Decades of research in decision making have established that there are some situations where human judgments cannot be modelled according to classical probability theory. Yet if we abandon classical (Bayesian) probability theory as an overarching framework for constructing cognitive models, what do we replace it with? In this contribution we outline a way to divide the space of possible computational level models of probabilistic judgment into a hierarchy of levels of increasing complexity, with classical Bayesian probability models occupying the lowest level. Each level has a unique experimental signature, and we describe an experiment performed to test which level is best able to describe human probabilistic reasoning.