The Estimation of Subjective Probabilities via Categorical Judgments of Uncertainty

03/27/2013
by   Alf C. Zimmer, et al.
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Theoretically as well as experimentally it is investigated how people represent their knowledge in order to make decisions or to share their knowledge with others. Experiment 1 probes into the ways how people 6ather information about the frequencies of events and how the requested response mode, that is, numerical vs. verbal estimates interferes with this knowledge. The least interference occurs if the subjects are allowed to give verbal responses. From this it is concluded that processing knowledge about uncertainty categorically, that is, by means of verbal expressions, imposes less mental work load on the decision matter than numerical processing. Possibility theory is used as a framework for modeling the individual usage of verbal categories for grades of uncertainty. The 'elastic' constraints on the verbal expressions for every sing1e subject are determined in Experiment 2 by means of sequential calibration. In further experiments it is shown that the superiority of the verbal processing of knowledge about uncertainty guise generally reduces persistent biases reported in the literature: conservatism (Experiment 3) and neg1igence of regression (Experiment 4). The reanalysis of Hormann's data reveal that in verbal Judgments people exhibit sensitivity for base rates and are not prone to the conjunction fallacy. In a final experiment (5) about predictions in a real-life situation it turns out that in a numerical forecasting task subjects restricted themselves to those parts of their knowledge which are numerical. On the other hand subjects in a verbal forecasting task accessed verbally as well as numerically stated knowledge. Forecasting is structurally related to the estimation of probabilities for rare events insofar as supporting and contradicting arguments have to be evaluated and the choice of the final Judgment has to be Justified according to the evidence brought forward. In order to assist people in such choice situations a formal model for the interactive checking of arguments has been developed. The model transforms the normal-language quantifiers used in the arguments into fuzzy numbers and evaluates the given train of arguments by means of fuzzy numerica1 operations. Ambiguities in the meanings of quantifiers are resolved interactively.

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