Novel Bounds on the Probability of Misclassification in Majority Voting: Leveraging the Majority Size

Majority voting is often employed as a tool to increase the robustness of data-driven decisions and control policies, a fact which calls for rigorous, quantitative evaluations of the limits and the potentials of majority voting schemes. This letter focuses on the case where the voting agents are binary classifiers and introduces novel bounds on the probability of misclassification conditioned on the size of the majority. We show that these bounds can be much smaller than the traditional upper bounds on the probability of misclassification. These bounds can be used in a `Probably Approximately Correct' (PAC) setting, which allows for a practical implementation.