Local and Global Optima in Decision-Making: a Sheaf-theoretical Analysis of the Difference between the Classical and the Behavioral Approach to Decision-Making

FERNANDO TOHMÉ; CATERINA, GIANLUCA; GANGLE, ROCCO

Málaga

Jornada; XI Reunión del Grupo Español de Decisión Multicriterio; 2017

Grupo Español de Decisión Multicriterio

One of the main differences between the traditional and thebehavioral approaches to decision-making is that the latter hasnot yet been captured in a unifying framework. This hampers in acertain way the whole research program and raises the questionof whether this competing approach can provide an encompassingalternative to the classical one. We analyze this issue in light of theproblem of reconstructing global choices of an agent up from thesolutions found for local problems. We show that a representationbased on category theory of the conditions for such reconstructionis general and robust enough to represent both the case in whichproblems are non-contextual and local as well as that, typical in theliterature on behavioral decision-making, in which such propertiesdo not hold. In the first case, we show how a sheaf-theoreticalrepresentation provides an abstract characterization of the globalsolution. In the latter case, we show how locality and contextualitygenerate obstructions toward the reconstruction of global solutions,yielding a possible clue for the intrinsic difference between behavioraland classical decision theory.