Mathematics has always been the language of science. Thus, since its birth as a scientific discipline, psychology has aspired at describing the phenomena under study in mathematical terms. For example, early research in psychophysics strived to describe people's perception of simple sensory stimulations in the form of mathematical laws, such as the famous Weber's law. Mathematics has remained central in psychology ever since, at least at two levels. At an empirical level, mathematical statistical methods are fundamental for any quantitative data analysis in psychology. But even more deeply, at a theoretical level psychological processes are often interpreted as following laws that are ultimately mathematical. With this regard, Marr famously proposed to distinguish three levels of theoretical analysis of a psychological phenomenon: the computational, algorithmic, and implementational level; all to be understood in mathematical terms.

On this basis, mathematical theories have prospered in cognitive psychology and neuroscience to explain basic phenomena such as perception, memory, learning, and decision-making. However, though important exceptions exist, mathematical accounts are rarer in the realm of social and political psychology, where theories usually rely on verbal descriptions. Why this is the case remains a matter of speculation, a possible reason being that, for complex and multifaceted manifestations of the human mind such as in social and political psychology, mathematical accounts appear to many as too simplistic.

Computational political psychology challenges this view with regard to studying how psychological processes unfold in political contexts. Inspired by recent progress in mathematical psychology and computational neuroscience, some scholars have recently argued that mathematical theories in political psychology can offer tremendous insight. The new discipline of computational political psychology arises from this argument. Building upon multiple sources including research in social and political psychology, in mathematical psychology and computational neuroscience, and in related social science disciplines (such as sociology, economics, history, anthropology, and political science), computational political psychology aims at building mathematical theories of the human psyche in political contexts, and at testing these theories empirically. Although the main focus is psychological, the discipline stresses the importance of embedding any political psychological description within the social context, and of grounding it on biological foundations. The aspiration of adopting a computational political psychological approach is that, although simplifications are inherent in a mathematical outlook, these can be compensated by the precision and clarity afforded by mathematics, hence fostering theoretical debate and identification of clear empirical predictions.