Title: The impossibility of "fairness": a generalized impossibility result for decisions,
Abstract: Various measures can be used to estimate bias or unfairness in a predictor.
Previous work has already established that some of these measures are
incompatible with each other. Here we show that, when groups differ in
prevalence of the predicted event, several intuitive, reasonable measures of
fairness (probability of positive prediction given occurrence or
non-occurrence; probability of occurrence given prediction or non-prediction;
and ratio of predictions over occurrences for each group) are all mutually
exclusive: if one of them is equal among groups, the other two must differ. The
only exceptions are for perfect, or trivial (always-positive or
always-negative) predictors. As a consequence, any non-perfect, non-trivial
predictor must necessarily be "unfair" under two out of three reasonable sets
of criteria. This result readily generalizes to a wide range of well-known
statistical quantities (sensitivity, specificity, false positive rate,
precision, etc.), all of which can be divided into three mutually exclusive
groups. Importantly, The results applies to all predictors, whether algorithmic
or human. We conclude with possible ways to handle this effect when assessing
and designing prediction methods.