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Ensemble pruning aims to increase efficiency by reducing the number of base classifiers, without sacrificing and preferably enhancing performance. In this brief, a novel pruning paradigm is proposed. Two class supervised learning problems are pruned using a combination of first- and second-order Walsh coefficients. A comparison is made with other ordered aggregation pruning methods, using multilayer perceptron base classifiers. The Walsh pruning method is analyzed with the help of a model that shows the relationship between second-order coefficients and added classification error with respect to Bayes error.