Abstract
Excessive variability in binary choice (categorical judgment) can take the form of probability matching rather than the normatively correct behavior of deterministically choosing the more likely alternative. Excessive variability in continuous choice (judgment rating) can take the form of underconfidence, understating the probability of highly likely events and overstating the probability of very unlikely events. We investigated the origins of choice variability in terms of noise prior to decision (at the evidence stage) and at the decision stage. A version of the well-known medical diagnosis task was conducted with binary and continuous choice on each trial. Noise at evidence stage was reduced by allowing the subjects to view historical summaries of prior relevant trials, and noise at the decision stage was reduced by giving the subjects a numerical score on the basis of their continuous choice and the actual outcome. Both treatments greatly reduced variability. Cash payments based on the numerical score had a less reliable incremental effect in our experiment. The overall results are more consistent with a Logit model of decision than with a simple criterion (or maximization) rule or a simple probabilitymatching rule.
Article PDF
Similar content being viewed by others
References
Allen, F. (1987). Discovering personal probabilities when utility functions are unknown.Management Science33, 542–544.
Anderson, N. H. (1981).Foundations of information integration theory. New York: Academic Press.
Anderson, N. H. (1982).Methods of information integration theory. New York: Academic Press.
Anderson, S., de Palma, A., &Thisse, J. F. (1992).Discrete choice theory of product differentiation. Cambridge, MA: MIT Press.
Camerer, C. (1995). Individual decision making. In J. H. Kagel & A. E. Roth (Eds.),The handbook of experimental economics. Princeton: Princeton University Press.
Cheung, Y. W., &Friedman, D. (1997). Individual learning in normal form games: Some laboratory results.Games & Economic Behavior,19, 46–76.
Davison, M., &McCarthy, D. (1988).The matching law: A research review. Hillsdale, NJ: Erlbaum.
Estes, W. K. (1954). Individual behavior in uncertain situations: An interpretation in terms of statistical association theory. In R. M. Thrall, C. H. Coombs, & R. L. Davis (Eds.),Decision processes (pp. 127–137). New York: Wiley.
Estes, W. K. (1984). Global and local control of choice behavior by cyclically varying outcome probabilities.Journal of Experimental Psychology: Learning, Memory, & Cognition,10, 258–270.
Estes, W. K., Campbell, J. A., Hatsopoulos, N., &Hurwitz, J. B. (1989). Base-rate effects in category learning: A comparison of parallel network and memory storage-retrieval models.Journal of Experimental Psychology: Learning, Memory, & Cognition,15, 556–571.
Friedman, D. (1983). Effective scoring rules for probabilistic forecasts.Management Science,29, 447–454
Friedman, D., &Aoki, M. (1992). Inefficient information aggregation as a source of asset price bubbles.Bulletin of Economic Research,44, 251–279.
Friedman, D., Massaro, D. W., Kitzis, S. N., &Cohen, M. M. (1995). A comparison of learning models.Journal of Mathematical Psychology,39, 164–178.
Gluck, M. A., &Bower, G. H. (1988). From conditioning to category learning: An adaptive network model.Journal of Experimental Psychology: General,117, 225–244.
Green, D. M., &Swets, J. A. (1966).Signal detection theory and psychophysics. New York: Wiley.
Greene, W. H. (1990).Econometric analysis. New York: MacMillan.
Kahneman, D., &Tversky, A. (1979). Prospect theory: An analysis of decision under risk.Econometrica,47, 263–291.
Luce, R. D. (1959).Individual choice behavior: A theoretical analysis. New York: Wiley.
Luce, R. D. (1986).Response times: Their role in inferring elementary mental organization. New York: Oxford University Press.
Macmillan, N. A., &Creelman, C. D. (1991).Detection theory: A user’s guide. New York: Cambridge University Press.
Marks, L. E. (1976).Sensory processes: The new psychophysics. New York: Academic Press.
Massaro, D. W. (1969). A three state Markov model for discrimination learning.Journal of Mathematical Psychology,6, 62–80.
Massaro, D. W. (1987).Speech perception by ear and eye: A paradigm for psychological inquiry. Hillsdale, NJ: Erlbaum.
Massaro, D. W. (1989).Experimental psychology: An information processing approach. San Diego: Harcourt Brace Jovanovich.
