Quantum models for decision making

doi:10.3724/SP.J.1042.2018.01365

Abstract

Abstract:

During the recent decade, quantum decision-making models were established based on the mathematical structure and methodologies of quantum mechanics. Owing to its unique theoretical structure, the quantum decision-making models can be applied to explain problems that violate the classical decision models, especially for judgments under uncertainty and decisions under conflicts. Quantum decision-making models have been used to explain phenomena such as disjunction effect, conjunction fallacy and interference of categorization on decision making which are difficult to account for with classical decision models. A model called quantum question equality has been tested for its accurate prediction of order effects. Being a new research field contributing to analysis of decision making, quantum decision-making models worth further investigations both in theoretical and applicative levels.

Key words: quantum, decision making, model, probability

CLC Number:

B841.2

XIN Xiaoyang, XU Chenhong, CHEN Hongyu, LI Ying. Quantum models for decision making[J]. Advances in Psychological Science, 2018, 26(8): 1365-1373.

Figures/Tables 6

References 47

1	顾樵 . ( 2014). 量子力学Ⅰ. 北京: 科学出版社.
2	李红, 谢松法 . ( 2013). 复变函数与积分变换 (第4版). 北京: 高等教育出版社.
3	刘程浩, 徐富明, 王伟, 李燕, 史燕伟 . ( 2015). 概率判断中的合取谬误. 心理科学进展, 23( 6), 967-978. doi: 10.3724/SP.J.1042.2015.00967 URL
4	罗俊明 . ( 2002). 概率论与数理统计. 郑州: 郑州大学出版社.
5	史荣昌, 魏丰 . ( 2010). 矩阵分析 (第3版). 北京: 北京理工大学出版社.
6	苏汝铿 . ( 2002). 量子力学 (第2版). 北京: 高等教育出版社.
7	孙炯, 王万义, 赫建文 . ( 2010). 泛函分析. 北京: 高等教育出版社.
8	汪祚军, 李纾 . ( 2008). 行为决策中出现的分离效应. 心理科学进展, 16( 4), 513-517.
9	曾谨言 . ( 2014). 量子力学教程 (第3版). 北京: 科学出版社.
10	Aerts, D . ( 2009). Quantum structure in cognition. Journal of Mathematical Psychology, 53( 5), 314-348. doi: 10.1016/j.jmp.2009.04.005 URL
11	Aerts, D., & Gabora, L . ( 2005). A theory of concepts and their combinations II: A Hilbert space representation. Kybernetes, 34( 1-2), 192-221. doi: 10.1108/03684920510575807 URL
12	Aerts D., Gabora L., & Sozzo S . ( 2013). Concepts and their dynamics: A quantum-theoretic modeling of human thought. Topics in Cognitive Science, 5( 4), 737-772. doi: 10.1111/tops.12042 URL pmid: 24039114
13	Aerts D., Sozzo S., & Veloz T . ( 2016). New fundamental evidence of non-classical structure in the combination of natural concepts. Phil. Trans. R. Soc. A, 374(2058), 20150095.
14	Artemenkov, S. L . ( 2006). Kansei versus extensional reasoning: The scientific illusion of the conjunction fallacy in probability judgment. In Proceedings of the First International Workshop on Kansei ( pp. 8-11). Fukuoka, Japan.
15	Asano M., Basieva I., Khrennikov A., Ohya M., & Tanaka Y . ( 2012). Quantum-like generalization of the Bayesian updating scheme for objective and subjective mental uncertainties. Journal of Mathematical Psychology, 56( 3), 166-175. doi: 10.1016/j.jmp.2012.02.003 URL
16	Atmanspacher, H., & Filk, T. . ( 2010). A proposed test of temporal nonlocality in bistable perception. Journal of Mathematical Psychology, 54( 3), 314-321. doi: 10.1016/j.jmp.2009.12.001 URL
17	Bagassi, M., & Macchi, L . ( 2006). Pragmatic approach to decision making under uncertainty: The case of the disjunction effect. Thinking & Reasoning, 12( 3), 329-350. doi: 10.1080/13546780500375663 URL
18	Baron, J . ( 1988). Thinking and deciding. Cambridge: Cambridge University Press.
19	Blutner R., Pothos E. M., & Bruza P . ( 2013). A quantum probability perspective on borderline vagueness. Topics in Cognitive Science, 5( 4), 711-736. doi: 10.1111/tops.12041 URL pmid: 24039093
20	Brainerd C. J., Wang Z., & Reyna V. F . ( 2013). Superposition of episodic memories: Overdistribution and quantum models. Topics in Cognitive Science, 5( 4), 773-799. doi: 10.1111/tops.12039 URL pmid: 24027175
21	Bruza P., Kitto K., Nelson D., & McEvoy C . ( 2009). Is there something quantum-like about the human mental lexicon? Journal of Mathematical Psychology, 53( 5), 363-377.
22	Bruza P. D., Wang Z., & Busemeyer J. R . ( 2015). Quantum cognition: A new theoretical approach to psychology. Trends in Cognitive Sciences, 19( 7), 383-393. doi: 10.1016/j.tics.2015.05.001 URL pmid: 26058709
23	Busemeyer J. R., & Bruza, P. D. .( 2012) . Quantum models of cognition and decision. Cambridge: Cambridge University Press.
