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A number of applications (e.g., AI bot tournaments, sports, peer grading,crowdsourcing) use pairwise comparison data and the Bradley-Terry-Luce (BTL)model to evaluate a given collection of items (e.g., bots, teams, students,search results). Past work has shown that under the BTL model, the widely-usedmaximum-likelihood estimator (MLE) is minimax-optimal in estimating the itemparameters, in terms of the mean squared error. However, another importantdesideratum for designing estimators is fairness. In this work, we considerfairness modeled by the notion of bias in statistics. We show that the MLEincurs a suboptimal rate in terms of bias. We then propose a simplemodification to the MLE, which "stretches" the bounding box of themaximum-likelihood optimizer by a small constant factor from the underlyingground truth domain. We show that this simple modification leads to an improvedrate in bias, while maintaining minimax-optimality in the mean squared error.In this manner, our proposed class of estimators provably improves fairnessrepresented by bias without loss in accuracy.

Stretching the Effectiveness of MLE from Accuracy to Bias for Pairwise Comparisons