Fatal errors and misuse of mathematics in the Hong-Page Theorem and Landemore's epistemic argument

In the pursuit of understanding collective intelligence, the Hong-Page Theorems have been presented as cornerstones of the interplay between diversity and ability. However, upon rigorous examination, there seem to be inherent problems and misinterpretations within these theorems. Hélène Landemore’s application of these results in her epistemic argument and her political proposal showcases a invalid use of mathematical principles. This paper critically dissects the Hong-Page Theorems, revealing significant inconsistencies and oversights, and underscores the indispensable role of ``ability" in group problem-solving contexts. This paper aims not to undermine the importance of diversity, but rather to highlight the dangers of misusing mathematical principles and the necessity for a more careful analysis of mathematical results when applying them to social sciences.d the necessity for a more nuanced comprehension of mathematical results when applying them to social sciences.