An evidence accumulation model of forced-choice decision making is proposed to unify the fast and frugaltake the best (TTB) model and the alternativerational (RAT) model with which it is usually contrasted. The basic idea is to treat the TTB model as a sequential-sampling process that terminates as soon as any evidence in favor of a decision is found and the rational approach as a sequential-sampling process that terminates only when all available information has been assessed. The unified TTB and RAT models were tested in an experiment in which participants learned to make correct judgments for a set of real-world stimuli on the basis of feedback, and were then asked to make additional judgments without feedback for cases in which the TTB and the rational models made different predictions. The results show that, in both experiments, there was strong intraparticipant consistency in the use of either the TTB or the rational model but large interparticipant differences in which model was used. The unified model is shown to be able to capture the differences in decision making across participants in an interpretable way and is preferred by the minimum description length model selection criterion.
Allen, C. (2000). The evolution of rational demons [Abstract].Behavioral & Brain Sciences,23, 742.
Anderson, J. R. (1990).The adaptive character of thought. Hillsdale, NJ: Erlbaum.
Anderson, J. R. (1991). The adaptive nature of human categorization.Psychological Review,98, 409–429.
Anderson, J. R. (1992). Is human cognition adaptive?Behavioral & Brain Sciences,14, 471–517.
Ashby, F. G. (1983). A biased random walk model of two choice reaction times.Journal of Mathematical Psychology,27, 277–297.
Bröder, A. (2000). Assessing the empirical validity of the “take-thebest” heuristic as a model of human probabilistic inference.Journal of Experimental Psychology: Learning, Memory, & Cognition,26, 1332–1346.
Brunswik, E. (1943). Organismic achievement and environmental probabilities.Psychological Review,50, 255–272.
Bullock, S., &Todd, P. M. (1999). Made to measure: Ecological rationality in structured environments.Minds & Machines,9, 497–541.
Busemeyer, J. R., &Rapoport, A. (1988). Psychological models of deferred decision making.Journal of Mathematical Psychology,32, 91–134.
Busemeyer, J. R., &Townsend, J. T. (1993). Decision field theory: A dynamic cognition approach to decision making.Psychological Review,100, 432–459.
Cousineau, D., &Larochelle, S. (1997). PASTIS: A program for curve and distribution analyses.Behavior Research Methods, Instruments, & Computers,29, 542–548.
Czerlinski, J., Gigerenzer, G., &Goldstein, D. C. (1999). How good are simple heuristics? In G. Gigerenzer & P. M. Todd (Eds.),Simple heuristics that make us smart (pp. 97–117). New York: Oxford University Press.
Diederich, A. (1997). Dynamic stochastic models for decision making under time constraints.Journal of Mathematical Psychology,41, 260–274.
Doyle, J. (1999). Rational decision making. In R. A. Wilson & F. C. Keil (Eds.),MIT encyclopedia of the cognitive sciences (pp. 701–703). Cambridge, MA: MIT Press.
Gelman, A., Carlin, J. B., Stern, H. S., &Rubin, D. B. (1995).Bayesian data analysis. London: Chapman & Hall.
Gigerenzer, G., &Goldstein, D. G. (1996). Reasoning the fast and frugal way: Models of bounded rationality.Psychological Review,103, 650–669.
Gigerenzer, G., &Todd, P. M. (1999).Simple heuristics that make us smart. New York: Oxford University Press.
Grünwald, P. (1999). Viewing all models as “probabilistic.” InProceedings of the Twelfth Annual Conference on Computational Learning Theory (COLT ’99) (pp.171–182). New York: ACM Press.
Grünwald, P. (2000). Model selection based on minimum description length.Journal of Mathematical Psychology,44, 133–152.
Hintzman, D. L. (1984). MINERVA 2: A simulation model of human memory.Behavior Research Methods, Instruments, & Computers,16, 96–101.
Ida, M. (1980). The application of the Weibull distribution to the analysis of the reaction time data.Japanese Psychological Research,22, 207–212.
Johnson, M. P., &Raven, P. H. (1973). Species number and endemism: The Galapagos archipelago revisited.Science,179, 893–895.
Juslin, P., &Olsson, H. (1997). Thurstonian and Brunswikian origins of uncertainty in judgment: A sampling model of confidence in sensory discrimination.Psychological Review,104, 344–366.
Kass, R. E., &Raftery, A. E. (1995). Bayes factors.Journal of the American Statistical Association,90, 773–795.
Kruschke, J. K. (1992). ALCOVE: An exemplar-based connectionist model of category learning.Psychological Review,99, 22–44.
Laming, D. R. J. (1968).Information theory and choice-reaction time. London: Academic Press.
Lee, M. D., Chandrasena, L. H., &Navarro, D. J. (2002). Using cognitive decision models to prioritize e-mails. In W. G. Gray & C. D. Schunn (Eds.),Proceedings of the 24th Annual Conference of the Cognitive Science Society (pp. 478–483). Mahwah, NJ: Erlbaum.
Lee, M. D., &Corlett, E. Y. (2003). Sequential sampling models of human text classification.Cognitive Science,27, 159–193.
Lee, M. D., Loughlin, N., &Lundberg, I. B. (2002). Applying one reason decision making: The prioritization of literature searches.Australian Journal of Psychology,54, 137–143.
Link, S. W., &Heath, R. A. (1975). A sequential theory of psychological discrimination.Psychometrika,40, 77–105.
Logan, G. D. (1992). Shapes of reaction-time distributions and shapes of learning curves: A test of the instance theory of automaticity.Journal of Experimental Psychology: Learning, Memory, & Cognition,18, 883–914.
