The hazards of underspecified models: the case of symmetry in everyday predictions.

Should one be more confident when predicting the whole (or an event based on a larger sample) from the part (or an event based on a smaller sample) than when predicting the reverse? The relevant literature on judgment under uncertainty argues that such predictions are symmetrical but that, as an empirical matter, people often fail to appreciate this symmetry. The authors show that symmetry in prediction does not necessarily hold. In addition to an empirical study involving predictions about soccer games, they develop a theoretical model showing that, at least for the ranges of numerical values usually found in everyday judgment problems, symmetry in predictions is uncommon when 2 different sample sizes are involved. The complexity of the theoretical model used in this analysis raises questions about model specification in judgmental research.

[1]  M. Bar-Hillel,et al.  Some teasers concerning conditional probabilities , 1982, Cognition.

[2]  R. Nisbett,et al.  The psychometrics of everyday life , 1986, Cognitive Psychology.

[3]  G. Gigerenzer,et al.  Teaching Bayesian reasoning in less than two hours. , 2001, Journal of experimental psychology. General.

[4]  Lola L. Lopes The Rhetoric of Irrationality , 1991 .

[5]  Gerd Gigerenzer,et al.  How to Make Cognitive Illusions Disappear , 2002 .

[6]  R R Macdonald,et al.  Credible conceptions and implausible probabilities. , 1986, The British journal of mathematical and statistical psychology.

[7]  G. Gigerenzer How to Make Cognitive Illusions Disappear: Beyond “Heuristics and Biases” , 1991 .

[8]  A. Tversky,et al.  Judgment under Uncertainty: Heuristics and Biases , 1974, Science.

[9]  John Beatty,et al.  The Empire of Chance: How Probability Changed Science and Everyday Life , 1989 .

[10]  D. Hilton THE SOCIAL CONTEXT OF REASONING : CONVERSATIONAL INFERENCE AND RATIONAL JUDGMENT , 1995 .

[11]  Leszek Nowak Poznań studies in the philosophy of the sciences and the humanities , 1975 .

[12]  Peter Sedlmeier,et al.  Improving Statistical Reasoning: Theoretical Models and Practical Implications , 1999 .

[13]  Gerd Gigerenzer,et al.  How to Improve Bayesian Reasoning Without Instruction: Frequency Formats , 1995 .

[14]  A. Tversky,et al.  Causal Schemata in Judgments under Uncertainty , 1982 .

[15]  Richard E. Nisbett,et al.  Prediction and the partial understanding of the law of large numbers , 1986 .

[16]  L. Cohen Can human irrationality be experimentally demonstrated? , 1981, Behavioral and Brain Sciences.

[17]  K. Fiedler The dependence of the conjunction fallacy on subtle linguistic factors , 1988 .

[18]  M. Birnbaum Base Rates in Bayesian Inference: Signal Detection Analysis of the Cab Problem , 1983 .