Abstract
Social norms can be understood as the grammar of social interaction. Like grammar in speech, they specify what is acceptable in a given context (Bicchieri in The grammar of society: the nature and dynamics of social norms, Cambridge University Press, New York, 2006). But what are the specific rules that direct human compliance with the norm? This paper presents a quantitative model of self- and the other-perspective interaction based on a ‘quantum model of decision-making’, which can explain some of the ‘fallacies’ of the classical model of strategic choice. By (re)connecting two fields of social science research—norms compliance, and strategic decision-making—we aim to show how the novel quantum approach to the later can advance our understanding of the former. From the cacophony of different quantum models, we distill the minimal structure necessary to account for the known dynamics between the expectations and decisions of an actor. This model was designed for the strategic interaction of two players and successfully tested in the case of the one-shot Prisoners’ Dilemma game. Quantum models offer a new conceptual framework for examining the interaction between self- and other-perspective in the process of social interaction which enables us to specify how social norms influence individual behavior.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Notes
Knowledge of the norm is not necessarily a binary variable (as the actor can understand the norm differently than the others) which is another aspect of social norms compliance that could be analyzed with the use of the quantum model.
For the consistency with the above-mentioned literature the Dirac notation is used. The symbol \({|{A}\rangle }\) denotes the column vector whose number of rows corresponds to the dimension of the respective Hilbert space.
Even though, as shown by Yukalov and Sornette (2014), the term could be somehow misleading in the context of the toy model, I decided to keep it following the standard terminology in the quantum decision-making literature.
If alpha were outside the defined interval, we could simply switch the vectors \({|{C}\rangle }\) and \({|{D}\rangle }\) in our analysis and the findings would remain the same.
Here we follow the convention of defining the angles as positive in the counter-clockwise direction and negative in the clockwise direction.
As pointed out by the anonymous reviewer, the players show an extra tendency to think of having “bad luck”. As regards the level of cooperation they expect much less form the others (39.1%) than they are willing to show themselves (64.9%). This discrepancy between the perspectives is the key feature of the game.
References
Accardi, L., Khrennikov, A., & Ohya, M. (2009). Quantum Markov model for data from Shafir–Tversky experiments in cognitive psychology. Open Systems & Information Dynamics, 16(04), 371. https://doi.org/10.1142/S123016120900027X.
Aerts, D. (2009). Quantum structure in cognition. Journal of Mathematical Psychology, 53(5), 314. https://doi.org/10.1016/j.jmp.2009.04.005.
Bicchieri, C. (2006). The grammar of society: The nature and dynamics of social norms. New York: Cambridge University Press.
Bicchieri, C., & Muldoon, R. (2014). In E. N. Zalta (Ed.), The Stanford encyclopedia of philosophy, spring 2014 edn. Metaphysics Research Lab, Stanford University. http://plato.stanford.edu/archives/spr2014/entries/social-norms/. Accessed 16 Feb 2018.
Bicchieri, C., & Xiao, E. (2009). Do the right thing: But only if others do so. Journal of Behavioral Decision Making, 22(2), 191. https://doi.org/10.1002/bdm.621.
Binmore, K. G. (2005). Natural justice. New York: Oxford University Press. OCLC: 56324785.
Busemeyer, J. R., & Bruza, P. D. (2014). Quantum models of cognition and decision. Cambridge: Cambridge University Press.
Busemeyer, J. R., Matthew, M. R., & Wang, Z. (2006). In Proceedings of the cognitive science society (Vol. 28)
Busemeyer, J. R., Pothos, E. M., Franco, R., & Trueblood, J. S. (2011). A quantum theoretical explanation for probability judgment errors. Psychological Review, 118(2), 193. https://doi.org/10.1037/a0022542.
Camerer, C. (2003). Behavioral game theory: Experiments in strategic interaction. New York: Russell Sage Foundation.
Croson, R. T. A. (1999). The disjunction effect and reason-based choice in games. Organizational Behavior and Human Decision Processes, 80(2), 118. https://doi.org/10.1006/obhd.1999.2846.
Elster, J. (1989). The cement of society: A study of social order. New York: Cambridge University Press.
Gintis, H. (2014). The bounds of reason: Game theory and the unification of the behavioral sciences, revised paperback edition first printing edition. Princeton: Princeton University Press.
Khrennikov, A. Y., & Haven, E. (2009). Quantum mechanics and violations of the sure-thing principle: The use of probability interference and other concepts. Journal of Mathematical Psychology, 53(5), 378. https://doi.org/10.1016/j.jmp.2009.01.007.
Lewis, D. K. (1969). Convention: A philosophical study. Cambridge: Harvard University Press.
Li, S., Wang, Z. J., Rao, L. L., & Li, Y. M. (2010). Is there a violation of Savage’s sure-thing principle in the Prisoner’s Dilemma game? Adaptive Behaviour, 18(3–4), 3.
Moore, D. W. (2002). Measuring new types of question-order effects: Additive and subtractive. The Public Opinion Quarterly, 66(1), 80.
Moreira, C., & Wichert, A. (2017). Are quantum models for order effects quantum? International Journal of Theoretical Physics, 56(12), 4029. https://doi.org/10.1007/s10773-017-3424-5.
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, 1, 1. https://doi.org/10.1098/rspb.2009.0121.
Savage, L. J. (1972). The foundations of statistics (2nd ed.). New York: Dover Publications. OCLC: 390018.
Scharnhorst, K. (2001). Angles in complex vector spaces. Acta Applicandae Mathematica, 69(1), 95. https://doi.org/10.1023/A:1012692601098.
Schelling, T. C. (1960). The strategy of conflict. Cambridge. http://hdl.handle.net/2027/mdp.39015020741057. Accessed 16 Feb 2018.
Shafir, E., & Tversky, A. (1992). Thinking through uncertainty: Nonconsequential reasoning and choice. Cognitive Psychology, 24(4), 449. https://doi.org/10.1016/0010-0285(92)90015-T.
Sugden, R. (1986). The economics of rights, co-operation, and welfare. New York: B. Blackwell, Oxford [Oxfordshire].
Tversky, A., & Shafir, E. (1992). The disjunction effect in choice under uncertainty. Psychological Science, 3(5), 305.
Ullmann-Margalit, E. (1977). The emergence of norms. Oxford: Clarendon Press.
Yukalov, V. I., & Sornette, D. (2011). Decision theory with prospect interference and entanglement. Theory and Decision, 70(3), 283. https://doi.org/10.1007/s11238-010-9202-y.
Yukalov, V. I., & Sornette, D. (2014). Conditions for quantum interference in cognitive sciences. Topics in Cognitive Science, 6(1), 79. https://doi.org/10.1111/tops.12065.
Acknowledgements
The analysis is the outcome of the projects “Quantum Theory of International Relations” (GAUK 904414), and “Human-Machine Nexus and Its Implications for International Order” (UNCE/HUM/037) supported by the Charles University Grant Agency.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Tesar, J. How Do Social Norms and Expectations About Others Influence Individual Behavior?. Found Sci 25, 135–150 (2020). https://doi.org/10.1007/s10699-019-09582-y
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10699-019-09582-y