EURO 2024 Copenhagen
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796. Pairwise Comparisons: Gauge Theoretical Aspects and Beyond

Invited abstract in session TD-44: Pairwise comparisons and preference relations 2, stream Multiple Criteria Decision Analysis.

Tuesday, 14:30-16:00
Room: 20 (building: 324)

Authors (first author is the speaker)

1. Jean-Pierre Magnot
LAREMA, Université d'Angers

Abstract

I will review the existing links between pairwise comparisons and gauge theory in physics. These links already exist in portfolio management since 1999 but are highlighted only recently in pairwise comparisons, even if the mathematical structures are the same. After a indroduction in which the necessary notions of connexion, holonomy and gauge are refreshed for the audience, I will give an in-depth description of the mathematical analogy between priority vectors with Yang-Mills fields, both in a deterministic and a stochastic way. In this picture, the notion of inconsistency indicator will have a plurality of natural meanings in terms of mathematical concepts. At the end of this short talk, I hope to have the time to discuss perspectives both for decision theory from physic, in particular with the controversal use of the theory of Lie groups but also with a minimal setting for pairwise comparisons in the framework of categories and also with quantization procedures, and for physics from decision theory, in particular with inconsistency reduction for scalar gauge fields (e.g. electromagnetic fields).

Keywords

Status: accepted

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