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

TL;DR

This paper introduces a novel method for ranking agents or opinions using objective, correlation-based metrics grounded in linear response theory, aiming to improve consensus processes across various fields.

Contribution

It proposes a new theoretical framework for best choice selection based on statistical mechanics, avoiding arbitrary ordering of criteria and enhancing decision accuracy.

Findings

Correlation functions provide a robust ranking metric.

Order of criteria influences traditional methods, but not the proposed approach.

Application examples demonstrate the method's versatility.

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.