Contextuality and the Weak Axiom in the Theory of Choice

TL;DR

This paper applies concepts from quantum contextuality to economics, analyzing when individual choices can be coherently combined into a global choice rule and relating this to the weak axiom of revealed preference.

Contribution

It introduces a framework using contextuality to characterize when collective choices can be derived from individual choices in economic models.

Findings

Identifies conditions under which a global choice rule is possible

Links contextuality to the weak axiom of revealed preference

Maps logical space of empirical principles in choice theory

Abstract

Recent work on the logical structure of non-locality has constructed scenarios where observations of multi-partite systems cannot be adequately described by compositions of non-signaling subsystems. In this paper we apply these frameworks to economics. First we construct a empirical model of choice, where choices are understood as observable outcomes in a certain sense. An analysis of contextuality within this framework allows us to characterize which scenarios allow for the possible construction of an adequate global choice rule. In essence, we mathematically characterize when it makes sense to consider the choices of a group as composed of individual choices. We then map out the logical space of some relevant empirical principles, relating properties of these contextual choice scenarios to no-signalling theories and to the weak axiom of revealed preference.