rule of succession

Principle used by Laplace in his Essai philosophique sur les probabilités (1814), and named by Venn, for determining a probability of the repetition of an event from its frequency of occurrence in some kind of trial. It is an ‘inverse method’, i.e. one that gives an allegedly formal or mathematical rule for deriving probabilities from experienced frequencies. It states that if an event has occurred m times and failed n times under given conditions, then the probability of its occurrence when those conditions are next fulfilled is m + 1/m + n + 2. Laplace uses the principle to prove that given the experience of the human race, the probability of the sun rising tomorrow is 1,826,214 to 1. Unhappily the same reasoning suggests that the chance of it rising every day for the next 4,000 years is not more than 2/3. Some form of the principle was accepted by De Morgan, Lotze, and the statistician Karl Pearson; it was rejected by Boole, Venn, J. Bertrand (1822–1900), and Keynes.