Rational Imprecision : Information-Processing , Neural , and Choice-Rule Perspectives ∗

People make mistakes. A rationally imprecise decision maker optimally balances the cost of reducing mistakes against the value of choosing correctly. We provide three models of rationally imprecise behavior: (1) an information-processing formulation where the costs of reducing mistakes are modeled as the corresponding reduction in Shannon entropy; (2) a neural implementation in terms of a stochastic and contextdependent utility function consistent with how the brain is thought to represent value; and (3) a choice-rule characterization. Our main result proves an equivalence between these three models which shows that they are different perspectives on the same behavior. The three perspectives answer, respectively, the questions of why rationally imprecise behavior should arise, how it can be implemented within the brain, and what such behavior looks like. ∗Financial support from NIH grant R01DA038063, NYU Stern School of Business, NYU Shanghai, and J.P. Valles is gratefully acknowledged. We have greatly benefited from discussions with Andrew Caplin, Faruk Gul, Kenway Louie, Paula Miret, Anthony Marley, Wolfgang Pesendorfer, Doron Ravid, Shellwyn Weston, Jan Zimmerman, members of the Glimcher Lab at NYU, and seminar audiences at Columbia, HKUST, NYU Shanghai, PHBS Shenzhen, Princeton, and Yale. †Institute for the Interdisciplinary Study of Decision Making, New York University, New York, NY 10012, U.S.A., ksteverson@nyu.edu, https://sites.google.com/site/ksteverson/ ‡Stern School of Business, Tandon School of Engineering, Institute for the Interdisciplinary Study of Decision Making, New York University, New York, NY 10012, U.S.A., adam.brandenburger@stern.nyu.edu, http://www.adambrandenburger.com §Center for Neural Science, Institute for the Interdisciplinary Study of Decision Making, New York University, New York, NY 10012, U.S.A., paul.glimcher@nyu.edu, http://www.neuroeconomics.nyu.edu/people/paul-glimcher/

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