DOI: 10.14704/nq.2015.13.1.788

The Synchronicity Principle Under Quantum Probabilistic Inferences

Catarina Moreira, Andreas Wichert

Abstract


We propose a new quantum Bayesian Network model in order to compute probabilistic infer¬ences in decision making scenarios. The application of a quantum paradigm to decision making generates interference effects that influence probabilistic inferences. These effects do not exist in a classical setting and constitute a major issue in the decision process, because they generate quantum parameters that highly increase with the amount of uncertainty of the problem. To automatically compute these quantum parameters, we propose a heuristic inspired by Jung’s Synchronicity principle. Synchronicity can be defined by a significant coincidence that appears be¬tween a mental state and an event occurring in the external world. It is the occurrence of meaningful, but not causally connected events. We tested our quantum Bayesian Network together with the Synchronicity inspired heuristic in empirical experiments related to categorization/decision in which the law of total probability was being violated. Results showed that the proposed quantum model was able to simulate the observed empirical findings from the experiments. We then applied our model to a more general scenario and showed the differences between classical and quantum inferences in a Lung Cancer medical diagnosis Bayesian Network.

Keywords


Bayesian Networks; Decision Making; Quantum Probability; Synchronicity Principle; Quantum Cognition

Full Text:

Full Text PDF

References


Accardi L, Khrennikov A, Ohya M. Quantum markov model for data from shafir-tversky experiments in cognitive psychology. Open Systems and Information Dynamics 2009; 14: 371-385.

Aerts D. Quantum structures: An attempt to explain the origin of their appearance in nature. Interna¬tional Journal of Theoretical Physics 1995; 34: 1-22.

Aerts D, Broekaert J, Gabora L. A case for applying an abstracted quantum formalism to cognition. Journal of New Ideas in Psychology 2011; 29: 136-146.

Aerts D, Broekaert J, Smets S. A quantum structure description of the liar paradox. International Journal of Theoretical Physics 2004; 38: 3231-3239.

Aerts D, Durt T. Quantum, classical and intermediate, an illustrative example. Foundations of Physics 1994; 24: 1353-1369.

Aerts S. Interactive probability models: Inverse problems on the sphere. International Journal of Theo¬retical Physics 1998; 37: 305-309.

Asano M, Basieva I, Khrennikov A, Ohya M, Tanaka Y. Quantum-like generalization of the bayesian updating scheme for objective and subjective mental uncertainties. Journal of Mathematical Psychol¬ogy 2012; 56: 166-175.

Asano M, Ohya M, Khrennikov A. Quantum-like model for decision making process in two players game, a non-kolmogorovian model. Journal of Foundations of Physics 2010; 41: 538-548.

Atmanspacher H, Romer H, Walach H. Weak quantum theory - complementarity and entanglement in physics and beyond. Foundations of Physics 2002; 32: 379-406.

Birnbaum M. New paradoxes of risky decision making. Journal of Psychological Review 2008; 115:463-501.

Blutner R, Hochnadel E. Two qubits for c.g. jung’s theory of personality. Journal of Cognitive Systems Research 2010; 11: 243-259.

Bordley R. Quantum mechanical and human violations of compound probability principles: Toward a generalized heisenberg uncertainty principle. Journal of Operations Research 1998; 46: 923-926.

Busemeyer J, Bruza P. Quantum Model of Cognition and Decision. Cambridge University Press, 2012.

Busemeyer J, Diederich A. Cognitive Modeling. SAGE Publications, Inc, 2010.

Busemeyer J, Matthew M, Wang Z. A quantum information processing explanation of disjunction ef¬fects, in Proceedings of the 28th Annual COnference of the Cognitive Science Society, 2006a.

Busemeyer J, Pothos E, Franco R, Trueblood J. A quantum theoretical explanation for probability judg¬ment errors. Journal of Psychology Review 2011; 118: 193-218.

Busemeyer J, Trueblood J. Comparison of quantum and bayesian inference models, in Proceedings of the 3rd International Symposium on QUantum Interaction, 2009.

Busemeyer J, Wang Z, Lambert-Mogiliansky A. Empirical comparison of markov and quantum models of decision making. Journal of Mathematical Psychology 2009; 53: 423-433.

Busemeyer J, Wang Z, Townsend J. Quantum dynamics of human decision making. Journal of Mathe¬matical Psychology 2006b; 50: 220-241.

