We consider the problem of dealing with irrelevant votes when a multi-case classifier is built from an ensemble of binary classifiers. We show how run-off elections can be used to limit the effects of irrelevant votes and the occasional errors of binary classifiers, improving classification accuracy. We consider as a concrete classification problem the recognition of handwritten mathematical characters. A succinct representation of handwritten symbol curves can be obtained by computing truncated Legendre-Sobolev expansions of the coordinate functions. With this representation, symbol classes are well linearly separable in low dimension which yields fast classification algorithms based on linear support vector machines. A set of 280 different symbols was considered, which gave 1635 classes when different variants are labelled separately. With this number of classes, however, the effect of irrelevant classifiers becomes significant, often causing the correct class to be ranked lower. We introduce a general technique to correct this effect by replacing the conventional majority voting scheme with a runoff election scheme. We have found that such runoff elections further cut the top-1 mis-classification rate by about half. 1
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