Ever since Galileo rolled balls down an inclined plane and realized that he could use mathematics to describe that motion, mathematical models have been central to the understanding of natural phenomena – physical, biological, and social. Such models are abstract representations of real phenomena that help us understand how, but not necessarily why, the phenomena occur. Social science uses mathematical models as mechanisms for the study of selected features of human social behavior. A complex social problem is defined and factors that are deemed to be relevant are encoded into mathematical expressions, while those factors considered to be irrelevant are ignored. Such models can be used to conduct systematic investigations, test theories, simulate behavior, and evaluate performance. They can also be used to design and synthesize artificial social systems that are intended to function in ways that are compatible with human social behavior.

Since the days of Condorcet, the problem of how a collective of autonomous individuals should choose from a set of distinct and mutually exclusive alternatives has been subjected to intense mathematical modeling. There are two basic ways to address this question. Either the rationale for making the choice is a direct attribute of the collective viewed as single entity, or it is derived from the desires of the individuals by some process of aggregation. To comply with democratic principles, social choice theory has adopted the latter approach, and focuses first on the individual.

The classical way to construct a social choice model is to make only minimal assumptions about the behavior of the individuals and then investigate what can be deduced about the behavior of the collective. The behavioral assumption generally used to define a social choice model is the doctrine of individual rationality: The members of a collective are primarily (some might argue exclusively) motivated by self-interest. Philosophers may argue about the veracity of such a claim; nevertheless, individual rationality continues to be at the core of much of decision theory. Tversky and Kahneman explain why individual rationality is so dominant.