24	Busemeyer, J. R., & Wang, Z. . ( 2015). What is quantum cognition, and how is it applied to psychology? Current Directions in Psychological Science, 24( 3), 163-169. doi: 10.1177/0963721414568663 URL
25	Busemeyer J. R., Wang Z., Khrennikov A., & Basieva I . ( 2014). Applying quantum principles to psychology. Physica Scripta, 2014, 014007. doi: 10.1088/0031-8949/2014/T163/014007 URL
26	Busemeyer J. R., Wang Z., & Lambert-Mogiliansky A . ( 2009). Empirical comparison of Markov and quantum models of decision making. Journal of Mathematical Psychology, 53( 5), 423-433. doi: 10.1016/j.jmp.2009.03.002 URL
27	Busemeyer J. R., Wang Z., & Townsend J. T . ( 2006). Quantum dynamics of human decision-making. Journal of Mathematical Psychology, 50( 3), 220-241. doi: 10.1016/j.jmp.2006.01.003 URL
28	Chater N., Tenenbaum J. B., & Yuille A . ( 2006). Probabilistic models of cognition: Conceptual foundations. Trends in Cognitive Sciences, 10( 7), 287-291. doi: 10.1016/j.tics.2006.05.007 URL pmid: 16807064
29	De Barros, J. A., & Suppes, P . ( 2009). Quantum mechanics, interference, and the brain. Journal of Mathematical Psychology, 53( 5), 306-313. doi: 10.1016/j.jmp.2009.03.005 URL
30	Gilboa, I . ( 2009). Theory of decision under uncertainty. Cambridge: Cambridge University Press.
31	Lewinski, P . ( 2015). Commentary: Extensional versus intuitive reasoning: The conjunction fallacy in probability judgment. Frontiers in Psychology, 6, 1832.
32	Li S., Jiang C. M., Dunn J. C., & Wang Z. J . ( 2012). A test of “reason-based” and “reluctance-to-think” accounts of the disjunction effect. Information Sciences, 184( 1), 166-175 doi: 10.1016/j.ins.2011.09.002 URL
33	Li, S., & Taplin, J . ( 2002). Examining whether there is a disjunction effect in prisoner's dilemma games. Chinese Journal of Psychology, 44( 1), 25-46.
34	Moore, D. W . ( 2002). Measuring new types of question-order effects: Additive and subtractive. Public Opinion Quarterly, 66( 1), 80-91. doi: 10.1086/338631 URL
35	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, 276( 1665), 2171-2178. doi: 10.1098/rspb.2009.0121 URL pmid: 19324743
36	Pothos E. M., Busemeyer J. R., & Trueblood J. S . ( 2013). A quantum geometric model of similarity. Psychological Review, 120( 3), 679-696. doi: 10.1037/a0033142 URL pmid: 23915087
37	Savage L J . ( 1954). The Foundations of Statistics. New York: Wiley.
38	Sun Y., Li S., & Li Y. M . ( 2008). Reexamining the role of the description of problem texts in the disjunction effect. The Journal of Psychology, 142( 3), 261-265. doi: 10.3200/JRLP.142.3.261-266 URL pmid: 18589936
39	Tenenbaum J. B., Griffiths T. L., & Kemp C . ( 2006). Theory-based Bayesian models of inductive learning and reasoning. Trends in Cognitive Sciences, 10( 7), 309-318. doi: 10.1016/j.tics.2006.05.009 URL pmid: 16797219
40	Townsend J. T., Smith J. S., Wenger M. J., & Silva K. M . ( 2000). Exploring the relations between categorization and decision making with regard to realistic face stimuli. Pragmatics & Cognition, 8( 1), 83-106.
41	Trueblood, J. S., & Busemeyer, J. R . ( 2012). A quantum probability model of causal reasoning. Frontiers in Psychology, 3, 138. doi: 10.3389/fpsyg.2012.00138 URL pmid: 3350941
42	Tversky, A., & Kahneman, D . ( 1974). Judgment under uncertainty: Heuristics and biases. Science, 185( 4157), 1124-1131. doi: 10.1126/science.185.4157.1124 URL pmid: 17835457
43	Tversky, A., & Shafir, E . ( 1992). The disjunction effect in choice under uncertainty. Psychological Science, 3( 5), 305-309. doi: 10.1111/j.1467-9280.1992.tb00678.x URL
44	Wang, Z., & Busemeyer, J. R . ( 2013). A quantum question order model supported by empirical tests of an A priori and precise prediction. Topics in Cognitive Science, 5, 689-710.
45	Wang, Z., & Busemeyer, J. R . ( 2016). Interference effects of categorization on decision making. Cognition, 150, 133-149. doi: 10.1016/j.cognition.2016.01.019 URL pmid: 26896726
46	Wang Z. J., Li S., & Jiang C. M . ( 2012). Emotional response in a disjunction condition. Journal of Economic Psychology, 33( 1), 71-78.
47	Yearsley, J. M., & Busemeyer, J. R . ( 2016). Quantum cognition and decision theories: A tutorial. Journal of Mathematical Psychology, 74, 99-116. doi: 10.1016/j.jmp.2015.11.005 URL

