Mathematical models of confirmation bias

TL;DR

This paper develops mathematical models to understand confirmation bias, showing how opinion updates are influenced by the distance of new observations from prior beliefs, affecting belief persistence and polarization.

Contribution

It introduces a general framework for modeling confirmation bias through opinion discounting based on observation distance, exploring diverse behaviors and classification of models.

Findings

Influence of observations varies with their distance from prior opinion.

Models demonstrate belief persistence and attitude polarization.

Some models show influence increasing with distance, others show the opposite.

Abstract

Confirmation bias is a cognitive bias that adversely affects management decisions, and mathematical modelling is an aid to its detailed understanding. Bias in opinion update about the value of a parameter is modelled here assuming that observations are discounted depending on their distance from prior opinion. The models allow belief persistence, attitude polarization, and the irrational primacy effect to be explored. A general framework for exploring large-sample properties of these models is given, and an attempt made to classify the models. An interesting result is that in some models the influence of an observation always increases with distance from the prior opinion, whereas in others observations greatly at odds with prior opinion are given very little weight. The models could be useful to those exploring these phenomena in detail.