Local and global optima in decision-making: a sheaf-theoretical analysis of the difference between classical and behavioral approaches

Abstract

One of the main differences between the traditional and the behavioral approaches to decision-making is that the latter has not yet been captured in a unifying framework. This hampers in a certain way the whole research program and raises the question of whether this competing approach can provide an encompassing alternative to the classical one. We analyze this issue in light of the problem of reconstructing global choices of an agent up from the solutions found for local problems. We show that a representation based on category theory of the conditions for such reconstruction is general and robust enough to represent both the case in which problems are non-contextual and local as well as that, typical in the literature on behavioral decision-making, in which such properties do not hold. In the first case, we show how a sheaf-theoretical representation provides an abstract characterization of the global solution. In the latter case, we show how locality and contextuality generate obstructions toward the reconstruction of global solutions, yielding a possible clue for the intrinsic difference between behavioral and classical decision theory.