  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.