Massaro, D. W. (1998).Perceiving talking faces: From speech perception to a behavioral principle. Cambridge, MA: MIT Press.
Massaro, D. W., &Friedman, D. (1990). Models of integration given multiple sources of information.Psychological Review,97, 225–252.
Massaro, D. W., &Hary, J. M. (1986). Addressing issues in letter recognition.Psychological Research,48, 123–132.
McClelland, J. L. (1991). Stochastic interactive processes and the effect of context on perception.Cognitive Psychology,23, 1–44.
McDowell, B. D., &Oden, G. C. (1995).Categorical decisions, rating judgments, and information preservation. Unpublished manuscript, University of Iowa, Iowa City.
McFadden, D. (1973). Conditional logit analysis of qualitative choice behavior. In P. Zarembka (Ed.),Frontiers of econometrics. New York: Academic Press.
McKelvey, R., &Page, T. (1990). Public and private information: An experimental study of information pooling.Econometrica,58, 1321–1339.
McKelvey, R., &Palfrey, T. R. (1995). Quantal response equilibria for normal form games.Games & Economic Behavior,10, 6–38.
Myers, J. L. (1976). Probability learning and sequence learning. In W. K. Estes (Ed.),Handbook of learning and cognitive processes (pp. 171–205). Hillsdale, NJ: Erlbaum.
Myers, J. L., &Cruse, D. (1968). Two-choice discrimination learning as a function of stimulus and event probabilities.Journal of Experimental Psychology,77, 453–459.
Nosofsky, R. M., Kruschke, J. K., &McKinley, S. C. (1992). Combining exemplar-based category representations and connectionist learning rules.Journal of Experimental Psychology: Learning, Memory, & Cognition18, 211–233.
Savage, L. (1971). Elicitation of personal probabilities and expectations,Journal of the American Statistical Association,66, 783–801.
Selten, R. (1996).Axiomatic characterization of the quadratic scoring rule (Discussion Paper No. B-390). University of Bonn, Department of Economics.
Shepard, R. N. (1957). Stimulus and response generalization: A stochastic model relating generalization to distance in psychological space.Psychometrika,22, 325–345.
Smith, V. L., &Walker, J. M. (1993). Rewards, experience and decision costs in first price auctions.Economic Inquiry,31, 237–245.
Tang, F. F. (1996).Anticipatory learning in two-person games: An experimental study [Working paper]. University of Bonn, Department of Economics. .
Thomas, E. A. C., &Legge, D. (1970). Probability matching as a basis for detection and recognition decisions.Psychological Review,77, 65–72.
Thurstone, L. L. (1927). A law of comparative judgment.Psychological Review,34, 273–286.
Townsend, J. T., &Busemeyer, J. (1995). Dynamic representation of decision-making. R. F. Port & T. von Gelder (Eds.),Mind as motion: Explorations in the dynamics of cognition (pp. 101–120). Cambridge, MA: MIT Press.
Varey, C. A., Mellers, B. A., &Birnbaum, M. H. (1990). Judgments of proportions.Journal of Experimental Psychology: Human Perception & Performance,16, 613–625.
Yellott, J. I., Jr. (1977). The relationship between Luce’s choice axiom, Thurstone’s theory of comparative judgment, and the double exponential distribution.Journal of Mathematical Psychology,15, 109–144.
Author information
Authors and Affiliations
Corresponding author
Additional information
This work was supported by NSF Grant SBR 9310347 and Public Health Service Grant PHS R01 DC 00236 and was presented at the 1996 Economic Science Association meeting. We are grateful to Stephen Kitzis, Tamara Torrence, Anne Shin, and Lisa Lima for research assistance on earlier stages of the project and to Nitai Farmer, Eric Berg, and Hugh Kelley for helping us run the main set of experiments and analyze the data reported here. Hugh Kelley and Seble Menkir polished the tables and figures. The final exposition owes much to Duncan Luce, Gregg Oden, an anonymous referee, and Richard Schweickert. D.F. is in the Department of Economics.
Rights and permissions
About this article
Cite this article
Friedman, D., Massaro, D.W. Understanding variability in binary and continuous choice. Psychonomic Bulletin & Review 5, 370–389 (1998). https://doi.org/10.3758/BF03208814
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.3758/BF03208814