Fair classification and social welfare

Now that machine learning algorithms lie at the center of many important resource allocation pipelines, computer scientists have been unwittingly cast as partial social planners. Given this state of affairs, important questions follow. How do leading notions of fairness as defined by computer scientists map onto longer-standing notions of social welfare? In this paper, we present a welfare-based analysis of fair classification regimes. Our main findings assess the welfare impact of fairness-constrained empirical risk minimization programs on the individuals and groups who are subject to their outputs. We fully characterize the ranges of Δ'e perturbations to a fairness parameter 'e in a fair Soft Margin SVM problem that yield better, worse, and neutral outcomes in utility for individuals and by extension, groups. Our method of analysis allows for fast and efficient computation of "fairness-to-welfare" solution paths, thereby allowing practitioners to easily assess whether and which fair learning procedures result in classification outcomes that make groups better-off. Our analyses show that applying stricter fairness criteria codified as parity constraints can worsen welfare outcomes for both groups. More generally, always preferring "more fair" classifiers does not abide by the Pareto Principle---a fundamental axiom of social choice theory and welfare economics. Recent work in machine learning has rallied around these notions of fairness as critical to ensuring that algorithmic systems do not have disparate negative impact on disadvantaged social groups. By showing that these constraints often fail to translate into improved outcomes for these groups, we cast doubt on their effectiveness as a means to ensure fairness and justice.