WP 2016-01 Recovering Subjective Probability Distributions
This was originally posted as WP 2015-01, but was duplicated. In order to maintain the accuracy of links already given out, the 2015-01 page redirects to this page.
ABSTRACT: An individual reports subjective beliefs over continuous events using a proper scoring rule, such as the popular Quadratic Scoring Rule. Under some mild additional assumption, it is known that these reports reflect latent subjective beliefs if the individual is risk neutral and obeys Subjective Expected Utility (SEU) theory. It is also known that these reports are very close to latent subjective beliefs if the individual obeys SEU and has a concave utility function in the range observed over typical payments in experiments. We extend these results in three ways. First, we demonstrate how to fully recover latent subjective beliefs if the individual obeys SEU and has a concave utility function within or beyond the “observed range” in experiments. Second, and more significantly for practical purposes, we demonstrate how to fully recover latent subjective beliefs if the individual is known to distort probabilities into decision weights using Rank Dependent Utility (RDU) theory. We illustrate with a range of beliefs elicited from individuals in experiments, and for whom we also have estimates of their risk preferences to allow us to identify SEU and RDU individuals. Third, we generalize all results for the complete class of proper scoring rules. These theoretical results and empirical applications significantly widen the domain of applicability of proper scoring rules for eliciting latent subject belief distributions.