760

**Measuring Incoherence**

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

### Abstract:

The degree of incoherence, when previsions are not
made in accordance with a probability measure, is measured by the
rate at which an incoherent bookie can be made a sure loser. Each bet
is rescaled by one of several normalizations to account for the
overall sizes of bets. For each normalization, the sure
loss for incoherent previsions is divided by the normalization to determine
the rate of incoherence. We study several properties of normalizations
and degrees of incoherence and present some examples. Potential
applications include the degree of
incoherence of classical statistical procedures.

*Heidi Sestrich*

*12/19/2001*
Here is the .pdf file for this
technical report.