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There is a striking relationship between a three hundred years old PoliticalScience theorem named "Condorcet's jury theorem" (1785), which states thatmajorities are more likely to choose correctly when individual votes are oftencorrect and independent, and a modern Machine Learning concept called "Strengthof Weak Learnability" (1990), which describes a method for converting a weaklearning algorithm into one that achieves arbitrarily high accuracy and standsin the basis of Ensemble Learning. Albeit the intuitive statement ofCondorcet's theorem, we could not find a compact and simple rigorousmathematical proof of the theorem neither in classical handbooks of MachineLearning nor in published papers. By all means we do not claim to discover orreinvent a theory nor a result. We humbly want to offer a more publiclyavailable simple derivation of the theorem. We will find joy in seeing moreteachers of introduction-to-machine-learning courses use the proof we providehere as an exercise to explain the motivation of ensemble learning.

Majority Voting and the Condorcet's Jury Theorem