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A trade-off between accuracy and fairness is almost taken as a given in theexisting literature on fairness in machine learning. Yet, it is not preordainedthat accuracy should decrease with increased fairness. Novel to this work, weexamine fair classification through the lens of mismatched hypothesis testing:trying to find a classifier that distinguishes between two ideal distributionswhen given two mismatched distributions that are biased. Using Chernoffinformation, a tool in information theory, we theoretically demonstrate that,contrary to popular belief, there always exist ideal distributions such thatoptimal fairness and accuracy (with respect to the ideal distributions) areachieved simultaneously: there is no trade-off. Moreover, the same classifieryields the lack of a trade-off with respect to ideal distributions whileyielding a trade-off when accuracy is measured with respect to the given(possibly biased) dataset. To complement our main result, we formulate anoptimization to find ideal distributions and derive fundamental limits toexplain why a trade-off exists on the given biased dataset. We also deriveconditions under which active data collection can alleviate thefairness-accuracy trade-off in the real world. Our results lead us to contendthat it is problematic to measure accuracy with respect to data that reflectsbias, and instead, we should be considering accuracy with respect to ideal,unbiased data.

Is There a Trade-Off Between Fairness and Accuracy? A Perspective Using Mismatched Hypothesis Testing