C-then-D					D-alone
p (G)	p (A\|G)	p (B)	p (A\|B)	p_T(A)	p (A)
0.17	0.41	0.83	0.63	0.59	0.69

C-then-D					D-alone
p (G)	p (A\|G)	p (B)	p (A\|B)	p_T(A)	p (A)
0.17	0.41	0.83	0.63	0.59	0.69

[1]	ZHANG Kaili, ZHENG Hong, WANG Fengyan. “One prelude” and “two movements”: A portrayal of the research process of wisdom psychology in the past 50 years [J]. Advances in Psychological Science, 2023, 31(5): 721-735.
[2]	FANG Junyan, WEN Zhonglin. The endogeneity issue in longitudinal research: Sources and solutions [J]. Advances in Psychological Science, 2023, 31(4): 507-518.
[3]	GUO Li, JIA Suosuo, LI Guiquan, LI Manlin. Lonely at the top? Exploring the multi-level double-edged sword effect of leader workplace loneliness [J]. Advances in Psychological Science, 2023, 31(4): 582-596.
[4]	YU Jie, CHEN Youguo. Spatiotemporal interference effect: An explanation based on Bayesian models [J]. Advances in Psychological Science, 2023, 31(4): 597-607.
[5]	FENG Tingyong, ZHANG Biying. The cognitive neural model of procrastination and related interventions [J]. Advances in Psychological Science, 2023, 31(3): 350-360.
[6]	SUN Hui, XU Jie. Prompt reply: Workplace telepressure in the information and communications technology (ICT) era [J]. Advances in Psychological Science, 2023, 31(3): 467-479.
[7]	WAN Jin, ZHOU Wenjun, ZHOU Haiming, LI Pingping, SHI Kan. The impact of psychological detachment on work engagement: Promotion or inhibition? [J]. Advances in Psychological Science, 2023, 31(2): 209-222.
[8]	ZHAI Hongkun, LI Qiang, WEI Xiaowei. Power analysis in structural equation modeling: Principles and methods [J]. Advances in Psychological Science, 2022, 30(9): 2117-2130.
[9]	WEN Zhonglin, FANG Jie, XIE Jinyan, OUYANG Jinying. Methodological research on mediation effects in China’s mainland [J]. Advances in Psychological Science, 2022, 30(8): 1692-1702.
[10]	WANG Yang, WEN Zhonglin, LI Wei, FANG Jie. Methodological research and model development on structural equation models in China’s mainland from 2001 to 2020 [J]. Advances in Psychological Science, 2022, 30(8): 1715-1733.
[11]	YANG Qi, JIANG Xiaoming, ZHOU Xiaolin. Presupposition processing in language comprehension [J]. Advances in Psychological Science, 2022, 30(7): 1511-1523.
[12]	LI Xi, LI Tongmao, HU Jihao. The mechanism and influences of multilingual packaging strategy for tourism product: From the perspective of selective accessibility model [J]. Advances in Psychological Science, 2022, 30(6): 1216-1229.
[13]	HAN Yuting, XIAO Yue, LIU Hongyun. Feature extraction and ability estimation of process data in the problem-solving test [J]. Advances in Psychological Science, 2022, 30(6): 1393-1409.
[14]	LI Liang, LI Hong. Cognitive mechanism and neural basis of shyness [J]. Advances in Psychological Science, 2022, 30(5): 1038-1049.
[15]	ZAHNG Yuyan, XU Liying, YU Feng, DING Xiaojun, WU Jiahua, ZHAO Liang. A three-dimensional motivation model of algorithm aversion [J]. Advances in Psychological Science, 2022, 30(5): 1093-1105.