A Dutch Book theorem for partial subjective probability

Abstract

The aim of this paper is to show that partial probability can be justified from the standpoint of subjective probability in much the same way as classical probability does. The seminal works of Ramsey and De Finetti have furnished a method for assessing subjective probabilities: ask about the bets the decision-maker would be willing to place. So we introduce the concept of partial bet and partial Dutch Book and prove for partial probability a result similar to the Ramsey-De Finetti theorem. Finally, we make a comparison between two concepts of bet: we can bet our money on a sentence describing an event, or we can bet our money on the event itself, generally conceived as a set. These two ways of understanding a bet are equivalent in classical probability, but not in partial probability.