The author proposes a set of mathematical equations attempting to simulate perceptual assimilation and contrast, which has rarely been quantitatively studied. The author bases the equations on the model of dimensional range overlap, which is the most integrative model available now. Underlying the model is the assumption of various concepts possibly describing a given object which is being evaluated, with differing salience on a dimension, which may be compared to the possible outcomes of a random variable. The author investigates the roles of the location (extremity), scale (ambiguity), skewness, peak and tail behaviour of the distribution of concepts in shifting the best representation of the given object. In addition to the distribution characteristics, the author introduces evaluative volatility, cognitive consumption, and attention to dissimilarities to the discussion.

By means of the equations, the author is hoping to allow for clearer academic communication, and more accurate predictions of people’s perception after their exposure to contexts. The author urges future scholars to devise more sophisticated psychological measurement methods and tools, so as to empirically test the equations.

Chiěn, Y.-W. & Hsiāo, C.-C. (2001). Dimensional range overlap model for explanation of contextual priming effects. In M. C. Gilly & J. Meyers-Levy (Eds.), Advances in Consumer Research (Vol. 28, p. 136). Valdosta, GA: Association for Consumer Research.
Chiěn, Y.-W., Wegener, D. T., Hsiāo, C.-C., & Petty, R. E. (2010). Dimensional range overlap and context effects in consumer judgments. Journal of Consumer Research, 37(3), 530–542. https://doi.org/10.1086/652415.
Cooper, M. R., Runyon, R. P., Tatz, S. J., & Heimer, W. I. (1972). The Sander illusion as a function of relative space and component lines. Perception & Psychophysics, 11(1), 102–104. https://doi.org/10.3758/bf03212695.
Draine, S. C., & Greenwald, A. G. (1998). Replicable unconscious semantic priming. Journal of Experimental Psychology: General, 127(3), 286–303. https://doi.org/10.1037/0096-3445.127.3.286.
Givon, M. M., & Shapira, Z. (1984). Response to rating scales: A theoretical model and its application to the number of categories problem. Journal of Marketing Research, 21(4), 410–419. https://doi.org/10.2307/3151467.
Herr, P. M. (1989). Priming price: Prior knowledge and context effects. Journal of Consumer Research, 16(1), 67–75. https://doi.org/10.1086/209194.
Hsiāo, C.-C. (2002). The Reciprocity Hypothesis as an Explanation of Perception Shifts in Consumer Judgments (AAI3099155) [doctoral dissertation]. Purdue University.
Karremans, J. C., Stroebe, W., & Claus, J. (2006). Beyond Vicary’s fantasies: The impact of subliminal priming and brand choice. Journal of Experimental Social Psychology, 42(6), 792–798. https://doi.org/10.1016/j.jesp.2005.12.002.
Keelin, T. W. (2016). The metalog distributions. Decision Analysis, 13(4), 243–277. https://doi.org/10.1287/deca.2016.0338.
Kullback, S. & Leibler, R. A. (1951). On information and sufficiency. The Annals of Mathematical Statistics, 22(1), 79–86. https://doi.org/10.1214/aoms/1177729694.
Li, R. & Nadarajah, S. (2018). A review of Student’s t distribution and its generalisations. Empirical Economics, 58(3), 1461–1490. https://doi.org/10.1007/s00181-018-1570-0.
Lin, J. (1991). Divergence measures based on the Shannon entropy. IEEE Transactions on Information Theory, 37(1), 145–151. https://doi.org/10.1109/18.61115.
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.
Martin, L. L. (1986). Set/reset: Use and disuse of concepts in impression formation. Journal of Personality and Social Psychology, 51(3), 493–504. https://doi.org/10.1037/0022-3514.51.3.493.
Massaro, D. W. & Anderson, N. H. (1971). Judgmental model of the Ebbinghaus illusion. Journal of Experimental Psychology, 89(1), 147–151. https://doi.org/10.1037/h0031158.
Panaretos, V. M., & Zemel, Y. (2019). Statistical aspects of Wasserstein distances. Annual Review of Statistics and Its Application, 6(1), 405–431. https://doi.org/10.1146/annurev-statistics-030718-104938.
Petty, R. E. & Wegener, D. T. (1999). The elaboration likelihood model: Current status and controversies. In S. Chaiken & Y. Trope (Eds.), Dual Process Theories in Social Psychology (pp. 41–72), New York: Guildford Press.
Purves, D., Lotto B. R., & Nundy S. (2002) Why we see what we do: A probabilistic strategy based on past experience explains the remarkable difference between what we see and physical reality. American Scientist, 90(3), 236–243.
Thurstone, L. L. (1927a). Psychophysical analysis. The American Journal of Psychology, 38(3), 368. https://doi.org/10.2307/1415006.
Thurstone, L. L. (1927b). A law of comparative judgment. Psychological Review, 34(4), 273–286. https://doi.org/10.1037/h0070288.
Tversky, A. & Kahneman, D. (1992). Advances in prospect theory: Cumulative representation of uncertainty. Journal of Risk and Uncertainty, 5(4), 297–323. https://doi.org/10.1007/bf00122574.
Wegener, D. T. & Petty, R. E. (1997). The flexible correction model: The role of naïve theories of bias in bias correction. In M. P. Zanna (Ed.), Advances in Experimental Social Psychology (Vol. 29, pp. 141c208). San Diego: Academic Press.