# The psychology of dynamic probability judgment: order effect, normative theories, and experimental methodology

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## Abstract

The Bayesian model is used in psychology as the reference for the study of dynamic probability judgment. The main limit induced by this model is that it confines the study of revision of degrees of belief to the sole situations of revision in which the universe is static (*revising* situations). However, it may happen that individuals have to revise their degrees of belief when the message they learn specifies a change of direction in the universe, which is considered as changing with time (*updating* situations). We analyze the main results of the experimental literature with regard to elementary qualitative properties of these two situations of revision. First, the order effect phenomenon is confronted with the commutative property. Second, an apparent new phenomenon is presented: the redundancy effect that is confronted with the idempotence property. Finally, results obtained in this kind of experimental situations are reinterpreted in the light of pragmatic analysis.

## Keywords

Dynamic probability judgment Bayesian coherence Probability revising Probability updating Linguistic pragmatics Order effect Redundancy effect## Notes

### Acknowledgments

The authors thank Laura Macchi for her comments on a first draft of this paper.

## References

- Adelman L, Bresnick TA (1992) Examining the effect of information sequence on patriot air defense officers’ judgments. Organ Behav Hum Dec 53:204–228CrossRefGoogle Scholar
- Adelman L, Bresnick TA, Black PK, Marvin FF, Sak SG (1996) Research with patriot air defense officers: examining information order effects. Hum Factors 38:250–261CrossRefGoogle Scholar
- Adelman L, Tolcott MA, Bresnick TA (1993) Examining the effect of information order on expert judgment. Organ Behav Hum Dec 56:348–369CrossRefGoogle Scholar
- Anderson NH (1968) Application of a linear-serial model to a personality-impression task using serial presentation. J Pers Soc Psychol 64:1–8Google Scholar
- Adler JE (1991) An optimist’s pessimism conversation and conjunction. In: Eells E, Maruszewski T (eds) Probability and rationality: studies on L. Jonathan Cohen’s philosophy of science. Rodopi, Amsterdam, Atlanta, GA, pp 251–282Google Scholar
- Baratgin J (1999) Psychologie du raisonnement probabiliste dynamique. Recherches historiques, pragmatiques et expérimentales sur la règle de Bayes. [The psychology of dynamic probabilistic reasoning. Historical, pragmatic, and experimental research on Bayes’ rule]. Unpublished doctorate dissertation. Ecole Polytechnique, FranceGoogle Scholar
- Baratgin J (2002) Is the human mind definitely not Bayesian? A review of the various arguments. Cah Psychol Cogn 21:653–680Google Scholar
- Baratgin J, Politzer G (2006) Is the mind Bayesian? The case for agnosticism. Mind Soc 21:653–680Google Scholar
- Bar-Hillel M, Falk R (1982) Some teasers concerning conditional probabilities. Cognition 11:109–122CrossRefGoogle Scholar
- Baumann M, Krems JF (2002) Frequency learning and order effects in belief updating. In: Sedlmeier P, Betsch T (eds) Frequency processing and cognition. Oxford University Press, OxfordGoogle Scholar
- Birbaum MH, Mellers BA (1983) Bayesian inference: combining base rates with opinions of sources who vary in credibility. J Pers Soc Psychol 45:792–803CrossRefGoogle Scholar
- Curley SP, Golden JI (1994) Using belief functions to represent degree of belief. Organ Behav Hum Dec 58:271–303CrossRefGoogle Scholar
- de Finetti B (1964) Foresight: its logical laws, its subjective sources. In: Kyburg HE Jr, Smokler HE (eds) Studies in subjective probability. Wiley, New York, pp 53–118 (1st edn, 1937)Google Scholar
