Published online by Cambridge University Press: 05 June 2014
Paris, 16 November 1835 Things of every kind are subject to a universal law that we may call the law of large numbers. It consists in this: if one observes a very considerable number of events of the same kind, depending on causes that vary irregularly, that is to say, without any systematic variation in one direction, then one finds that the ratios between the numbers of events are very nearly constant.
Paris, 16 April 1842 The Law of Large Numbers does not exist.
The ministry of justice published annual data for the years following 1826. It highlighted summary figures for trials and convictions. They led Poisson to the great work of 1837 in which he proved a law of large numbers, and gave us the very phrase, ‘law of large numbers’, that still finds a place in every probability primer. His book distinguished more clearly than any predecessor between ‘relative frequency’ and ‘degree of belief’ approaches to probability. It applied statistical tests and measures of reliability in a way that makes clear, as Stigler has shown, that Poisson understood their logic in an unequivocal way. It provided the first sound mathematics for quite rare events, now called the Poisson distribution, work well reported by O.B. Sheynin. The deductions from jury data have recently been analysed by Gelfand and Solomon, because of the 1967 decision of the United States Supreme Court, declaring it constitutional for juries to decide by majority and not unanimously. In the same year England allowed conviction by a majority vote of ten against two.
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