DeepAI

# Majority Voting and the Condorcet's Jury Theorem

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.

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10/11/2022

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This report presents a formalization of May's theorem in the proof assis...
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### A formalisation of Gallagher's ergodic theorem

Gallagher's ergodic theorem is a result in metric number theory. It stat...
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### Gács-Kučera's Theorem Revisited by Levin

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### A Constructive Formalization of the Weak Perfect Graph Theorem

The Perfect Graph Theorems are important results in graph theory describ...
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Theorem 12 of Simon-Gabriel Schölkopf (JMLR, 2018) seemed to close a...
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### A solution to Ringel's circle problem

We construct families of circles in the plane such that their tangency g...
04/28/2022

### Skolem Meets Schanuel

The celebrated Skolem-Mahler-Lech Theorem states that the set of zeros o...