Abstract
In recent years, there has been a surge in research addressing the question which properties predictive algorithms ought to satisfy in order to be considered fair. Three of the most widely discussed criteria of fairness are the criteria called equalized odds, predictive parity, and counterfactual fairness. In this paper, I will present a new impossibility result involving these three criteria of algorithmic fairness. In particular, I will argue that there are realistic circumstances under which any predictive algorithm that satisfies counterfactual fairness will violate both other fairness criteria, that is, equalized odds and predictive parity. As will be shown, this impossibility result forces us to give up one of four intuitively plausible assumptions about algorithmic fairness. I will explain and motivate each of the four assumptions and discuss which of them can plausibly be given up in order to circumvent the impossibility.
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Notes
This is because after the intervention on S, L is screened off from \(U_2\).
For a discussion and defense of the two assumptions, see Pearl (2009, pp. 61–64) and Zhang and Spirtes (2016). Note, that some authors occassionally use an assumption weaker than faithfulness, namely causal minimality (Zhang and Spirtes, 2011) The argument in this paper, however, relies on inferential steps in both directions: from (conditional) independencies to properties of the causal graph, as well as from properties of the causal graph to (conditional) indepenencies. The minimality condition alone would not suffice to allow for these steps under all possible probabilistic parameters in the causal model (if, say, the effect of one causal path were to exactly undo the effect along another one in terms of a change in the probability distribution).
See, e.g., Title VII of the Civil Rights Act of 1964, the Age Discrimination in Employment Act of 1967, the Rehabilitation Act of 1973, and the Americans with Disabilities Act of 1990.
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Beigang, F. Yet Another Impossibility Theorem in Algorithmic Fairness. Minds & Machines 33, 715–735 (2023). https://doi.org/10.1007/s11023-023-09645-x
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DOI: https://doi.org/10.1007/s11023-023-09645-x