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. (shrink)

Using the flexibility of recently developed methods for causal discovery based on Boolean satisfiability solvers, we encode a variety of assumptions that weaken the Faithfulness assumption. The encoding results in a number of SAT-based algorithms whose asymptotic correctness relies on weaker conditions than are standardly assumed. This implementation of a whole set of assumptions in the same platform enables us to systematically explore the effect of weakening the Faithfulness assumption on causal discovery. An important effect, suggested by simulation results, is (...) that adopting weaker assumptions greatly alleviates the problem of conflicting constraints and substantially shortens solving time. As a result, SAT-based causal discovery is potentially more scalable under weaker assumptions. (shrink)