Invitation to Mathematical Psychology
Models and Benefits of Formal Theorizing
DOI:
https://doi.org/10.1590/0102.3772e39515.enKeywords:
Mathematical psychology, Formal theorizing, Quantitative modelingAbstract
In most areas, psychological phenomena tend to be explained only through textual constructions. Several authors, however, point to the need for theories that have a more formal nature, based on mathematical reasoning. In order to encourage broader access to its applications, we present the models and advantages of a mathematical psychology approach to the study of behavior. We review the limitations of verbal theorizing, then a common taxonomy in mathematical psychology follows, that classifies formal models as descriptive, process characterization, and explanatory. As well succeeded cases, we examine the mathematical psychology of decision making, of helping behavior, of memory, and of romantic relationships. Finally, we discuss the potential benefits and uses of this approach. Welcome to mathematical psychology.
Downloads
References
Adner, R., Polos, L., Ryall, M., & Sorenson, O. (2009). The case for formal theory. Academy of Management Review, 34(2), 201-208. https://doi.org/10.5465/amr.2009.36982613
Altman, M. (2004). The Nobel Prize in behavioral and experimental economics: A contextual and critical appraisal of the contributions of Daniel Kahneman and Cernon Smith. Review of Political Economy, 16(1), 3-41. https://doi.org/10.1080/0953825032000145445
Amato, P. R. (2007). Alone together: How marriage in America is changing. Harvard University Press.
Baron, J. (2007). Thinking and deciding. Cambridge University Press.
Batchelder, W. H., Colonius, H., Dzhafarov, E. N., & Myung, J. (Eds.). (2016). New handbook of mathematical psychology: Volume 1, Foundations and Methodology. Cambridge University Press.
Box, G. E. P., & Draper, N. R. (1987). Empirical model-building and response surfaces. John Wiley & Sons.
Brown, G. D. A., Neath, I., & Chater, N. (2007). A temporal ratio model of memory. Psychological Review, 114, 539-576.
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. https://doi.org/10.1016/j.tics.2015.05.001
Busemeyer, J. R., & Bruza, P. D. (2012). Quantum models of cognition and decision. Cambridge University Press.
Busemeyer, J. R., Wang, Z., Eidels, A., & Townsend, J. T. (2015). Review of basic mathematical concepts used in computational and mathematical psychology. In J.R. Busemeyer, Z. Wang, A. Eidels & J.T. Townsend (Eds.), The Oxford handbook of computational and mathematical psychology (pp. 1-10). Oxford University Press.
Coombs, C. H., Dawes, R. M., & Tversky, A. (1970). Mathematical psychology: An elementary introduction. Prentice Hall.
Dancey, C., & J. Reidy (2006). Estatística sem matemática para psicologia [Statistics without Maths for Psychology]. Bookman/Artmed.
Devlin, K. J. (2012). Introduction to mathematical thinking. Keith Devlin.
Doignon, J. P., & Falmagne, J. C. (1991). Mathematical psychology: Current developments. Springer-Verlag.
Edwards, W. (1977). How to use multiattribute utility measurement for social decisionmaking. IEEE Transactions on Systems, Man, and Cybernetics, 7(5), 326-340. https://doi.org/10.1109/TSMC.1977.4309720
Falmagne, J. C. (2005). Mathematical psychology: a perspective. Journal of Mathematical Psychology, 49(6), 436-439. https://doi.org/10.1016/j.jmp.2005.06.007
Fischhoff, B., & Broomell, S. B. (2020). Judgment and decision making. Annual Review of Psychology, 71, 331-355. https://doi.org/10.1146/annurev-psych-010419-050747
Fum, D., Del Missier, F., & Stocco, A. (2007). The cognitive modeling of human behavior: Why a model is (sometimes) better than 10,000 words. Cognitive Systems Research, 8, 135-142. https://doi.org/10.1016/j.jmp.2005.06.007
Gigerenzer, G., & Murray, D. J. (2015). Cognition as intuitive statistics. Psychology Press.
Gottman, J. M., Murray, J. D., Swanson, C. C., Tyson, R., & Swanson, K. R. (2002). The mathematics of marriage: Dynamic nonlinear models. MIT Press.
Heathcote, A., Brown, S., & Mewhort, D. J. (2000). The power law repealed: The case for an exponential law of practice. Psychonomic Bulletin & Review, 7, 185-207. https://doi.org/10.3758/BF03212979
Hunt, E. (2006). The mathematics of behavior. Cambridge University Press.
Janis, I. L., & Mann, L. (1977). Decision making: A psychological analysis of conflict, choice, and commitment. Free Press.
Kahana, M. J. (2020). Computational models of memory search. Annual Review of Psychology, 71, 107-138. https://doi.org/10.1146/annurev-psych-010418-103358
Kahneman, D. (2003). Maps of bounded rationality: Psychology for behavioral economics. American Economic Review, 1449-1475.
