Unifying models of belief dynamics: a meta-model with Personal, Expressed and Social beliefs

Beliefs are central to individual decision-making and societal dynamics, and they are shaped through complex interactions between personal cognition and social environments. Traditional models of belief dynamics often fail to capture the interplay between internal belief systems and external influences. We present a meta-model that represents belief dynamics through three belief types: Personal beliefs, Expressed beliefs, and Social beliefs about others (PES). This distinction allows the model to account for the potential misperception of others' beliefs as well as distortions in the belief expression, and it permits the formalization of psychological processes such as ego projection, social influence, authenticity, and conformity. These processes have been studied extensively in social psychology but are rarely integrated into a comprehensive formal model. The PES meta-model also encompasses many existing belief dynamics models, such as versions of the Voter, Ising, DeGroot, and bounded confidence models. Its nested structure enables comparative analyses between different models and supports the construction of new models by recombining its components, providing a flexible framework for cumulative theory development.