  There is a striking relationship between a three hundred years old Political
Science theorem named "Condorcet's jury theorem" (1785), which states that
majorities are more likely to choose correctly when individual votes are often
correct and independent, and a modern Machine Learning concept called "Strength
of Weak Learnability" (1990), which describes a method for converting a weak
learning algorithm into one that achieves arbitrarily high accuracy and stands
in the basis of Ensemble Learning. Albeit the intuitive statement of
Condorcet's theorem, we could not find a compact and simple rigorous
mathematical proof of the theorem neither in classical handbooks of Machine
Learning nor in published papers. By all means we do not claim to discover or
reinvent a theory nor a result. We humbly want to offer a more publicly
available simple derivation of the theorem. We will find joy in seeing more
teachers of introduction-to-machine-learning courses use the proof we provide
here as an exercise to explain the motivation of ensemble learning.
