Exploring Simpson’s Paradox Through the Lens of Fuzzy Causal Inference

In this paper, we demonstrate the utility of probabilistic fuzzy logic in providing a flexible and sound framework for analyzing causality. Initially, we identify a limitation associated with the conventional Average Treatment Effect (ATE) methodology for non-binary treatments, which requires a threshold to segregate treatment values into treatment and control groups. This dichotomy becomes problematic near the threshold, where it is unreasonable to categorize similar values distinctly into treatment or control groups. We propose the Fuzzy Average Treatment Effect (FATE) as a generalization of ATE to address this issue, ensuring a smoother transition between groups. To address this, we adopt a probabilistic fuzzy perspective, which allows us to tackle questions like: “What is the probability of selecting a value of a random variable \(T\) to be high, equal to \(t\) ?” Moreover, we explore the resolution of Simpson’s paradox, exemplifying the shortcomings of traditional probability and statistics theories, thereby underscoring the advantages of our approach.