Caves C, Fuchs C, Schack R. Quantum probabilities as bayesian probabilities. Physical Review A 2002; 65: 022305-6.

Cheon T, Tahahashi T. Interference and inequality in quantum decision theory. Journal of Physics Letters A 2010; 375: 100-104.

Conte E, Khrennikov A, Todarello O, Federici A, Mendolicchio L, Zbilut J. Mental states follow quan¬tum mechanics during perception and cognition of ambiguous figures. Journal of Open Systems and Information Dynamics 2009; 16: 1-17.

Conte E, Khrennikov A, Todarello O, Federici A, Robertis R. D, Zbilut J. On the existence of quantum wave function and quantum interference effects in quantum states: An experimental confirmation during perception and cognition in humans. Chaos, Solitons and Fractals 2007a; 31: 1076-1088.

Conte E, Todarello O, Federici A, Vitiello F, Lopane M, Khrennikov A, Zbilut J. Some remarks on an experiment suggesting quantum like behavior of cognitive entities and formulation of an abstract quantum mechanical formalism to describe cognitive entity and its dynamics. Journal of Chaos, Soli- tons and Fractals 2007b; 31: 1076-1088.

Croson R. The disjunction effect and reason-based choice in games. Journal of Organizational and Human Decision Processes 1999; 80: 118-133.

Danilov V, Lambert-Mogiliansky A. Expected utility theory under non-classical uncertainty. Journal of Theory and Decision 2010; 68: 25-47.

DeGroot M, Schervish M. Probability and Statistics. Pearson Education (4th Edition), 2011.

Ellsberg D. Risk, ambiguity and the savage axioms. Quaterly Journal of Economics 1961; 75: 643-669.

Franco R. The conjunction fallacy and interference effects. Journal of Mathematical Psychology 2009; 53: 415-422.

Gigerenzer G, Goldstein DG. Reasoning the fast and frugal way: Models of bounded rationality. Journal of Psychological Review 1996; 103: 650-669.

Gigerenzer G, Hoffrage U,. How to improve bayesian reasoning without instruction: Frequency formats. Journal of Psychological Review 1995; 102: 684-704.

Griffiths T, Kemp C, Tenenbaum J. Bayesian models of inductive learning, in Proceedings of the Annual Conference of the Cognitive Science Society, 2008.

Hirvensalo M. Quantum Computing (Second Edition). Springer, 2003.

Hristova E, Grinberg M. Disjunction effect in prisonner’s dilemma: Evidences from an eye-tracking study, in Proceedings of the 30th Annual Conference of the Cognitive Science Society, 2008.

Jung C, Pauli W. The Interpretation of Nature and the Psyche. Ishi Press, 2012.

Kahneman D, Slovic P, Tversky A. Judgment Under Uncertainty: Heuristics and Biases. Cambridge University Press, 1982.

Khrennikov A. Classical and quantum mechanics on information spaces with applications to cognitive psychological, social and anomalous phenomena. Foundations of Physics 1999; 29: 1065-1098.

Khrennikov A. Linear representations of probabilistic transformations induced by context transitions. Journal of Physics A: Mathematical and General 2001; 34: 9965-9981.

Khrennikov A. Representation of the kolmogorov model having all distinguishing features of quantum probabilistic model. Journal of Physics Letters A 2003; 316: 279-296.

Khrennikov A. Information Dynamics in Cognitive, Psychological, Social, and Anomalous Phenomena. Springer, 2004.

Khrennikov A. From classical statistical model to quantum model through ignorance of information, in Proceedings of the Third Conference on the Foundations of Information Science, 2005a.

Khrennikov A. Linear and nonlinear analogues of the schrodinger equation in the contextual approach to quantum mechanics. Journal of Doklady Mathematics 2005b; 72: 791-794.

Khrennikov A. Quantum-like brain: Interference of minds. Journal of BioSystems 2006; 84: 225-241.

Khrennikov A. Interpretations of Probability. Springer, 2009a.

Khrennikov A. Ubiquitous Quantum Structures: From Psychology to Finance. Springer, 2009b.

Khrennikov A. Contextual Approach to Quantum Formalism. Springer, 2010.

