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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 charac