A Mathematical Approach to Law and Deal Modelling: Legislation and Agreements

Social norms are a set of rules to be followed by the people of a community in order to have a better coexistence, to which the behaviors, tasks, and activities of the human being must be adjusted. The set or system of norms, rules, or duties regulates the actions of individuals among themselves. This work presents a new and original approach to the situations of agreement as well as to the constructions of regulations. This is done by giving a mathematical formalization to the set of all possible agreements or regulations, so that, then, the proximity between them is defined by means of a premetric. Thanks to this mathematical structure that tries to capture the problematic of agreements and modifications of regulations, some currently issues related to game theory or law are now reduced to mathematical optimization problems.

Automated summary

This work explores the role of social norms and presents a mathematical approach to solving agreement situations and regulation construction issues. By formalizing mathematically and defining the proximity between agreements or regulations, complex problems related to game theory or law can now be simplified into mathematical optimization problems.