WP 2020-13 The Probability Discounting Model of Choice Under Risk: A Critique
AUTHORS: Andre Hofmeyr
ABSTRACT: The probability discounting model has become a popular framework for investigating choice under risk in psychology. But it is not clear how the model relates to standard theories of choice under risk, such as expected utility theory and prospect theory. I critically review the theoretical development of the model and argue that it rests on an outdated conception of reinforcement learning. I also show that it is formally isomorphic to the dual theory of choice under risk, but that it is limited to simple prospects with a specific parametric probability weighting function. I discuss the methodological and statistical approaches typically used in studies of probability discounting and develop a structural statistical framework to test the efficacy of the model’s implied probability weighting function in applied work. Using data from a widely-cited study, I show that the probability discounting model is needlessly restrictive since it does not allow for the simultaneous overweighting and underweighting of probabilities, which is a common pattern identified in the experimental literature on choice under risk.