Don't Label Twice: Quantity Beats Quality when Comparing Binary Classifiers on a Budget

ArXi:2402.02249v3 Announce Type: replace We study how to best spend a budget of noisy labels to compare the accuracy of two binary classifiers. It's common practice to collect and aggregate multiple noisy labels for a given data point into a less noisy label via a majority vote. We prove a theorem that runs counter to conventional wisdom. If the goal is to identify the better of two classifiers, we show it's best to spend the budget on collecting a single label for samples. Our result follows from a non-trivial application of Cram\'er's theorem, a staple in the theory of large deviations.