Martignon, L., &Hoffrage, U. (1999). Why does one-reason decision making work? In G. Gigerenzer & P. Todd (Eds.),Simple heuristics that make us smart (pp. 119–140). New York: Oxford University Press.
Martignon, L., &Laskey, K. B. (1999). Bayesian benchmarks for fast and frugal heuristics. In G. Gigerenzer & P. M. Todd (Eds.),Simple heuristics that make us smart (pp. 169–188). New York: Oxford University Press.
Medin, D. L., &Schaffer, M. M. (1978). Context theory of classification.Psychological Review,85, 207–238.
Myung, I. J., &Pitt, M. A. (1997). Applying Occam’s razor in modeling cognition: A Bayesian approach.Psychonomic Bulletin & Review,4, 79–95.
Myung, I. J., Pitt, M. A., & Kim, W. J. (in press). Model evaluation, testing and selection. In K. Lamberts & R. Goldstone (Eds.),Handbook of cognition. Thousand Oaks, CA: Sage.
Myung, I. J., &Shepard, R. N. (1996). Maximum entropy inference and stimulus generalization.Journal of Mathematical Psychology,40, 342–347.
Newell, B. R., Weston, N. J., &Shanks, D. R. (2003). Empirical tests of a fast-and-frugal heuristic: Not everyone “takes-the-best.”Organizational Behavior & Human Decision Processes,91, 82–96.
Nosofsky, R. M. (1984). Choice, similarity, and the context theory of classification.Journal of Experimental Psychology: Learning, Memory, & Cognition,10, 104–114.
Nosofsky, R. M., &Palmeri, T. J. (1997). An exemplar-based random walk model of speeded classification.Psychological Review,104, 266–300.
Pietsch, A., &Vickers, D. (1997). Memory capacity and intelligence: Novel techniques for evaluating rival models of a fundamental information processing mechanism.Journal of General Psychology,124, 229–339.
Pinker, S. (1997).How the mind works. New York: Norton.
Pitt, M. A., Myung, I. J., &Zhang, S. (2002). Toward a method of selecting among computational models of cognition.Psychological Review,109, 472–491.
Ratcliff, R. (1978). A theory of memory retrieval.Psychological Review,85, 59–108.
Rissanen, J. (2001). Strong optimality of the normalized ML models as universal codes and information in data.IEEE Transactions on Information Theory,47, 1712–1717.
Roberts, S., &Pashler, H. (2000). How persuasive is a good fit? A comment on theory testing.Psychological Review,107, 358–367.
Schwarz, G. (1978). Estimating the dimension of a model.Annals of Statistics,6, 461–464.
Shepard, R. N. (1987). Toward a universal law of generalization for psychological science.Science,237, 1317–1323.
Simon, H. A. (1956). Rational choice and the structure of environments.Psychological Review,63, 129–138.
Simon, H. A. (1976). From substantive to procedural rationality. In S. J. Latsis (Ed.),Method and appraisal in economics (pp. 129–148). London: Cambridge University Press.
Simon, H. A. (1982).Models of bounded rationality. Cambridge, MA: MIT Press.
Smith, P. L. (2000). Stochastic dynamic models of response time and accuracy: A foundational primer.Journal of Mathematical Psychology,44, 408–463.
Tenenbaum, J. B. (1999). Bayesian modeling of human concept learning. In M. S. Kearns, S. A. Solla, & D. A. Cohn (Eds.),Advances in neural information processing systems (Vol. 11, pp. 59–65). Cambridge, MA: MIT Press.
Tenenbaum, J. B., &Griffiths, T. L. (2001). Generalization, similarity, and Bayesian inference.Behavioral & Brain Sciences,24, 629–640.
Todd, P. M., &Gigerenzer, G. (2000). Précis of Simple heuristics that make us smart.Behavioral & Brain Sciences,23, 727–780.
Tversky, A. (1977). Features of similarity.Psychological Review,84, 327–352.
Usher, M., &McClelland, J. L. (2001). On the time course of perceptual choice: The leaky competing accumulator model.Psychological Review,108, 550–592.
Vandierendonck, A., &Rosseel, Y. (2000). Interaction of knowledgedriven and data-driven processing in category learning.European Journal of Cognitive Psychology,72, 37–63.
Van Zandt, T. (2000). How to fit a response time distribution.Psychonomic Bulletin & Review,7, 424–465.
Vickers, D. (1979).Decision processes in visual perception. New York: Academic Press.
Vickers, D. (2001, September).The elusive “interval of uncertainty”: Evidence for a dynamic normalizing of sensory magnitudes. Paper presented at the 32nd Meeting of the European Mathematical Psychology Group, Lisbon.
Vickers, D., &Pietsch, A. (2001). Decision-making and memory: A critique of Juslin and Olsson’s (1997) sampling model of sensory discrimination.Psychological Review,108, 789–804.
Wallsten, T. S., &Barton, C. (1982). Processing probabilistic multidimensional information for decisions.Journal of Experimental Psychology: Learning, Memory, & Cognition,8, 361–384.
This research was supported by Australian Research Council Grant DP0211406.
About this article
Cite this article
Lee, M.D., Cummins, T.D.R. Evidence accumulation in decision making: Unifying the “take the best” and the “rational” models. Psychonomic Bulletin & Review 11, 343–352 (2004). https://doi.org/10.3758/BF03196581
- Unify Model
- Stimulus Pair
- Evidence Accumulation
- Stimulus Domain
- Random Walk Move