Khrennikov A, Haven E. Quantum mechanics and violations of the sure-thing principle: The use of probability interference and other concepts. Journal of Mathematical Psychology 2009; 53: 378-388.

Korb KB, Nicholson AE. Bayesian Artificial Intelligence. CRC Press, 2011.

Krumhansl C. Concerning the applicability of geometric models to similarity data: The interrelationship between similarity and spatial density. Journal of Psychological Review 1978; 85: 445-463.

Kuhberger A, Komunska D, Josef P. The disjunction effect: Does it exist for two-step gambles?. Orga¬nizational Behavior and Human Decision Processes 2001; 85: 250-264.

Lambdin C, Burdsal C. The disjunction effect reexamined: Relevant methodological issues and the fal¬lacy of unspecified percentage comparisons. Organizational Behavior and Human Decision Processes 2007; 103: 268-276.

Lambert-Mogiliansky A, Zamir S, Zwirn H. Type indeterminacy: A model for the kt(kahneman- tversky)-man. Journal of Mathematics Psychology 2009; 53: 349-361.

Leifer M, Poulin D. Quantum graphical models and belief propagation. Annals of Physics Journal 2008; 323: 1899-1946. eprint arxiv-ph/0708.1337 [quant-ph].

Li S, Taplin J. Examining whether there is a disjunction effect in prisoner’s dilemma game. Chinese Journal of Psychology 2002; 44: 25-46.

Limar I. A version of Carl Jung’s synchronicity in the event of correlation of mental processes in the past and the future: Possible role of quantum entanglement in quantum vacuum. NeuroQuantology 2012;10: 1-3.

Lindorff D. Pauli and Jung: The Meeting of Two Great Minds. Quest Books, 2004.

Martin F, Carminati F, Carminati GG. Synchronicity, quantum information and the psyche. Journal of Cosmology 2009; 3: 580-589.

Mura PL. Projective expected utility. Journal of Mathematical Psychology 2009; 53: 408-414.

Nielsen MA, Chuang IL. Quantum Computation and Quantum Information. Cambridge University Press, 2000.

Osherson D. Thinking. MIT Press, 1995.

Peto R, Darby S. Smoking, smoking cessation, and lung cancer in the uk since 1950: combination of national statistics with two case-control studies. British Medical Journal 2000; 7257: 323-329.

Piotrowski E. Quantum-like approach to financial risk: Quantum anthropic principle. Acta Physica Polonica B 2001; 32: 3873-3879.

Pothos E, Busemeyer J. A quantum probability explanation for violations of rational decision theory. Proceedings of the Royal Society B 2009; 276: 2171-2178.

Rieffel E, Polak W. Quantum Computing: A Gentle Introduction. MIT Press, 2011.

Russel S, Norvig P. Artificial Intelligence: A Modern Approach. Pearson Education (3rd Edition), 2010.

Savage L. The Foundations of Statistics. John Wiley, 1954.

Trueblood J, Busemeyer J,. A quantum probability account of order of effects in inference. Journal of Cognitive Science 2011; 35: 1518 - 1552.

Tucci R. Quantum bayesian nets. International Journal of Modern Physics B 1995; 9: 295-337.

Tversky A, Kahneman D. Causal schemata in judgments under uncertainty, Technical report, Cybernet¬ics Technology Office of the Defense Advanced Research Projects Agency, 1977.

Tversky A, Kahneman D. Extension versus intuitive reasoning: The conjunction fallacy in probability judgment. Journal of Psychological Review 1983; 90: 293-315.

Tversky A, Kahnenman D. Judgment under uncertainty: Heuristics and biases. Science 1974; 185: 1124-1131.

Tversky A, Koehler D. Support theory: A nonextensional representation of subjective probability. Jour¬nal of Psychological Review 1994; 10: 547-567.

Tversky A, Shafir E. The disjunction effect in choice under uncertainty. Journal of Psychological Sci¬ence 1992; 3: 305-309.

Wang Z, Busemeyer J. A quantum question order model supported by empirical tests of an apriori and precise prediction. Journal of Topics in Cognitive Science 2013; 5: 689-710.

Yukalov V, Sornette D. Decision theory with prospect interference and entanglement. Theory and De¬cision 2011; 70: 283-328.


Supporting Agencies





| NeuroScience + QuantumPhysics> NeuroQuantology :: Copyright 2001-2017