Nested dichotomies are a standard statistical technique for tackling certain polytomous classification problems with logistic regression. They can be represented as binary trees that recursively split a multi-class classification task into a system of dichotomies and provide a statistically sound way of applying two-class learning algorithms to multi-class problems (assuming these algorithms generate class probability estimates). However, there are usually many candidate trees for a given problem and in the standard approach the choice of a particular tree is based on domain knowledge that may not be available in practice. An alternative is to treat every system of nested dichotomies as equally likely and to form an ensemble classifier based on this assumption. We show that this approach produces more accurate classifications than applying C4.5 and logistic regression directly to multi-class problems. Our results also show that ensembles of nested dichotomies produce more accurate classifiers than pairwise classification if both techniques are used with C4.5, and comparable results for logistic regression. Compared to error-correcting output codes, they are preferable if logistic regression is used, and comparable in the case of C4.5. An additional benefit is that they generate class probability estimates. Consequently they appear to be a good general-purpose method for applying binary classifiers to multi-class problems.