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Assessing Group Fairness with Social Welfare Optimization

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Integration of Constraint Programming, Artificial Intelligence, and Operations Research (CPAIOR 2024)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14742))

Abstract

Statistical parity metrics have been widely studied and endorsed in the AI community as a means of achieving fairness, but they suffer from at least two weaknesses. They disregard the actual welfare consequences of decisions and may therefore fail to achieve the kind of fairness that is desired for disadvantaged groups. In addition, they are often incompatible with each other, and there is no convincing justification for selecting one rather than another. This paper explores whether a broader conception of social justice, based on optimizing a social welfare function (SWF), can be useful for assessing various definitions of parity. We focus on the well-known alpha fairness SWF, which has been defended by axiomatic and bargaining arguments over a period of 70 years. We analyze the optimal solution and show that it can justify demographic parity or equalized odds under certain conditions, but frequently requires a departure from these types of parity. In addition, we find that predictive rate parity is of limited usefulness. These results suggest that optimization theory can shed light on the intensely discussed question of how to achieve group fairness in AI.

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References

  1. Angwin, J., Larson, J., Mattu, S., Kirchner, L.: Machine bias: There’s software used across the country to predict future criminals. And it’s biased against blacks. ProPublica (2016). Accessed 23 May 2016

    Google Scholar 

  2. Anwar, S., Fang, H.: Testing for racial prejudice in the parole board release process: theory and evidence. J. Legal Stud. 44, 1–37 (2015)

    Article  Google Scholar 

  3. Barocas, S., Hardt, M., Narayanan, A.: Fairness and Machine Learning: Limitations and Opportunities. MIT Press, Cambridge (2023)

    Google Scholar 

  4. Baumann, J., Hannó, A., Heitz, C.: Enforcing group fairness in algorithmic decision making: utility maximization under sufficiency. In: Proceedings of FAccT 2022 (2022)

    Google Scholar 

  5. Bertsimas, D., Farias, V., Trichakis, N.: On the fairness-efficiency trade-off. Manag. Sci. 58, 2234–2250 (2012)

    Article  Google Scholar 

  6. Binmore, K., Rubinstein, A., Wolinsky, A.: The Nash bargaining solution in economic modelling. RAND J. Econ. 176–188 (1986)

    Google Scholar 

  7. Binns, R.: Fairness in machine learning: lessons from political philosophy. Proc. Mach. Learn. Res. 8, 1–11 (2018)

    Google Scholar 

  8. Card, D., Smith, N.: On consequentialism and fairness. Front. Artif. Intell. 3, 34 (2020)

    Article  Google Scholar 

  9. Carter, I., Page, O.: When is equality basic. Aust. J. Philos. 101, 983–997 (2022)

    Article  Google Scholar 

  10. Castelnovo, A., Crupi, R., Greco, G., Regoli, D., Penco, I.G., Cosentini, A.C.: A clarification of the nuances in the fairness metrics landscape. Sci. Rep. 12, 4209 (2022)

    Article  Google Scholar 

  11. Chen, V., Hooker, J.N.: A just approach balancing Rawlsian leximax fairness and utilitarianism. In: Proceedings of the AAAI/ACM Conference on AI, Ethics, and Society, pp. 221–227 (2020)

    Google Scholar 

  12. Chen, V., Hooker, J.N.: Combining leximax fairness and efficiency in an optimization model. Eur. J. Oper. Res. 299, 235–248 (2022)

    Article  Google Scholar 

  13. Chen, V., Hooker, J.N.: A guide to formulating fairness in an optimization model. Ann. Oper. Res. 326, 581–619 (2023)

    Article  MathSciNet  Google Scholar 

  14. Chouldechova, A.: Fair prediction with disparate impact: a study of bias in recidivism prediction instruments. Big Data 5(2), 153–163 (2017)

    Article  Google Scholar 

  15. Corbett-Davies, S., Gaebler, J.D., Nilforoshan, H., Shroff, R., Goel, S.: The measure and mismeasure of fairness: a critical review of fair machine learning. J. Mach. Learn. Res. 24, 1–117 (2023)

    Google Scholar 

  16. Dieterich, W., Mendoza, C., Brennan, T.: COMPAS risk scales: Demonstrating accuracy equity and predictive parity. Report , Northpointe Inc., Research Department (2016)

    Google Scholar 

  17. Feldman, M., Friedler, S.A., Moeller, J., Scheidegger, C., Venkatasubramanian, S.: Certifying and removing disparate impact. In: Proceedings of 21st SIGKDD. ACM (2017)

    Google Scholar 

  18. Fjeld, J., Achten, N., Hilligoss, H., Nagy, A., Srikumar, M.: Principled artificial intelligence: mapping consensus in ethical and rights-based approaches to principles for AI. Berkman Klein Center Research Publication No. 2020-1 (2020)

    Google Scholar 

  19. Friedler, S.A., Scheidegger, C., Venkatasubramanian, S.: On the (im)possibility of fairness. Commun. ACM 64, 136–143 (2021)

    Article  Google Scholar 

  20. Greene, J.: Moral Tribes: Emotion, Reason, and the Gap between Us and Them. Penguin Press, London (2013)

    Google Scholar 

  21. Harsanyi, J.C.: Rational Behaviour and Bargaining Equilibrium in Games and Social Situations. Cambridge University Press, Cambridge (1977)

