frequency theory of probability

The view developed by Richard von Mises (1883–1953), in his Probability, Statistics, and Truth (1957; 1st German edn., 1928) that the probability of an event in a situation can be defined in terms of the frequency of occurrence of events of the same kind, in some hypothetical population of repetitions of the same situation. The theory gives the simplest relation between probabilities and the evidence of frequencies on which they are based. However, it needs to define the relevant kind of event, the situation, and the hypothetical population: if the latter is infinite then some notion of a limit must be defined, and probability becomes sensitive to the ordering of outcomes in the series. The theory does not easily apply to single events, such as the probability of Eclipse winning the Derby this year, since no unique ‘kind’ of event of which this is an instance, can apparently be defined. In other words, there is no unique way of specifying what would count as a repetition of the same situation, so that frequencies build up. The other problem facing the theory is that it is not clear that the limit gives what we actually want from judgements of probability: it is itself a non-empirical construction—the target of Keynes's famous remark that in the long run we are all dead.