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The themes of collective wisdom and cognitive advantages of diversity have benefited in recent years from a certain attraction in political theory, particularly in the so-called epistemic democracy movement. One of the main arguments is based on a set of mathematical demonstrations established by Lu Hong and Scott Page. We present these results and show that the models used to establish them are poorly constructed and that results are incorrect from a mathematical point of view. In the end, we point out that, even if the results were well constructed and exact, they would be inapplicable in political theory.