Samuel F Way, Daniel B Larremore, and Aaron Clauset. Gender, productivity, and prestige in computer science faculty hiring networks. In Proceedings of the 25th International Conference on World Wide Web, pages 1169-1179, 2016. Google Scholar
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