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

TL;DR

This paper critically examines the Hong-Page Theorems and Landemore's use of them, revealing errors and misinterpretations that highlight the importance of careful mathematical application in social science theories.

Contribution

It provides a rigorous critique of the theorems and their application, emphasizing the need for precise mathematical understanding in collective intelligence research.

Findings

Identifies errors in the Hong-Page Theorems

Highlights misinterpretations in Landemore's application

Underscores the importance of ability in group problem-solving

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.