On Selective Influences, Marginal Selectivity, and Bell/CHSH Inequalities

The Bell/CHSH inequalities of quantum physics are identical with the inequalities derived in mathematical psychology for the problem of selective influences in cases involving two binary experimental factors and two binary random variables recorded in response to them. The following points are made regarding cognitive science applications: (1) compliance of data with these inequalities is informative only if the data satisfy the requirement known as marginal selectivity; (2) both violations of marginal selectivity and violations of the Bell/CHSH inequalities are interpretable as indicating that at least one of the two responses is influenced by both experimental factors.

[1]  Harald Atmanspacher,et al.  The Potential of Using Quantum Theory to Build Models of Cognition , 2013, Top. Cogn. Sci..

[2]  Donald L. Fisher,et al.  Discovering Cognitive Architecture by Selectively Influencing Mental Processes , 2012 .

[3]  Arthur Fine,et al.  Joint distributions, quantum correlations, and commuting observables , 1982 .

[4]  Ehtibar N. Dzhafarov,et al.  Selectivity in Probabilistic Causality: Where Psychology Runs Into Quantum Physics , 2011, 1110.2388.

[5]  Ehtibar N. Dzhafarov,et al.  All-Possible-Couplings Approach to Measuring Probabilistic Context , 2012, PloS one.

[6]  Saul Sternberg,et al.  The discovery of processing stages: Extensions of Donders' method , 1969 .

[7]  Ehtibar N. Dzhafarov,et al.  Quantum Entanglement and the Issue of Selective Influences in Psychology: An Overview , 2012, QI.

[8]  Jose L. Cereceda.  QUANTUM MECHANICAL PROBABILITIES AND GENERAL PROBABILISTIC CONSTRAINTS FOR EINSTEIN–PODOLSKY–ROSEN–BOHM EXPERIMENTS , 2000 .

[9]  Ehtibar N. Dzhafarov,et al.  The Joint Distribution Criterion and the Distance Tests for Selective Probabilistic Causality , 2010, Front. Psychology.

[10]  M. Horne,et al.  Experimental Consequences of Objective Local Theories , 1974 .

[11]  D. Bohm,et al.  Discussion of Experimental Proof for the Paradox of Einstein, Rosen, and Podolsky , 1957 .

[12]  James T. Townsend,et al.  Uncovering mental processes with factorial experiments , 1984 .

[13]  Diederik Aerts,et al.  Concepts and Their Dynamics: A Quantum-Theoretic Modeling of Human Thought , 2012, Top. Cogn. Sci..

[14]  J. Kujala,et al.  Testing for selectivity in the dependence of random variables on external factors , 2008 .

[15]  A. Shimony,et al.  Proposed Experiment to Test Local Hidden Variable Theories. , 1969 .

[16]  James T. Townsend,et al.  Toward the trichotomy method of reaction times: laying the foundation of stochastic mental networks , 1989 .

[17]  N. Bohr.  II - Can Quantum-Mechanical Description of Physical Reality be Considered Complete? , 1935 .

[18]  E. Dzhafarov.  Selective influence through conditional independence , 2003 .

[19]  Albert Einstein,et al.  Can Quantum-Mechanical Description of Physical Reality Be Considered Complete? , 1935 .

[20]  J. Brožek.  Attention and Performance II. , 1971 .

[21]  Ehtibar N. Dzhafarov,et al.  Notes on selective influence, probabilistic causality, and probabilistic dimensionality , 2006 .

[22]  P. Grangier,et al.  Experimental Realization of Einstein-Podolsky-Rosen-Bohm Gedankenexperiment : A New Violation of Bell's Inequalities , 1982 .

[23]  Ehtibar N. Dzhafarov,et al.  Order-distance and other metric-like functions on jointly distributed random variables , 2011, ArXiv.

[24]  Ehtibar N. Dzhafarov,et al.  Mental architectures with selectively influenced but stochastically interdependent components , 2004 .

[25]  L. J. Landau,et al.  On the violation of Bell's inequality in quantum theory , 1987 .