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

Jon Benito-Ostolaza, María Jesús Campión, Asier Estevan

TL;DR

This work presents a new and original approach to the situations of agreement as well as to the constructions of regulations by giving a mathematical formalization to the set of all possible agreements or regulations, so that the proximity between them is defined by means of a premetric.

Abstract

This paper presents a new and original first approach to agreement situations as well as to regulations constructions. This is made by giving a mathematical formalization to the set of all possible deals or regulations, such 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 regulation modifications, now some questions related to game theory or law are reduced to mathematical optimization problems.

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

TL;DR

This work presents a new and original approach to the situations of agreement as well as to the constructions of regulations by giving a mathematical formalization to the set of all possible agreements or regulations, so that the proximity between them is defined by means of a premetric.

Abstract

This paper presents a new and original first approach to agreement situations as well as to regulations constructions. This is made by giving a mathematical formalization to the set of all possible deals or regulations, such 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 regulation modifications, now some questions related to game theory or law are reduced to mathematical optimization problems.
Paper Structure (7 sections, 7 theorems, 15 equations, 1 figure)

This paper contains 7 sections, 7 theorems, 15 equations, 1 figure.

Table of Contents

  1. Motivation. The need of going further when making agreements
  2. Preliminaries: Mathematical tools
  3. Comparing regulations and societies
  4. Applications: law modifications and no-agreement situations
  5. First application: The shortest path, the legal gradiant
  6. Second application: Searching agreement and consensus
  7. Conclusions

Key Result

Proposition 2.6

Let $d$ be a premetric on $X$. Then, $d$ induces a topology on $X$ by means of the following open balls, for any $r>0$ and any $x\in X$:

Figures (1)

  • Figure 1: The graph associated to all the possible regulations for the communal and the corresponding distances.

Theorems & Definitions (38)

  • Definition 2.1
  • Definition 2.2
  • Definition 2.3
  • Definition 2.4
  • Definition 2.5
  • Proposition 2.6
  • Definition 2.7
  • Definition 3.1
  • Remark 3.2
  • Definition 3.3
  • ...and 28 more