  In his seminal work, Schapire (1990) proved that weak classifiers could be
improved to achieve arbitrarily high accuracy, but he never implied that a
simple majority-vote mechanism could always do the trick. By comparing the
asymptotic misclassification error of the majority-vote classifier with the
average individual error, we discover an interesting phase-transition
phenomenon. For binary classification with equal prior probabilities, our
result implies that, for the majority-vote mechanism to work, the collection of
weak classifiers must meet the minimum requirement of having an average true
positive rate of at least 50% and an average false positive rate of at most
50%.
