Decisions Under Uncertainty as Bayesian Inference on Choice Options

Standard models of decision making under risk and uncertainty are deterministic. Inconsistencies in choices are accommodated by separate error models. The combination of decision model and error model, however, is arbitrary. Here, I derive a model of decision making under uncertainty in which choice options are mentally encoded by noisy signals, which are optimally decoded by Bayesian combination with preexisting information. The model predicts diminishing sensitivity toward both likelihoods and rewards, thus providing cognitive microfoundations for the patterns documented in the prospect theory literature. The model is, however, inherently stochastic, so that choices and noise are determined by the same underlying parameters. This results in several novel predictions, which I test on one existing data set and in two new experiments.