COMPARATIVE PROBABILITY FOR CONDITIONAL EVENTS - A NEW LOOK THROUGH COHERENCE

We study, from the standpoint of coherence, comparative probabilities on an arbitrary family E of conditional events. Given a binary relatio n less than or equal to, coherence conditions on less than or equal to are related to de Finetti's coherent betting system: we consider thei r connections to the usual properties of comparative probability and t o the possibility of numerical representations of less than or equal t o. In this context, the numerical reference frame is that of de Finett i's coherent subjective conditional probability, which is not introduc ed (as in Kolmogoroffs approach) through a ratio between probability m easures. Another relevant feature of our approach is that the family E need not have any particular algebraic structure, so that the orderin g can be initially given for a few conditional events of interest and then possibly extended by a step-by-step procedure, preserving coheren ce.