Data speak but sometimes lie: A game-theoretic approach to data bias and algorithmic fairness

• Novel logic-based approach to data bias in machine learning predictions for defining and quantifying fairness based on the Ulam game. • New perspectives on the rule of constrained monotonicity valid in the play process of the Ulam game and its generalisation to weighted evidence. • Connection between the notion of correctability and levels of monotonicity satisfied by machine learning algorithms. • Novel game-theoretic framework of algorithmic fairness. In the present work, we develop a novel information-theoretic and logic-based approach to data bias in Machine Learning predictions and show its relevance in the specific context of fairness evaluation. We frame predictions made on biased data as Ulam games, which formalise key aspects of data-driven inference, and from which a variation of the rational non-monotonic consequence relation can be defined. We investigate this framework to model how differential levels of noise in input features impact Machine Learning predictions. To the best of our knowledge, this is the first game-theoretic formalisation of ML unfairness.