Majority Voting and the Condorcet's Jury Theorem

TL;DR

This paper explores the connection between Condorcet's jury theorem and ensemble learning, providing a simple, rigorous proof to enhance understanding and teaching of the underlying principles in machine learning.

Contribution

The paper offers a clear, accessible mathematical proof of Condorcet's jury theorem, linking it to modern ensemble learning concepts and aiding educational efforts.

Findings

Provides a rigorous proof of Condorcet's theorem

Establishes a connection between voting theory and ensemble learning

Aims to improve teaching of machine learning fundamentals

Abstract

There is a striking relationship between a three hundred years old Political Science theorem named "Condorcet's jury theorem" (1785), which states that majorities are more likely to choose correctly when individual votes are often correct and independent, and a modern Machine Learning concept called "Strength of Weak Learnability" (1990), which describes a method for converting a weak learning algorithm into one that achieves arbitrarily high accuracy and stands in the basis of Ensemble Learning. Albeit the intuitive statement of Condorcet's theorem, we could not find a compact and simple rigorous mathematical proof of the theorem neither in classical handbooks of Machine Learning nor in published papers. By all means we do not claim to discover or reinvent a theory nor a result. We humbly want to offer a more publicly available simple derivation of the theorem. We will find joy in seeing more teachers of introduction-to-machine-learning courses use the proof we provide here as an exercise to explain the motivation of ensemble learning.