An Impossibility Theorem for Group Probability Functions.

by Norman Crolee Dalkey

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Aggregation functions which generate a group estimate based on a set of individual estimates have become of general interest for many decision problems where the best information available is the estimates of a group of experts. The question rather naturally arises whether a function can be defined which is consistent with the postulates of probability theory when the individual estimates are probabilities. The theorem is proved that under several natural assumptions, there is no aggregation function for individual probability estimates which itself is a probability function. 6 pp. Bibliog.

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