- Dubois D, Prade H (1988) Modelling uncertainty and inductive inference: a survey of recent non-additive probability systems. Acta Psychol 68:53–78CrossRefGoogle Scholar
- Dubois D, Prade H (1992) Evidence, knowledge, and belief Function. Int J Approx Reason 6:295–319CrossRefGoogle Scholar
- Falk R (1992) A closer look at the probabilities of the notorious three prisoners. Cognition 43:197–223CrossRefGoogle Scholar
- Funder DC (1987) Errors and mistakes: evaluating the accuracy of social judgment. Psychol Bull 101:75–90CrossRefGoogle Scholar
- Gardner M (1959a) Mathematical games: how three mathematicians disproved a celebrated conjecture of Leonard Euler. Sci Am 201(5):181–188Google Scholar
- Gardner M (1959b) Mathematical games: problems involving questions of probability and ambiguity. Sci Am 201(4):174–182Google Scholar
- Gärdenfors P (1988) Knowledge in flux, modeling the dynamics of epistemic states. The MIT Press, Cambridge, MAGoogle Scholar
- Hacking I (1975) The emergence of probability: a philosophy study of early ideas about probability, induction, and statistical inference. Cambridge University Press, CambridgeGoogle Scholar
- Hammond KR, McClelland GH, Mumpower J (1980) Human judgment and decision making. Theories, methods, and procedures. Hemisphere Publishing Corporation/Praeger, New YorkGoogle Scholar
- Hilton DJ (1995) The social context of reasoning: Conversational inference and rational judgment. Psychol Bull 118:248–271CrossRefGoogle Scholar
- Hinsz VB, Tindale RS, Nagao DH, Davis JH, Robertson BA (1988) The influence of the accuracy of individuating information on the use of base rate information in probability judgment. J Exp Soc Psychol 24:127–145CrossRefGoogle Scholar
- Hoffrage U, Gigerenzer G, Krauss S, Martignon L (2002) Representation facilitates reasoning: what natural frequencies are and what they are not. Cognition 84:343–352CrossRefGoogle Scholar
- Hogarth RM (1975) Cognitive processes and the assessment of subjective probability distributions. J Am Stat Assoc 70:271–289CrossRefGoogle Scholar
- Hogarth RM, Einhorn HJ (1992) Order effects in belief updating: the belief-adjustment model. Cognitive Psychol 24:1–55CrossRefGoogle Scholar
- Jeffrey R (1988) Conditioning, kinematics and exchangeability. In: Skyrms B, Harper W (eds) Causation, chance and credence, vol I. D. Reidel Publishing Company, Dordrecht, pp 221–255Google Scholar
- Kahneman D, Tversky A (1973) On the psychology of prediction. Psychol Rev 80:237–251CrossRefGoogle Scholar
- Katsuno H, Mendelzon AO (1992) On the difference between updating a knowledge base and revising it. In: Gärdenfors P (ed) Belief revision. Cambridge University Press, Cambridge, pp 183–203Google Scholar
- Klar Y (1990) Linking structures and sensitivity to judgment-relevant information in statistical and logical reasoning tasks. J Pers Soc Psychol 59:841–858CrossRefGoogle Scholar
- Koehler JJ (1996) The base rate fallacy reconsidered: descriptive, normative and methodological challenges. Behav Brain Sci 19:1–53CrossRefGoogle Scholar
- Krauss S, Wang XT (2003) The psychology of the Monty Hall problem: discovering psychological mechanisms for solving a tenacious brain teaser. J Exp Psychol Gen 132:3–22CrossRefGoogle Scholar
- Krosnick JA, Li F, Lehman DR (1990) Conversational conventions, order of information acquisition, and the effect of base rates and individuating information on social judgments. J Pers Soc Psychol 39:1140–1152Google Scholar
- Kruglanski AW, Ajzen I (1983) Bias and error in human judgment. Eur J Soc Psychol 13:1–44CrossRefGoogle Scholar
- Lewis D (1976) Probabilities of conditionals and conditional probabilities. Philos Rev 3:297–315CrossRefGoogle Scholar
- Lynch JG, Ofir C (1989) Effects of cue consistency and value on base-rate utilisation. J Pers Soc Psychol 56:170–181CrossRefGoogle Scholar
