Abstract
Recent advances in neuroscience suggest that 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-type models. 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.
Highlights
Choice is often modeled as behavior that seeks to maximize a utility function
We studied three different models that each presented a different perspective on choice behavior
The axiomatic characterization pinpoints exactly what behavior arises by providing a set of testable behavioral predictions
Summary
Choice is often modeled as behavior that seeks to maximize a utility function. Advances in neuroscience over the past few decades have pointed to a discrete set of brain areas apparently dedicated to representing a quantity that functions much like a utility representation (Fehr and Rangel, 2011; Glimcher, 2011; Knutson et al, 2001; Platt and Glimcher, 1999). 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 divisive normalization. We prove the one-to-one relationship as a corollary to our more general uniqueness result that shows that the parameters of the divisive normalization model are behaviorally identified up to a multiplicative scaling This level of identification is similar to other theories of stochastic choice, such as the Luce rule, and is enough to rank the alternatives by their values and to rank the choice sets by the expected value the agent receives when facing that set. Our theory provides a unified answer to the “how,” the “why,” and the “what” of choice behavior
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