English Translation of Poisson's "Recherches sur la probabilit\'e des jugements en mati\`ere criminelle et en mati\`ere civile" / "Researches into the Probabilities of Judgements in Criminal and Civil Cases"

Abstract

In spite of its title, the book mostly treats probability theory: the law of large numbers (regarded as a principle); formal definition of a random variable and law of distribution; the misnamed Cauchy distribution; functions now named after Dirac; difference between objective and subjective probabilities; approximation of the Bernoulli theorem for rare events (but not yet the Poisson distribution); investigation of the significance of empirical discrepancies. Following Laplace, he actually attributed probability to applied mathematics. Poisson calculated the optimal number of jurors and of their majority for conviction/exoneration of the accused and in general studied the conditions enabling to minimize miscarriage of justice. He replaced guilty and innocent by convictable or not.