Choice-Theoretic Foundations of the Divisive Normalization Model
34 Pages Posted: 23 Oct 2017 Last revised: 13 Dec 2018
Date Written: November 9, 2018
Abstract Recent advances in neuroscience suggest a utility-like calculation is involved in how the brain makes choices, and that this calculation may use a computation known as divisive normalization. While this tells us how the brain makes choices, it is not immediately evident why the brain uses this computation or exactly what behavior is consistent with it. In this paper, we address both of these questions by proving a three-way equivalence theorem between the normalization model, an information-processing model, and an axiomatic characterization. The information-processing model views behavior as optimally balancing the expected value of the chosen object against the entropic cost of reducing stochasticity in choice. This provides an optimality rationale for why the brain may have evolved to use normalization. The axiomatic characterization gives a set of testable behavioral statements equivalent to the normalization model. This answers what behavior arises from normalization. Our equivalence result unifies these three models into a single theory that answers the “how”, “why”, and “what” of choice behavior.
Keywords: Neuroeconomics, Decision Theory, Axioms, Stochastic Choice, Luce Rule
JEL Classification: D87, D81
Suggested Citation: Suggested Citation