    Book  Google Scholar 

  22. Hooker, J.N., Williams, H.P.: Combining equity and utilitarianism in a mathematical programming model. Manag. Sci. 58, 1682–1693 (2012)

    Article  Google Scholar 

  23. Hu, L., Chen, Y.: Welfare and distributional impacts of fair classification (2018). arXiv preprint arXiv:1807.01134

  24. Hu, L., Chen, Y.: Fair classification and social welfare. In: Proceedings of the 2020 Conference on Fairness, Accountability, and Transparency, pp. 535–545 (2020)

    Google Scholar 

  25. Jobin, A., Ienca, M., Vayena, E.: The global landscape of AI ethics guidelines. Nat. Mach. Intell. 1, 389–399 (2019)

    Article  Google Scholar 

  26. Kalai, E., Smorodinsky, M.: Other solutions to Nash’s bargaining problem. Econometrica 43, 513–518 (1975)

    Article  MathSciNet  Google Scholar 

  27. Karsu, O., Morton, A.: Inequality averse optimization in operational research. Eur. J. Oper. Res. 245, 343–359 (2015)

    Article  Google Scholar 

  28. Kelly, F.P., Maulloo, A.K., Tan, D.K.H.: Rate control for communication networks: shadow prices, proportional fairness and stability. J. Oper. Res. Soc. 49(3), 237–252 (1998)

    Article  Google Scholar 

  29. Kleinberg, J., Mullainathan, S., Raghavan, M.: Inherent trade-offs in the fair determination of risk scores. In: Proceedings, Innovations in Theoretical Computer Science (ITCS). Dagstuhl Publishing, Germany (2017)

    Google Scholar 

  30. Lan, T., Chiang, M.: An axiomatic theory of fairness in resource allocation. Technical report. Princeton University (2011)

    Google Scholar 

  31. Lan, T., Kao, D., Chiang, M., Sabharwal, A.: An axiomatic theory of fairness in network resource allocation. In: Proceedings of the 29th Conference on Information communications (INFOCOM), pp. 1343–1351 (2010)

    Google Scholar 

  32. Leben, D.: Normative principles for evaluating fairness in machine learning. In: Proceedings, AAAI/ACM Conference on AI, Ethics, and Society, pp. 86–92 (2020)

    Google Scholar 

  33. Loi, M., Herlitz, A., Heidari, H.: A philosophical theory of fairness for prediction-based decisions. SSRN Electron. J. (2019)

    Google Scholar 

  34. Mazumdar, R., Mason, L., Douligeris, C.: Fairness in network optimal flow control: optimality of product forms. IEEE Trans. Commun. 39(5), 775–782 (1991)

    Article  Google Scholar 

  35. Mehrabi, N., Morstatter, F., Saxena, N., Lerman, K., Galstyan, A.: A survey on bias and fairness in machine learning. ACM Comput. Surv. (CSUR) 54(6), 1–35 (2021)

    Article  Google Scholar 

  36. Mo, J., Walrand, J.: Fair end-to-end window-based congestion control. IEEE/ACM Trans. Network. 8, 556–567 (2000)

    Article  Google Scholar 

  37. Moss, J.: How to value equality. Philos. Compass 10, 187–196 (2015)

    Article  Google Scholar 

  38. Nash, J.F.: The bargaining problem. Econometrica 18, 155–162 (1950)

    Article  MathSciNet  Google Scholar 

  39. Ogryczak, W., Luss, H., Pióro, M., Nace, D., Tomaszewski, A.: Fair optimization and networks: a survey. J. Appl. Math. 2014, 1–25 (2014)

    MathSciNet  Google Scholar 

  40. Ogryczak, W., Wierzbicki, A., Milewski, M.: A multi-criteria approach to fair and efficient bandwidth allocation. Omega 36(3), 451–463 (2008)

    Article  Google Scholar 

  41. Rubinstein, A.: Perfect equilibrium in a bargaining model. In: Econometrica, pp. 97–109 (1982)

    Google Scholar 

  42. Selbst, A., Barocas, S.: Big data’s disparate impact. Calif. Law Rev. 671, 671–732 (2016)

    Google Scholar 

  43. Verloop, I.M., Ayesta, U., Borst, S.: Monotonicity properties for multi-class queueing systems. Disc. Event Dyn. Syst. 20, 473–509 (2010)

    Article  MathSciNet  Google Scholar 

  44. Williams, A., Cookson, R.: Equity in Health. In: Culyer, A.J., Newhouse, J.P. (eds.) Handbook of Health Economics (2000)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Stevens Institute of Technology, Hoboken, USA

    Violet Chen

  2. Carnegie Mellon University, Pittsburgh, USA

    J. N. Hooker & Derek Leben

Authors
  1. Violet Chen
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  2. J. N. Hooker
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  3. Derek Leben
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Correspondence to J. N. Hooker .

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Editors and Affiliations

  1. University of Southern California, Los Angeles, CA, USA

    Bistra Dilkina

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Chen, V., Hooker, J.N., Leben, D. (2024). Assessing Group Fairness with Social Welfare Optimization. In: Dilkina, B. (eds) Integration of Constraint Programming, Artificial Intelligence, and Operations Research. CPAIOR 2024. Lecture Notes in Computer Science, vol 14742. Springer, Cham. https://doi.org/10.1007/978-3-031-60597-0_14

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  • DOI: https://doi.org/10.1007/978-3-031-60597-0_14

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