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Information Systems Frontiers

, Volume 18, Issue 4, pp 735–764 | Cite as

A formulation of computational trust based on quantum decision theory

  • Mehrdad Ashtiani
  • Mohammad Abdollahi Azgomi
Article

Abstract

In this paper, we propose a new formulation of computational trust based on quantum decision theory (QDT). By using this new formulation, we can divide the assigned trustworthiness values to objective and subjective parts. First, we create a mapping between the QDT definitions and the trustworthiness constructions. Then, we demonstrate that it is possible for the quantum interference terms to appear in the trust decision making process. By using the interference terms, we can quantify the emotions and subjective preferences of the trustor in various contexts with different amounts of uncertainty and risk. The non-commutative nature of quantum probabilities is a valuable mathematical tool to model the relative nature of trust. In relative trust models, the evaluation of a trustee candidate is not only dependent on the trustee itself, but on the other existing competitors. In other words, the first evaluation is performed in an isolated context whereas the rest of the evaluations are performed in a comparative one. It is shown that a QDT-based model of trust can account for these order effects in the trust decision making process. Finally, based on the principles of risk and uncertainty aversion, interference alternation theorem and interference quarter law, quantitative values are assigned to interference terms. By performing empirical evaluations, we have demonstrated that various scenarios can be better explained by a quantum model of trust rather than the commonly used classical models.

Keywords

Trust model Quantum decision theory (QDT) Quantum interference Attraction factors Superposition axiom Delegation Order effect 

Notes

Acknowledgments

We would like to thank the editor and anonymous referees of this journal whose comments substantially improved this paper. We are also grateful to Iran National Science Foundation (INSF) for financial support of this research.

