A re‐examination of probability matching and rational choice

Abstract

In a typical probability learning task participants are presented with a repeated choice between two response alternatives, one of which has a higher payoff probability than the other. Rational choice theory requires that participants should eventually allocate all their responses to the high-payoff alternative, but previous research has found that people fail to maximize their payoffs. Instead, it is commonly observed that people match their response probabilities to the payoff probabilities. We report three experiments on this choice anomaly using a simple probability learning task in which participants were provided with (i) large financial incentives, (ii) meaningful and regular feedback, and (iii) extensive training. In each experiment large proportions of participants adopted the optimal response strategy and all three of the factors mentioned above contributed to this. The results are supportive of rational choice theory. Copyright # 2002 John Wiley & Sons, Ltd.key words probability matching; maximization; choice; rationality; feedback; payoffs; learning; reinforcement A striking violation of rational choice theory is commonly observed in simple repeated binary choice tasks in which a payoff is available with higher probability given one response than another. In such tasks people often tend to 'match' probabilities: That is, they allocate their responses to the two options in proportion to their relative payoff probabilities. Thus suppose that a monetary payoff of fixed size is given with probability p ¼ 0.7 for choosing left and with probability 1 À p ¼ 0.3 for choosing right. Probability matching refers to behavior in which left is chosen on about 70% of trials and right on 30%. Such responding violates rational choice theory because the optimal strategy in such tasks, after an initial period of experimentation and assuming that the payoff probabilities are stationary, is always to select the option associated with the higher probability of payoff. On any trial, the expected payoff for choosing left is higher than the expected payoff for choosing right.

Learning to avoid in older age.

“…There was also a marginal interaction between age group and win-stay versus loseshift performance during training (see Figure 3), F(1, 41) ϭ 3.3, p ϭ .078. A potential alternative account of the data is that, rather than showing differences in avoidance learning, perhaps O-O participants are more likely than their Y-O counterparts to optimize, rather than match, responding (e.g., Estes, 1961;Shanks, Tunney, & McCarthy, 2002). Optimizing is characterized by always choosing the stimulus with greatest reward probability, whereas matching reflects a tendency to allocate behavioral choices in proportion to the probabilities.…”

Stimulus–outcome learnability differentially activates anterior cingulate and hippocampus at feedback processing

“…Individually, subjects vary in the amount of optimally choosing the most likely outcome versus nonoptimal behaviors, such as probability matching (see also Shanks et al 2002). In the last two scanning runs, two subjects chose the most likely outcome in 100% of trials, two subjects chose it in at least 94.4% of trials, four subjects chose it in 91.6% of trials, and the other six chose it in a range of 66.6%-88.9% of trials.…”

Betting on Illusory Patterns: Probability Matching in Habitual Gamblers

“….25 9 .25). Probability matching is highly persistent (Healy and Kubovy 1981;Shanks et al 2002;for reviews, see Myers 1976;Vulkan 2000), even in tasks in which participants did not have to learn the outcome probabilities but were presented with a full description of outcomes and their probability (Gal and Baron 1996;Koehler and James 2009;Newell et al 2013;Newell and Rakow 2007;West and Stanovich 2003).…”