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We develop two tools to analyze the behavior of multiple-class, or multi-class, classifiers by means of entropic measures on their confusion matrix or contingency table. First we obtain a balance equation on the entropies that captures interesting properties of the classifier. Second, by normalizing this balance equation we first obtain a 2-simplex in a three-dimensional entropy space and then the de Finetti entropy diagram or entropy triangle. We also give examples of the assessment of classifiers with these tools.