Dynamical Model Of Overconfidence Phenomena Due To Ze-Type Confirmation Bias

This paper presents a dynamical model of overconfidence phenomena due to a confirmation bias. The model assumes an informational environment where a person updates one's belief about a state of the world through signals which may be misread and ignored due to a confirmation bias. A general type of confirmation bias, called ZE-type, is introduced and formalized using a model of noisy channels between signals and perceptions. It contains two subtypes of confirmation biases, called Z- and E-types, as its special cases. Persons suffering from Z-type receive a signal and perceive it incorrectly as a different signal with a certain probability, while those suffering from E-type fail to receive a signal with a certain probability. This paper derives a key factor, called a filtering coefficient, which plays a central role in analyzing the overconfidence phenomena. The analytical results suggest that the substantial part of the overconfidence phenomena due to the confirmation bias is regarded as a switched system with multiple linear time-invariant subsystems.