A quick scan of the political landscape reveals that people differ in the ideologies they embrace and advocate. Why do individuals prefer certain ideologies over others? A formal analysis of psychological needs and consumption desires suggests that it is possible to compute the subjective utility of selecting one ideology over another, as though it were a purchasing decision. Given resources, constraints, and available options, individuals can rationally choose the ideology that best matches or resonates with their interests. It is a compelling framework that can take into account how diverse ideologies satisfy people’s diverse and multidimensional psychological and material needs. This psycho-economic model is ambitious and informative, and I will argue that it can be even more encompassing and enlightening if it is expanded to incorporate two critical components of ideological cognition: (1) the nature of ideological conviction and extremism and (2) the dynamic, probabilistic mental computations that underlie belief formation, preservation, and change. Firstly, I will argue that a formal model of ideological choice cannot escape the question of the strength of ideological commitment. In other words, we need to ask not only about which ideologies individuals choose but also about how strongly they adhere to these ideologies once those are chosen. An analysis of ideological choice needs to be accompanied by an analysis of ideological conviction. Secondly, in order to build a robust sense of the rationality behind ideological thinking, it is useful to incorporate principles of uncertainty and probability-based belief updating into the formal model of ideological worldviews. Bayesian models highlight how human brains seek to build predictive models of the world by updating their beliefs and preferences in ways that are proportional to their prior expectations and sensory experiences. Consequently, incorporating Bayesian principles into the formal model of ideological choice will provide a more wholistic understanding of what happens when a mind enters the market for belief systems – and why a mind can, at times, purchase toxic doses of the ideologies that sellers and entrepreneurs offer on display.