Kahneman, D., & Tversky, A. (1979). Prospect theory: An analysis of decision under risk. Econometrica: Journal of the Econometric Society, 47, 263-291. https://doi.org/10.1142/9789814417358_0006
Kocher, M. G., & Sutter, M. (2005). The decision maker matters: Individual versus group behaviour in experimental beauty‐contest games. The Economic Journal, 115(500), 200-223. https://doi.org/10.1111/j.1468-0297.2004.00966.x
Lewandowsky, S., & Farrell, S. (2000). A redintegration account of the effects of speech rate, lexicality, and word frequency in immediate serial recall. Psychological Research, 63, 163-173. https://doi.org/10.1007/PL00008175
Lewandowsky, S., & Farrell, S. (2010). Computational modeling in cognition: Principles and practice. Sage.
Lieder, F., & Griffiths, T. L. (2020). Resource-rational analysis: Understanding human cognition as the optimal use of limited computational resources. Behavioral and Brain Sciences, 43, 1-85. https://doi.org/10.1017/S0140525X1900061X
Luce, R. D. (1995). Four tensions concerning mathematical modeling in psychology. Annual Review of Psychology, 46(1), 1-27. https://doi.org/10.1146/annurev.ps.46.020195.000245
Luce, R. D. (1997). Several unresolved conceptual problems of mathematical psychology. Journal of Mathematical Psychology, 41(1), 79-87. https://doi.org/10.1006/jmps.1997.1150
Luce, R. D., R. R. Bush, & E. Galanter (Eds.). (1963-1965a). Handbook of mathematical psychology (Vols. 1-2) . Wiley.
Luce, R. D., R. R. Bush, & E. Galanter (Eds.). (1963-1965b). Readings in mathematical psychology (Vols. 1-2). Wiley
Mertens, D. M. (2014). Research and evaluation in education and psychology: Integrating diversity with quantitative, qualitative, and mixed methods. Sage Publications.
McGrath, R. E. (2011). Quantitative models in psychology. American Psychological Association.
Millroth, P., & Collsiöö, A. (2020). Strictly Minskyian: Advancing theories of decision making under risk by carefully mapping current states of individuals. Unpublished manuscript. http://dx.doi.org/10.13140/RG.2.2.17034.49602
Nelson, L. D., Simmons, J., & Simonsohn, U. (2018). Psychology’s renaissance. Annual Review of Psychology, 69, 511-534. https://doi.org/10.1146/annurev-psych-122216-011836
Norris, D. (2005). How do computational models help us build better theories? In A. Cutler (Ed.), Twenty-first century psycholinguistics: Four cornerstones (pp. 331-346). Lawrence Erlbaum.
Pasquali, L. (2001). Técnicas de exame psicológico - TEP: Manual [Psychological exam techniques: Guide]. Casa do Psicólogo.
Regenwetter, M., Dana, J., & Davis-Stober, C. P. (2011). Transitivity of preferences. Psychological review, 118(1), 42-56. https://doi.org/10.1037/a0021150
Schweickert, R. (1993). A multinomial processing tree model for degradation and redintegration in immediate recall. Memory & Cognition, 21, 168-175. https://doi.org/10.3758/BF03202729
Simon, H. A. (1959). Theories of decision-making in economics and behavioral science. The American Economic Review, 49(3), 253-283.
Smaldino, P. E., & Epstein, J. M. (2015). Social conformity despite individual preferences for distinctiveness. Royal Society Open Science, 2(3), 140437. https://doi.org/10.1098/rsos.140437
Stanovich, K. E. (2015). Rational and irrational thought: The thinking that IQ tests miss. Scientific American Mind Special Collector’s Edition, 23(4), 12-17.
Srivastava, S. (2009, May 14). Making progress in the hardest science. https://thehardestscience.com/2009/03/14/making-progress-in-the-hardest-science/
Townsend, J. T. (2008). Mathematical psychology: Prospects for the 21st century: a guest editorial. Journal of Mathematical Psychology, 52(5), 269-280. https://doi.org/10.1016/j.jmp.2008.05.001
Turner, B. M., Forstmann, B. U., Wagenmakers, E. J., Brown, S. D., Sederberg, P. B., & Steyvers, M. (2013). A Bayesian framework for simultaneously modeling neural and behavioral data. NeuroImage, 72, 193-206. https://doi.org/10.1016/j.neuroimage.2013.01.048
Van Zandt, T., & Townsend, J. T. (2012). Mathematical psychology. In H. Cooper, P. M. Camic, D. L. Long, A. T. Panter, D. Rindskopf, & K. J. Sher (Eds.), APA handbook of research methods in psychology, Vol. 2. Research designs: Quantitative, qualitative, neuropsychological, and biological (pp. 369-386). American Psychological Association.https://doi.org/10.1037/13620-020
Von Bertalanffy, L. (1968). Organismic psychology and systems theory. Clark University Press.
Yarkoni, T., & Westfall, J. (2017). Choosing prediction over explanation in psychology: Lessons from machine learning. Perspectives on Psychological Science, 12(6), 1100-1122. https://doi.org/10.1177/1745691617693393
Yukalov, V. I., & Sornette, D. (2008). Quantum decision theory as quantum theory of measurement. Physics Letters A, 372(46), 6867-6871. https://doi.org/10.1016/j.physleta.2008.09.053
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2023 Víthor Rosa Franco, Fabio Iglesias
![Creative Commons License](http://i.creativecommons.org/l/by/4.0/88x31.png)
This work is licensed under a Creative Commons Attribution 4.0 International License.