References

  1. Aerts, D., Broekaert, J., Czachor, M., D’Hooghe, B. (2011). A quantum-conceptual explanation of violations of expected utility in economics. In Proceedings of the Quantum Interaction, Aberdeen, UK: Springer. Lecture Notes in Computer Science, 7052, 192–198.Google Scholar
  2. A. S. Ali and O. F. Rana, "A belief-based trust model for dynamic service selection," in Proceedings of the Economic Models and Algorithms for Distributed Systems, 2010, pp. 9–23.Google Scholar
  3. Anderson, N. H., & Hubert, S. (1963). Effects of concomitant verbal recall on order effects in personality impression formation. Journal of Verbal Learning and Verbal Behavior, 2, 379–391.CrossRefGoogle Scholar
  4. Ashtiani, M., & Azgomi, M. A. (2014). Contextuality, incompatibility and biased inference in a quantum-like formulation of computational trust. Advances in Complex Systems, 17(5, 1450020), 61.Google Scholar
  5. Axioms of Quantum Mechanics, MIT OpenCourseWare, Available: http://ocw.mit.edu, Last Visited: (2015/02/05).
  6. Bell, J. S. (1966). On the problem of hidden variables in quantum mechanics. Reviews of Modern Physics, 38, 447–452.CrossRefGoogle Scholar
  7. Busacca, B., Castaldo, S. (2011). Trust in market relationships: an interpretative model. Sinergie Rivista di Studi e Ricerche, 191–227.Google Scholar
  8. Busemeyer, J.R., Trueblood, J.S. (2011). Theoretical and empirical reasons for considering the application of quantum probability theory to human cognition. In Proceedings of the Quantum Cognition Meets TARK║ Workshop, Groningen, Netherlands, 12–14.Google Scholar
  9. Busemeyer, J.R., Franco, R., Pothos, E.M. (2009). Quantum probability explanations for probability judgment errors. arXiv preprint arXiv, 0909.2789.Google Scholar
  10. Busemeyer, J. R., Wang, Z., & Lambert-Mogiliansky, A. (2009b). Empirical comparison of Markov and quantum models of decision making. Journal of Mathematical Psychology, 53, 423–433.CrossRefGoogle Scholar
  11. Carnal, O., & Mlynek, J. (1991). Young’s double-slit experiment with atoms: a simple atom interferometer. Physical Review Letters, 66, 2689.CrossRefGoogle Scholar
  12. Castelfranchi, C. (2008). Reasons: belief support and goal dynamics. Mathware and Soft Computing, 3, 233–247.Google Scholar
  13. Castelfranchi, C., & Falcone, R. (1998). Towards a theory of delegation for agent-based systems. Robotics and Autonomous Systems, 24, 141–157.CrossRefGoogle Scholar
  14. Castelfranchi, C., Falcone,R. (2000). Trust is much more than subjective probability: Mental components and sources of trust. In Proceedings of the 33rd Annual Hawaii International Conference on System Sciences, Hawaii, US, 10.Google Scholar
  15. Castelfranchi C., & Falcone, R. (2010). Trust Theory: A Socio-Cognitive and Computational Model, Wiley, 18.Google Scholar
  16. Cofta, P. (2007). Trust, complexity and control: confidence in a convergent world. Chichester: Wiley.CrossRefGoogle Scholar
  17. DuBois,T., Golbeck, J., Srinivasan, A. (2011). Predicting trust and distrust in social networks. In Proceedings of the 2011 IEEE 3rd International Conference on Privacy, Security, Risk and Trust (PASSAT), and 2011 IEEE 3rd International Conference on Social Computing (SocialCom) 418–424.Google Scholar
  18. Eddy, D. M. (1982). Probabilistic reasoning in clinical medicine: Problems and opportunities. Judgment Under Uncertainty: Heuristics and Biases, 249–267.Google Scholar
  19. Einstein, A., Podolsky, B., & Rosen, N. (1935). Can quantum-mechanical description of physical reality be considered complete? Physical Review, 47, 777.CrossRefGoogle Scholar
  20. ElSalamouny, E., Sassone, V., Nielsen, M. (2010). HMM-based trust model. In Proceedings of the Formal Aspects in Security and Trust, Eindhoven, Netherlands: Springer. Lecture Notes in Computer Science, 5983, 21–35.Google Scholar
  21. Falcone, R., Castelfranchi, C. (2001). Social trust: a cognitive approach. In Proceedings of the Trust and Deception in Virtual Societies, Springer, 55–90.Google Scholar
  22. Falcone, R., Castelfranchi, C. (2012). Trust and transitivity: how trust-transfer works. In Proceedings of the Highlights on Practical Applications of Agents and Multi-Agent Systems, Madrid, Spain: Springer. Lecture Notes in Computer Science, 156, 179–187.Google Scholar
  23. Feng, L., & Huizhong, W. (2008). Research of trust valuation based on cloud model. Engineering Sciences, 10, 84–90.Google Scholar
  24. Franco, R. (2009). The conjunction fallacy and interference effects. Journal of Mathematical Psychology, 53, 415–422.CrossRefGoogle Scholar
  25. Franco, R., Busemeyer, J. (2008). A quantum probability explanation for the inverse fallacy. Psychonomic Review & Bulletin Google Scholar
  26. Frankel, T. (2005). Trust and honesty: America's business culture at a crossroad. USA: Oxford University Press.Google Scholar
  27. Gilovich, T., Griffin, D., Kahneman, D. (2002). Heuristics and Biases: The Psychology of Intuitive Judgment: Cambridge University Press.Google Scholar
  28. Gluzman, S., Yukalov, V., & Sornette, D. (2003). Self-similar factor approximants. Physical Review E, 67, 026109. doi: 10.1103/PhysRevE.67.026109.CrossRefGoogle Scholar
  29. Hang, C.W., Wang, Y., Singh, M.P. (2008). An adaptive probabilistic trust model and its evaluation. In Proceedings of the 7th International Joint Conference on Autonomous Agents and Multiagent Systems-Volume 3, Estoril, Portugal, 1485–1488.Google Scholar
  30. Hogarth, R. M., & Einhorn, H. J. (1992). Order effects in belief updating: the belief-adjustment model. Cognitive Psychology, 24, 1–55.CrossRefGoogle Scholar
  31. Hoogendoorn, M., Jaffry, S. W., Treur, J. (2008). Modeling dynamics of relative trust of competitive information agents. In Proceedings of the 12th International Workshop on Cooperative Information Agents XII (CIA'2008), Prague, Czech Republic, Sept. 10–12. Lecture Notes in Computer Science, Springer, 5180:55–70.Google Scholar
