•The predictive brain construes the world as consistent with top-down predictions, while minimizing error in predictions.•Individuals are motivated to minimize prediction error by learning accurate models and seeking predictable environments.•Ideology be understood as a shared process of prediction error minimization that promotes societal cohesion.•Social error minimization may lead to polarization and extremism as people converge on ideologies that direct social life.•This model outlines multiple directions of future study to understand ideological differences in society. Recent models of cognition suggest that the brain may implement predictive processing, in which top-down expectations constrain incoming sensory data. In this perspective, expectations are updated (error minimization) only if sensory data sufficiently deviate from these expectations (prediction error). Although originally applied to perception, predictive processing is thought to generally characterize cognitive architecture, including the social cognitive processes involved in ideological thinking. Scaling up these simple computational principles to the social sphere outlines a path by which group members may adopt shared ideologies and beliefs to predict behavior and cooperate with each other. Because ideological judgments are of specific interest to others in our political groups, we may increasingly regulate each other’s thinking, sharing the process of error minimization. In this paper, we outline how this process of shared error minimization may lead to shared ideologies and beliefs that allow group members to predict and cooperate with each other, and how, as a consequence, political polarization and extremism may result.