Measuring Incoherence

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.