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

\'Alvaro Romaniega

Papers from arXiv.org

Abstract: 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. H\'el\`ene 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.

Date: 2023-07, Revised 2025-01
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