Quantum dynamics of human decision-making

A quantum dynamic model of decision-making is presented, and it is compared with a previously established Markov model. Both the quantum and the Markov models are formulated as random walk decision processes, but the probabilistic principles differ between the two approaches. Quantum dynamics describe the evolution of complex valued probability amplitudes over time, whereas Markov models describe the evolution of real valued probabilities over time. Quantum dynamics generate interference effects, which are not possible with Markov models. An interference effect occurs when the probability of the union of two possible paths is smaller than each individual path alone. The choice probabilities and distribution of choice response time for the quantum model are derived, and the predictions are contrasted with the Markov model.

[1]  Ulf Böckenholt,et al.  A Thurstonian analysis of preference change , 2002 .

[2]  R. Hughes,et al.  The Structure and Interpretation of Quantum Mechanics , 1989 .

[3]  David R. Cox,et al.  The Theory of Stochastic Processes , 1967, The Mathematical Gazette.

[4]  D. A. Edwards The mathematical foundations of quantum mechanics , 1979, Synthese.

[5]  R. Duncan Luce,et al.  Choice, Decision, and Measurement: Essays in Honor of R. Duncan Luce , 1997 .

[6]  Robert F. Bordley,et al.  Experiment-dependent priors in psychology and physics , 1999 .

[7]  John R. Anderson,et al.  Rules of the Mind , 1993 .

[8]  A. Pike Stochastic models of choice behaviour: response probabilities and latencies of finite Markov chain systems. , 1966, The British journal of mathematical and statistical psychology.

[9]  Croson,et al.  The Disjunction Effect and Reason-Based Choice in Games. , 1999, Organizational behavior and human decision processes.

[10]  W. Heitler The Principles of Quantum Mechanics , 1947, Nature.

[11]  K. Pribram Brain and Perception: Holonomy and Structure in Figural Processing , 1991 .

[12]  Edward W. Piotrowski,et al.  An Invitation to Quantum Game Theory , 2002, ArXiv.

[13]  Thierry Paul,et al.  Quantum computation and quantum information , 2007, Mathematical Structures in Computer Science.

[14]  B. Muzykantskii,et al.  ON QUANTUM NOISE , 1995 .

[15]  Nancy J. Woolf,et al.  A quantum approach to visual consciousness , 2001, Trends in Cognitive Sciences.

[16]  G. Kane Parallel Distributed Processing: Explorations in the Microstructure of Cognition, vol 1: Foundations, vol 2: Psychological and Biological Models , 1994 .

[17]  J. Eisert,et al.  Quantum Games and Quantum Strategies , 1998, quant-ph/9806088.

[18]  Stuart R. Hameroff,et al.  QUANTUM COHERENCE IN MICROTUBULES: A NEURAL BASIS FOR EMERGENT CONSCIOUSNESS? 1 , 1994 .

[19]  Philipp Slusallek,et al.  Introduction to real-time ray tracing , 2005, SIGGRAPH Courses.

[20]  T. Gelder,et al.  Mind as Motion: Explorations in the Dynamics of Cognition , 1995 .

[21]  James L. McClelland,et al.  Parallel distributed processing: explorations in the microstructure of cognition, vol. 1: foundations , 1986 .

[22]  J. Townsend,et al.  Decision field theory: a dynamic-cognitive approach to decision making in an uncertain environment. , 1993, Psychological review.

[23]  B. Nordstrom FINITE MARKOV CHAINS , 2005 .

[24]  Donald Laming,et al.  Information theory of choice-reaction times , 1968 .

[25]  D. Meyer,et al.  Temporal properties of human information processing: Tests of discrete versus continuous models , 1985, Cognitive Psychology.

[26]  James T. Townsend,et al.  The Stochastic Modeling of Elementary Psychological Processes , 1983 .

[27]  H. Stowell The emperor's new mind R. Penrose, Oxford University Press, New York (1989) 466 pp. $24.95 , 1990, Neuroscience.

[28]  Diederik Aerts,et al.  Contextualizing concepts using a mathematical generalization of the quantum formalism , 2002, J. Exp. Theor. Artif. Intell..

[29]  David M. Riefer,et al.  Theoretical and empirical review of multinomial process tree modeling , 1999, Psychonomic bulletin & review.

[30]  Diederich,et al.  Dynamic Stochastic Models for Decision Making under Time Constraints , 1997, Journal of mathematical psychology.

[31]  John G. Kemeny,et al.  Finite Markov Chains. , 1960 .

[32]  S. Grossberg The complementary brain: unifying brain dynamics and modularity , 2000, Trends in Cognitive Sciences.

[33]  D. Vickers Decision processes in visual perception , 1979 .

[34]  Philip L. Smith,et al.  A comparison of sequential sampling models for two-choice reaction time. , 2004, Psychological review.

[35]  R. Leighton,et al.  Feynman Lectures on Physics , 1971 .

[36]  W. Godwin Article in Press , 2000 .

[37]  Karl H. Pribram,et al.  Rethinking neural networks : quantum fields and biological data , 1993 .

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

[39]  A. Tversky,et al.  The Disjunction Effect in Choice under Uncertainty , 1992 .

[40]  R. Shiffrin,et al.  Moments of transition-additive random variables defined on finite, regenerative random processes , 1988 .

[41]  Garrison Sposito,et al.  An introduction to quantum physics , 1970 .

[42]  Robert F. Bordley Quantum Mechanical and Human Violations of Compound Probability Principles: Toward a Generalized Heisenberg Uncertainty Principle , 1998, Oper. Res..

[43]  S. Link,et al.  A sequential theory of psychological discrimination , 1975 .

[44]  Henry P. Stapp,et al.  Attention, Intention, and Will in Quantum Physics , 1999, quant-ph/9905054.

[45]  I. G. MacKenzie,et al.  Stochastic Processes with Applications , 1992 .

[46]  Philip L. Smith,et al.  Stochastic Dynamic Models of Response Time and Accuracy: A Foundational Primer. , 2000, Journal of mathematical psychology.

[47]  James T. Townsend,et al.  Dynamic representation of decision-making , 1996 .

[48]  A. Tversky,et al.  Thinking through uncertainty: Nonconsequential reasoning and choice , 1992, Cognitive Psychology.

[49]  P. Glimcher Indeterminacy in brain and behavior. , 2005, Annual review of psychology.

[50]  Roger Ratcliff,et al.  A Theory of Memory Retrieval. , 1978 .

[51]  R. Feynman,et al.  The Feynman Lectures on Physics Addison-Wesley Reading , 1963 .

[52]  R Ratcliff,et al.  Continuous versus discrete information processing modeling accumulation of partial information. , 1988, Psychological review.

[53]  Donald L. Fisher,et al.  Stochastic PERT networks as models of cognition: Derivation of the mean, variance, and distribution of reaction time using Order-of-Processing (OP) diagrams , 1983 .

[54]  A. N. Kolmogorov,et al.  Foundations of the theory of probability , 1960 .

[55]  B. Grofman,et al.  A stochastic model of preference change and its application to 1992 presidential election panel data , 1999 .