Coherent Distorted Beliefs

TL;DR

This paper introduces a new consistency condition called distortion coherence for belief distortions, deriving a specific functional form and linking it to models of motivated beliefs and decision-making anomalies.

Contribution

It proposes the concept of distortion coherence, characterizes the form of belief distortions, and connects these to existing models of motivated beliefs and decision-making anomalies.

Findings

Distortion coherence restricts belief distortions to power-weighted forms.

Coherent distortions relate to models of motivated beliefs via a generalized Kullback-Liebler cost.

In lottery choice, coherent distortions explain non-expected utility phenomena like the Allais paradox.

Abstract

Many models of economics assume that individuals distort objective probabilities. We propose a simple consistency condition on distortion functions, which we term distortion coherence, that ensures that the function commutes with conditioning on an event. We show that distortion coherence restricts belief distortions to have a particular function form: power-weighted distortions, where distorted beliefs are proportional to the original beliefs raised to a power and weighted by a state-specific value. We generalize our findings to allow for distortions of the probabilities assigned to both states and signals, which nests the functional forms widely used in studying probabilistic biases (e.g., Grether, 1980 and Benjamin, 2019). We show how coherent distorted beliefs are tightly related to several extant models of motivated beliefs: they are the outcome of maximizing anticipated expected utility subject to a generalized Kullback-Liebler cost of distortion. Moreover, in the domain of lottery choice, we link coherent distortions to explanations of non-expected utility like the Allais paradox: individuals who maximize subjective expected utility maximizers conditional on coherent distorted beliefs are equivalent to the weighted utility maximizers studied by Chew [1983].