Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

A theory of best choice selection through objective arguments grounded in Linear Response Theory concepts

Marcel Ausloos, Giulia Rotundo, Roy Cerqueti

TL;DR

The paper tackles the problem of ranking 'agents' or opinions across many criteria without bias from the arbitrary ordering of criteria. It advocates a Linear Response Theory (LRT) based framework that defines the final score through correlations between all criterion evaluations, thus avoiding sequence-dependent distortions. Through geometrical toy models and illustrative examples, it shows how traditional order-based aggregation can bias rankings and how the LRT approach yields a more robust, objective hierarchy. The work points to broad applications in sociophysics and decision sciences, while acknowledging practical limitations and the continuing role of subjective factors in real-world choices.

Abstract

In this paper, we propose how to use objective arguments grounded in statistical mechanics concepts in order to obtain a single number, obtained after aggregation, which would allow to rank "agents", "opinions", ..., all defined in a very broad sense. We aim toward any process which should a priori demand or lead to some consensus in order to attain the presumably best choice among many possibilities. In order to precise the framework, we discuss previous attempts, recalling trivial "means of scores", - weighted or not, Condorcet paradox, TOPSIS, etc. We demonstrate through geometrical arguments on a toy example, with 4 criteria, that the pre-selected order of criteria in previous attempts makes a difference on the final result. However, it might be unjustified. Thus, we base our "best choice theory" on the linear response theory in statistical mechanics: we indicate that one should be calculating correlations functions between all possible choice evaluations, thereby avoiding an arbitrarily ordered set of criteria. We justify the point through an example with 6 possible criteria. Applications in many fields are suggested. Beside, two toy models serving as practical examples and illustrative arguments are given in an Appendix.

A theory of best choice selection through objective arguments grounded in Linear Response Theory concepts

TL;DR

The paper tackles the problem of ranking 'agents' or opinions across many criteria without bias from the arbitrary ordering of criteria. It advocates a Linear Response Theory (LRT) based framework that defines the final score through correlations between all criterion evaluations, thus avoiding sequence-dependent distortions. Through geometrical toy models and illustrative examples, it shows how traditional order-based aggregation can bias rankings and how the LRT approach yields a more robust, objective hierarchy. The work points to broad applications in sociophysics and decision sciences, while acknowledging practical limitations and the continuing role of subjective factors in real-world choices.

Abstract

In this paper, we propose how to use objective arguments grounded in statistical mechanics concepts in order to obtain a single number, obtained after aggregation, which would allow to rank "agents", "opinions", ..., all defined in a very broad sense. We aim toward any process which should a priori demand or lead to some consensus in order to attain the presumably best choice among many possibilities. In order to precise the framework, we discuss previous attempts, recalling trivial "means of scores", - weighted or not, Condorcet paradox, TOPSIS, etc. We demonstrate through geometrical arguments on a toy example, with 4 criteria, that the pre-selected order of criteria in previous attempts makes a difference on the final result. However, it might be unjustified. Thus, we base our "best choice theory" on the linear response theory in statistical mechanics: we indicate that one should be calculating correlations functions between all possible choice evaluations, thereby avoiding an arbitrarily ordered set of criteria. We justify the point through an example with 6 possible criteria. Applications in many fields are suggested. Beside, two toy models serving as practical examples and illustrative arguments are given in an Appendix.
Paper Structure (8 sections, 8 equations, 2 figures)

This paper contains 8 sections, 8 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Modern Ideas and Methods
  3. Maximum Likelihood Rule
  4. Technique for Order Preference by Similarity to Ideal Solution
  5. Score Rather than Rank Aggregation
  6. On the Sequence of Criteria. A Geometrical Perspective
  7. The problem and its solution
  8. Conclusions

Figures (2)

  • Figure 1: Demonstration that starting from 4 criteria the shape of the polygon based on the variable values leads to different areas; the toy values are $a=1,b=2,c=3,d=4$, leading to 6 possible polygons, but 3 different sizes; the areas values are given in arbitrary units.
  • Figure 2: A toy case of six criteria is presented in two sub-figures. The variables take values $a,b,c,d,e,f$ in both displays. Notice the disposition of the axes, whose arbitrariness concerns the discussion ground of the present study. A different disposition in the relative order of the axes leads to a different area for the hexagon.