{'fraction_non_alphanumeric': 0.01819454163750875, 'fraction_numerical': 0.0027991602519244225, 'mean_word_length': 5.651162790697675, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Confidence Theory: Belief Formation in Choice Under Risk

In confidence theory, the decision maker relies on statistical regularities from the economic environment to adopt prior beliefs about the probabilities stated on a lottery. Following the confidence principle, by which the weight of the prior in Bayesian inference is proportional to the uncertainty related to its distribution, the decision maker arrives at the posterior that is used in lottery evaluation. The confidence principle is justified by a rational analysis of belief formation in choice under risk. Three novel experiments are presented that demonstrate the ability of the new theory to explain the empirical correspondences among (1) judgments of similarity between monetary outcomes, (2) certainty equivalents of risky lotteries, (3) judgments of a priori probabilities to obtain a particular monetary outcome, and (4) judgments of revised stated probabilities that were used in the evaluation of certainty equivalents. The decision model employed in confidence theory is an elaboration of Viscusi’s prospective reference theory and accounts for the robust violations of expected utility theory, as well as for the “new paradoxes” that falsify cumulative prospect theory. The model is characterized by a class of outcome-dependent probability updating functions that jointly explain the structure of probability distortions in behavioral choice under risk.