Two Confirmation Bias Models for Analyzing Biased Pattern Classification Processes

This paper presents a mathematical model of the two types of the confirmation biases,
$Z$
- and
$E$
-types, for analyzing the pattern classification processes where the decision maker suffers from a confirmation bias. 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. In contrast to our previous models, which assume the signals and the options basically as the binary random variables, the models presented in this paper are based on the pattern classification processes, where (i) the state of world that maximizes the posterior probability is selected from more than or equal to two possible states and (ii) the time-series of the continuous-valued signals are used for the probability calculation. The proposed models enable us to analyze the dynamical properties of the confirmation biases in the context of the pattern classification processes.