- Marks DF, Clarkson KR (1972) An explanation of conservatism in the bookbag-and-pokerchip situation. Acta Psychol 36:145–160CrossRefGoogle Scholar
- Mosteller F (1965) Fifty challenging problems in probability with solutions. Addison Wesley, New YorkGoogle Scholar
- Nathan A (1984) Discussion: how not to solve it. Philos Sci 53:114–119CrossRefGoogle Scholar
- Nickerson RS (1996) Ambiguities and unstated assumptions in probabilistic reasoning. Psychol Bull 120(3):410–433CrossRefGoogle Scholar
- Ofir C (1988) Pseudodiagnosticity in judgment under uncertainty. Organ Behav Hum Perf 42:343–363CrossRefGoogle Scholar
- Pearl J (2000) Causality: models, reasoning, and inference. Cambridge University Press, CambridgeGoogle Scholar
- Politzer G (1991) L’informativité des énoncés: contraintes sur le jugement et le raisonnement. [The informativeness of statements: Constraints on judgment and reasoning]. Intellectica 11:11–147Google Scholar
- Politzer G, Macchi L (2000) Reasoning and pragmatics. Mind Soc 1(1):73–94CrossRefGoogle Scholar
- Ramsey FP (1926) Truth and probability. Later in Braithwaite RB (ed) (1931) The foundations of mathematics and other logical essays. Routledge and Kegan Paul, London, pp 156–198Google Scholar
- Robinson LB, Hastie R (1985) Revision of beliefs when a hypothesis is eliminated from consideration. J Exp Psychol Hum 11:443–456CrossRefGoogle Scholar
- Ruble DN, Feldman NS (1976) Order of consensus, distinctiveness, and consistency information, and causal attribution. J Pers Soc Psychol 34:930–937CrossRefGoogle Scholar
- Schlottmann A, Anderson NH (1995) Belief revision in children: serial judgment in social and decision-making domains. J Exp Psychol Learn 21:1349–1364CrossRefGoogle Scholar
- Schum DA, Martin AW (1982) Formal and empirical research on cascaded inference in jurisprudence. Law Soc Rev 17:105–151CrossRefGoogle Scholar
- Shafer G (1976) A mathematical theory of evidence. Princeton University Press, Princeton, NJGoogle Scholar
- Shafer G (1985) Conditional probability. Int Stat Rev 53:261–277CrossRefGoogle Scholar
- Shimojo S, Ichikawa I (1989) Intuitive reasoning about probability: theoretical and experimental analyses of the “problem of three prisoners”. Cognition 43:197–223Google Scholar
- Slovic P (1966) Cue consistency and cue utilization in judgment. Am J Psychol 79:427–434CrossRefGoogle Scholar
- Sperber D, Wilson D (1995) Relevance: communication and cognition. Blackwell, Oxford (1st edn, 1986)Google Scholar
- Teigen KH (1983) Studies in subjective probability. III. The unimportance of alternatives. Scand J Psychol 24:97–105Google Scholar
- Tubbs RM, Gaeth GJ, Levin IP, Van Osdol LA (1993) Order effect in belief updating with consistent and inconsistent evidence. J Behav Dec Making 6:257–269Google Scholar
- Walley P (1991) Statistical reasoning with imprecise probabilities. Chapman and Hall, LondonGoogle Scholar
- Walliser B, Zwirn D (2002) Can Bayes’ rule be justified by cognitive rationality principles. Theor Dec 53:95–135CrossRefGoogle Scholar
- Wang H, Zhang J, Johnson TR (2000) Order effects in human belief revision. In: Proceedings of the 22nd annual conference of the cognitive science society. Lawrence Erlbaum Associates, Hillsdale, NJ, pp 547–552Google Scholar
- Van Wallendael LR (1989) The quest for limits on noncomplementarity in opinion revision. Organ Behav Hum Dec 43:385–405CrossRefGoogle Scholar
- Van Wallendael LR, Hastie R (1990) Tracing the footsteps of Sherlock Holmes: cognitive representations of hypothesis testing. Mem Cogn 18:240–250Google Scholar
- Wolfe CR (1995) Information seeking on Bayesian conditional probability problems: a fuzzy-trace theory account. J Behav Dec Making 8:85–108Google Scholar
- Zhang J, Johnson TR, Wang H (1998) The relation between order effects and frequency learning in tactical decision-making. Thinking Reason 4:123–145CrossRefGoogle Scholar