Yet another impossibility theorem in algorithmic fairness

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.