Benjamin Skjold

Probability weighting describes a systematic discrepancy between subjective probabilities and the objective probabilities of a given generative process. Since its introduction as part of prospect theory, probability weighting has been considered an irrational cognitive bias --- an error of judgment committed by the decision maker. Recently, theories seeking to provide normative accounts for probability weighting have emerged. These attempt to explain why decision makers should express these discrepancies. One such theory, which we term the mechanistic model, proposes that probability weighting can be explained simply as a decision maker having greater uncertainty about the world than the experimenter. Such uncertainty arises naturally in decisions from experience, where the decision maker is expected to experience rare outcomes less often than the objective probabilities in the experimenter's code prescribe. Arcording to this theory, uncertainty decreases with increased experience, introducing a time-dependency whereby the discrepancy between subjective and objective probabilities narrows with time. This approach contrasts with prospect theory, a descriptive theory, which provides a functional form for describing the probability weighting, and treats the phenomena as a static trait of the decision maker. The two theoretical approaches thus make different experimental predictions. Here we present a Bayesian cognitive model that formalizes the two competing models, incorporating both models into one hierarchical latent mixture model. We explore how the different theories behave when faced with a simple experimental paradigm of decision making from experience. We simulate choice data from synthetic agents behaving in accordance with each theory, showing how this leads to discrepant experimental predictions that diverge as the agents acquire more experience. We show that the same modeling framework when applied to the synthetic choice data, can accurately recover the correct model and that it can recover ground truth parameters, wherever they occur. This work can be taken as preregistration of the formal hypotheses of the two models for a simple experimental paradigm and provides the code necessary for future experimental implementation, model comparison, and parameter inference. Together, this demonstrates the tractability of empirically discriminating between normative and descriptive theories of probability weighting.