Subjective Probability of Disjunctive Hypotheses: Local-Weight Models for Decomposition of Evidential Support

When the probability of a single member of a set of mutually exclusive and exhaustive possibilities is judged, its alternatives are evaluated as a composite "residual" hypothesis. Support theory (Rottenstreich & Tversky, 1997; Tversky & Koehler, 1994) implies that the process of packing alternatives together in the residual reduces the perceived evidential support for the set of alternatives and consequently inflates the judged probability of the focal hypothesis. Previous work has investigated the global weights that determine the extent to which the overall evidential support for the alternatives is discounted by this packing operation (Koehler, Brenner, & Tversky, 1997). In the present investigation, we analyze this issue in greater detail, examining the local weights that measure the specific contribution of each component hypothesis included implicitly in the residual. We describe a procedure for estimating local weights and introduce a set of plausible properties that impose systematic ordinal relationships among local weights. Results from four experiments testing these properties are reported, and a local-weight model is developed that accounts for nearly all of the variance in the probability judgments in these empirical tests. Local weights appear to be sensitive both to the individual component with which they are associated and to the residual hypothesis in which the component resides.

[1]  L. Cosmides,et al.  Are humans good intuitive statisticians after all? Rethinking some conclusions from the literature on judgment under uncertainty , 1996, Cognition.

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

[3]  D. Krantz,et al.  A Note on Superadditive Probability Judgment , 1999 .

[4]  Derek J. Koehler,et al.  A Strength Model of Probability Judgments for Tournaments , 1996 .

[5]  Rami Zwick,et al.  Comparing the calibration and coherence of numerical and verbal probability judgments , 1993 .

[6]  A. Tversky,et al.  Support theory: A nonextensional representation of subjective probability. , 1994 .

[7]  John Tooby,et al.  Are humans good intuitive statisticians after all , 1996 .

[8]  A. Tversky,et al.  A Belief-Based Account of Decision Under Uncertainty , 1998 .

[9]  Richard Gonzalez,et al.  On the Shape of the Probability Weighting Function , 1999, Cognitive Psychology.

[10]  A. Tversky,et al.  Unpacking, repacking, and anchoring: advances in support theory. , 1997 .

[11]  D A Redelmeier,et al.  Probability judgement in medicine: discounting unspecified possibilities. , 1995, Medical decision making : an international journal of the Society for Medical Decision Making.

[12]  Derek J. Koehler,et al.  The enhancement effect in probability judgment , 1997 .

[13]  C. Fox.  Strength of Evidence, Judged Probability, and Choice Under Uncertainty , 1999, Cognitive Psychology.

[14]  A Note on Superadditive Probability Judgment , 1999 .

[15]  Dane K. Peterson,et al.  Confidence, uncertainty, and the use of information , 1988 .

[16]  G. Gigerenzer,et al.  Probabilistic mental models: a Brunswikian theory of confidence. , 1991, Psychological review.

[17]  K. Teigen.  Subjective sampling distributions and the additivity of estimates , 1974 .

[18]  A. Tversky,et al.  Options traders exhibit subadditive decision weights , 1996 .

[19]  D Kahneman,et al.  On the reality of cognitive illusions. , 1996, Psychological review.

[20]  Karl Halvor Teigen,et al.  Overestimation of subjective probabilities , 1974 .

[21]  Lyle Brenner,et al.  Focus, repacking, and the judgment of grouped hypotheses , 1999 .