Probability matching behavior, association, and rational choice

Abstract

In two-event noncontingent probability learning experiments with individual human beings (systems at the organism level), probability matching behavior (the widely reported experimental finding that the prediction probability of subjects tends to match the outcome probability of events) has been regarded as anomalous by economists and decision theorists since in sight of the goal of maximizing the number of correct predictions, the maximize expected value strategy—always predict the more frequent event—dominates it as a strategy. In part one of this paper, a flexible explanation based upon the stipulation that subjects assume that there is positive association between the prediction and the outcome is proposed and grounded in the theory of reflexive predictions. Given this stipulation, probability matching is the dominant rational strategy. Numerous experiments which utilize a blocked sampling without replacement procedure introduce dependence between the remaining trials in a block and the past outcomes in violation of noncontingency. In part two of this paper, an exact solution to the amount of dependence introduced by sampling without replacement is given. Formulae are derived for the expected payoff and expected response proportions for an equivalence class of value maximizing decision rules. Two conclusions follow. First, precise limits are placed on the applicability of explanations which rely on the assumption that subjects can detect patterns in the outcomes. Second, experiments with relatively large block sizes are approximately equivalent to the analogous noncontingent experiment at least for the middle to high range of outcome probability.

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