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Condorcet's Jury Theorem has been invoked for ensemble classifiers toindicate that the combination of many classifiers can have better predictiveperformance than a single classifier. Such a theoretical underpinning isunknown for consensus clustering. This article extends Condorcet's Jury Theoremto the mean partition approach under the additional assumptions that a uniqueground-truth partition exists and sample partitions are drawn from asufficiently small ball containing the ground-truth. As an implication ofpractical relevance, we question the claim that the quality of consensusclustering depends on the diversity of the sample partitions. Instead, weconjecture that limiting the diversity of the mean partitions is necessary forcontrolling the quality.

Condorcet's Jury Theorem for Consensus Clustering and its Implications for Diversity