A Note on Law in Mathematical Models:

Norms and Law

Abstract

The purpose of this paper is to examine how law as social phenomenon can be described in mathematical models, especially in comparison with social norms. As a beginning we try to untangle the concepts of “law” used in the literature on social norms, and classify them into a few categories. We then point out the problems with assumptions made when analyzing the law in the usual mathematical models, including economic models. Particularly, we argue that public institutions are not always necessary to establish legal order and that law cannot affect human behavior without coordinating many more actors than usual models assume. In the latter part of the paper, we offer a simple model that describes the enforcement of social norms through collective and decentralized sanctions. On the basis of this model, we discuss the problem of how to capture the distinction between social norms and law, and conclude that the law can have an impact on players’ behavior only by changing people’s beliefs concerning other people’s action.