Mathematical modelling is popular in cognitive psychology because it enables clear and formal descriptions of the processes at play; yet, this approach has rarely been applied to political psychology. Here we adopt mathematical modelling to develop a theory of political motivation, which is a central concept in political psychology. The theory assumes that, in certain contexts, individuals entertain a set of representations of society, for example of the past, present and future (but also of fictive societies such as utopias). To each representation of society, an incentive value is attached which is not absolute, but (following theories of motivation in cognitive psychology) reference-dependent; namely, dependent on the context, corresponding to the whole set of representations of society. In turn, the model proposes that these subjective values determine two central aspects: a motivation for performing an appropriate political action and the ensuing political mood. We discuss the model with respect to theoretical and empirical research (and we examine Marx and Engel’s communist manifesto as an example of the latter). In short, we offer a new mathematical perspective on political motivation which emphasises the role of multiple representations of society in determining political motivation and the ensuing political mood.