On the (im)possibility of fairness
This work addresses foundational issues in algorithmic fairness for researchers and practitioners, highlighting the need for explicit assumptions in future treatments.
The paper tackles the problem of defining algorithmic fairness by showing that different fairness notions are mutually incompatible under a formal mathematical framework, and demonstrates that proving desirable properties requires specific assumptions about unobservable construct spaces.
What does it mean for an algorithm to be fair? Different papers use different notions of algorithmic fairness, and although these appear internally consistent, they also seem mutually incompatible. We present a mathematical setting in which the distinctions in previous papers can be made formal. In addition to characterizing the spaces of inputs (the "observed" space) and outputs (the "decision" space), we introduce the notion of a construct space: a space that captures unobservable, but meaningful variables for the prediction. We show that in order to prove desirable properties of the entire decision-making process, different mechanisms for fairness require different assumptions about the nature of the mapping from construct space to decision space. The results in this paper imply that future treatments of algorithmic fairness should more explicitly state assumptions about the relationship between constructs and observations.