FIRST INTERNATIONAL SYMPOSIUM ON
IMPRECISE PROBABILITIES AND THEIR APPLICATIONS

Ghent, Belgium
30 June - 2 July 1999

ELECTRONIC PROCEEDINGS

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

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

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 Bookie experiences in a Dutch Book, or maximizing the rate of profit the Gambler achieves who makes Dutch Book against the incoherent Bookie. 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

The paper is available in the following formats and sites:

Authors addresses:

Dept. of Statistics
Carnegie Mellon University
Pgh PA 15213
USA

E-mail addresses:

Mark J. Schervish mark@stat.cmu.edu
Teddy Seidenfeld teddy@stat.cmu.edu
Joseph B. Kadane kadane@stat.cmu.edu

Related Web Sites

CMU Stats. Tech Report 660 "Two Measures of Incoherence: How not to Gamble if you must."


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