  32. Hoogendoorn, M., Jaffry, S.W., Treur, J. (2008). Modeling dynamics of relative trust of competitive information agents. In Proceedings of the 12th International Workshop on Cooperative Information Agents XII (CIA’2008), Prague, Czech Republic: Springer. Lecture Notes in Computer Science, 5180, 55–70.Google Scholar
  33. Hoogendoorn, M., Jaffry, S.W., Treur, J. (2010). Incorporating interdependency of trust values in existing trust models for trust dynamics. In Proceedings of the Trust Management IV, Morioka, Japan: Springer. Lecture Notes in Computer Science, 321,263–276.Google Scholar
  34. Hoogendoorn, M., Jaffry, S.W., Van Maanen, P.P., Treur, J. (2011). Modeling and validation of biased human trust. In Proceedings of the 2011 IEEE/WIC/ACM International Conferences on Web Intelligence and Intelligent Agent Technology, Lyon, France. 256–263.Google Scholar
  35. Huang, H., & Wang, R. (2008). Subjective trust evaluation model based on membership cloud theory. Journal of Communication, 29, 13–19.Google Scholar
  36. Klüwer, J.W., Waaler, A. (2006). Relative trustworthiness. In Proceedings of the Formal Aspects in Security and Trust, Newcastle, UK: Springer. Lecture Notes in Computer Science, 3866, 158–170.Google Scholar
  37. Klüwer, J.W., Waaler, A. (2006). Trustworthiness by default. In Proceedings of the Computational Logic in Multi-Agent Systems, London, UK: Springer. Lecture Notes in Computer Science, 3900, 96–111.Google Scholar
  38. Lesani, M., Bagheri, S. (2006). Fuzzy trust inference in trust graphs and its application in semantic web social networks. In Proceedings of the World Automation Congress (WAC’06), Budapest, Hungary 1–6.Google Scholar
  39. Lewicki, R. J., McAllister, D. J., & Bies, R. J. (1998). Trust and distrust: new relationships and realities. Academy of Management Review, 23, 438–458.Google Scholar
  40. Lewis, J. D., & Weigert, A. J. (2012). The social dynamics of trust: theoretical and empirical research. Social Forces, 91, 25–31.CrossRefGoogle Scholar
  41. Marsh, S., Dibben, M.R. (2005). Trust, untrust, distrust and mistrust–an exploration of the dark (er) side. In Proceedings of the Trust Management, Paris, France: Springer. Lecture Notes in Computer Science, 3477, 17–33.Google Scholar
  42. Mayer, R. C., & Davis, J. H. (1999). The effect of the performance appraisal system on trust for management: a field quasi-experiment. Journal of Applied Psychology, 84, 123.CrossRefGoogle Scholar
  43. Mayer, R. C., Davis, J. H., Schoorman, F. D. (1995). An integrative model of organizational trust. Academy of Management Review,709–734.Google Scholar
  44. Nguyen, H.T., Zhao, W., Yang, J. (2010). A trust and reputation model based on bayesian network for Web services. In Proceedings of the 2010 IEEE International Conference on Web Services (ICWS), Miami, US, 251–258.Google Scholar
  45. Nielsen M. A., & Chuang I. L. (2010). Quantum Computation and Quantum Information: Cambridge university press.Google Scholar
  46. Pothos, E. M., & Busemeyer, J. R. (2009). A quantum probability explanation for violations of rational decision theory. Proceedings of the Royal Society B: Biological Sciences, 282, 2171–2178.CrossRefGoogle Scholar
  47. Shah, A. K., & Oppenheimer, D. M. (2008). Heuristics made easy: an effort-reduction framework. Psychological Bulletin, 134, 207.CrossRefGoogle Scholar
  48. Shi, J., Bochmann, G. V., & Adams, C. (2005). A trust model with statistical foundation. Proceedings of the Formal Aspects in Security and Trust, 173, 145–158.CrossRefGoogle Scholar
  49. Trueblood, J. S., & Busemeyer, J. R. (2011). A quantum probability account of order effects in inference. Cognitive Science, 35, 1518–1552.CrossRefGoogle Scholar
  50. Verbiest, N., Cornelis, C., Victor, P., & Herrera-Viedma, E. (2012). Trust and distrust aggregation enhanced with path length incorporation. Fuzzy Sets and Systems, 202, 61–74.CrossRefGoogle Scholar
  51. Yao, Y., Tong, H., Yan, X., Xu, F., Lu, J. (2013). Multi-aspect+ transitivity+ bias: an integral trust inference model. IEEE Transaction on Knowledge and Data Engineering, 90.Google Scholar
  52. Yukalov, V., & Sornette, D. (2008). Quantum decision theory. arXiv preprint arXiv:0802.3597.Google Scholar
  53. Yukalov, V. I., & Sornette, D. (2008b). Quantum decision theory as quantum theory of measurement. Physics Letters A, 372, 6867–6871.CrossRefGoogle Scholar
  54. Yukalov, V., & Sornette, D. (2009a). Physics of risk and uncertainty in quantum decision making. The European Physical Journal B, 71, 533–548.CrossRefGoogle Scholar
  55. Yukalov, V. I., & Sornette, D. (2009b). Processing information in quantum decision theory. Entropy, 11, 1073–1120.CrossRefGoogle Scholar
  56. Yukalov, V., & Sornette, D. (2010a). Entanglement production in quantum decision making. Physics of Atomic Nuclei, 73, 559–562.CrossRefGoogle Scholar
  57. Yukalov, V. I., & Sornette, D. (2010b). Mathematical structure of quantum decision theory. Advances in Complex Systems, 13, 659–698.CrossRefGoogle Scholar
  58. Yukalov, V., & Sornette, D. (2011). Decision theory with prospect interference and entanglement. Theory and Decision, 70, 283–328.CrossRefGoogle Scholar
  59. Yukalov, V., & Sornette, D. (2012). Quantum decision making by social agents. Swiss Finance Institute Research Paper.Google Scholar
  60. Yukalov, V. I., & Sornette, D. (2014). Manipulating decision making of typical agents. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 44, 1155–1168.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Trustworthy Computing Laboratory, School of Computer EngineeringIran University of Science and TechnologyTehranIran

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