703

**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

### Abstract:

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*

*10/20/1999*