Probability discounting and economic theories of choice under risk: a translation and critique

Probability discounting is a widely used framework for studying attitudes to risk in psychology, with applications spanning addiction, gambling and clinical research. Despite its prevalence, the model’s connection to established economic theories of choice under risk, such as expected utility theory and prospect theory, remains poorly understood. I critically examine the theoretical foundations of the probability discounting model, arguing that it rests on an outdated conception of reinforcement learning. I show that the model is formally isomorphic to the dual theory of choice under risk, but limited to binary prospects with a fixed parametric probability weighting function. I review the methodological and statistical approaches commonly used in probability discounting research and employ a structural econometric framework to test the validity of the model’s implied probability weighting function. Using data from a widely cited study, I demonstrate that the probability discounting model is overly restrictive because it cannot capture the simultaneous overweighting and underweighting of probabilities, a common finding in experimental studies of choice under risk. These results suggest that researchers in applied domains should transition to the more flexible, well-established models of choice under risk used in economics and decision theory.