How Sets of Coherent Probabilities May Serve as Models for Degrees of Incoherence

Mark J. Schervish, Teddy Seidenfeld and Joseph B. Kadane

Revised 03/00


We introduce two indices for the degree of incoherence in a set of lower and upper previsions: maximizing the rate of loss the incoherent bookmaker experiences in a Dutch Book, or maximizing the rate of profit the gambler achieves who makes Dutch Book against the incoherent bookmaker. We report how efficient bookmaking is achieved against these two indices in the case of incoherent previsions for events on a finite partition, and for incoherent previsions that include also a simple random variable. We relate the epsilon-contamination model to efficient bookmaking in the case of the rate of profit.

Keywords: Dutch Book, coherence, epsilon-contamination model

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Heidi Sestrich