A note on probability matching and rational choice

For two decades many scholars have considered the behavior of human subjects in two-choice noncontingent probability learning experiments as evidence that subjects' choices are not optimal in a decision theoretic sense. In this paper we argue that experimenters have made a crucial logical error in forming the sequences of events for the two-choice experiments. The probability of occurrence of each of two events is not constant over the sequence but instead varies considerably from trial to trial, in violation of noncontingency. This experimental procedure has at least three important consequences: (1) Most experimenters test the wrong hypothesis. (2) Subjects are justified in departing from a maximizing strategy at certain points in the schedule of events. (3) The gambler's fallacy is sometimes less a fallacy than an astute choice of strategy.