  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.
