English Translation of Cournot's "Exposition de la th\'eorie des chances et des probabilit\'es" / "Exposition of the Theory of Chances and Probabilities"

TL;DR

This paper analyzes Cournot's foundational contributions to probability theory, highlighting his innovative definitions, concepts like stratified sampling, and his philosophical approach, despite some limitations in scientific knowledge.

Contribution

It provides a detailed analysis of Cournot's work, emphasizing his novel ideas and their influence on the development of probability and statistics.

Findings

Cournot introduced the median and a unified definition of probability.

He studied mixtures of densities and explained randomness qualitatively.

Cournot advocated for a dedicated theory of statistics.

Abstract

In spite of the wide range of his book, Cournot did not know some essential discoveries in natural sciences (William Herschel, Daniel Bernoulli, Humboldt) and his deliberations about measurement were almost useless. But he introduced the median and a definition of probability that covered both the discrete and continuous cases; studied mixtures of densities; qualitatively explained randomness anticipating one of Poincar\`e's interpretations (small causes leading to considerable effects) and introducing an embryo of irregularity as a condition of randomness; introduced a pattern of stratified sampling; attempted to study dependence between the decisions of jurors; introduced (after J. F. Fries) philosophical, i.e. qualitative probabilities. Cournot stated that statistics ought to have its own theory, rules and principles and should penetrate into the essence of things (which was not yet a received opinion). Many of his pronouncements were thoughtful and echoed the statistical thought of the time. In 1849 his book was translated into German.