Contextuality and the Weak Axiom in the Theory of Choice

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.

[1]  Samson Abramsky,et al.  Contextual Semantics: From Quantum Mechanics to Logic, Databases, Constraints, and Complexity , 2014, Bull. EATCS.

[2]  Shmuel Zamir,et al.  Type Indeterminacy: A Model for the KT(Kahneman-Tversky)-Man , 2006, physics/0604166.

[3]  Shane Manseld.  The Mathematical Structure of Non-locality & Contextuality , 2013 .

[4]  H. Raiffa,et al.  Games and Decisions: Introduction and Critical Survey. , 1958 .

[5]  Adam Brandenburger,et al.  Team decision problems with classical and quantum signals , 2016, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[6]  A. Mas-Colell,et al.  Microeconomic Theory , 1995 .

[7]  H. Raiffa,et al.  GAMES AND DECISIONS; INTRODUCTION AND CRITICAL SURVEY. , 1958 .

[8]  J. Busemeyer,et al.  A quantum probability explanation for violations of ‘rational’ decision theory , 2009, Proceedings of the Royal Society B: Biological Sciences.

[9]  Nicole Yunger Halpern,et al.  Quantum voting and violation of Arrow's Impossibility Theorem , 2015, 1501.00458.

[10]  Noah Linden,et al.  Connection between Bell nonlocality and Bayesian game theory , 2012, Nature Communications.

[11]  Donald G. Saari,et al.  The profile structure for Luce's choice axiom , 2004 .

[12]  A. Zeilinger,et al.  Going Beyond Bell’s Theorem , 2007, 0712.0921.

[13]  Andrea Klug,et al.  Bells Theorem Quantum Theory And Conceptions Of The Universe , 2016 .

[14]  Jerome R. Busemeyer,et al.  A Quantum Question Order Model Supported by Empirical Tests of an A Priori and Precise Prediction , 2013, Top. Cogn. Sci..

[15]  Jerome R. Busemeyer,et al.  Quantum Models of Cognition and Decision , 2012 .

[16]  Samson Abramsky,et al.  Logical Bell Inequalities , 2012, ArXiv.

[17]  Vladimir I. Danilov,et al.  Measurable systems and behavioral sciences , 2008, Math. Soc. Sci..

[18]  Pierfrancesco La Mura,et al.  Quantum Decision Theory , 2011, ArXiv.

[19]  Shane Mansfield,et al.  The mathematical structure of non-locality and contextuality , 2013 .

[20]  Samson Abramsky,et al.  The sheaf-theoretic structure of non-locality and contextuality , 2011, 1102.0264.

[21]  Samson Abramsky,et al.  The Cohomology of Non-Locality and Contextuality , 2011, QPL.