Fairness and Randomness in Machine Learning: Statistical Independence and Relativization

Fair Machine Learning endeavors to prevent unfairness arising in the context of machine learning applications embedded in society. Despite the variety of definitions of fairness and proposed "fair algorithms", there remain unresolved conceptual problems regarding fairness. In this paper, we argue that randomness and fairness can be considered equivalent concepts in machine learning. We obtain a relativized notion of randomness expressed as statistical independence by appealing to Von Mises' century-old foundations for probability. Via fairness notions in machine learning, which are expressed as statistical independence as well, we then link the ante randomness assumptions about the data to the ex post requirements for fair predictions. This connection proves fruitful: we use it to argue that randomness and fairness are essentially relative and that randomness should reflect its nature as a modeling assumption in machine learning.