When Fair Betting Odds Are Not Degrees of Belief

The "Dutch Book" argument, tracing back to Ramsey and to deFinetti, offers prudential grounds for action in conformity with personal probability. Under several structural assumptions about combinations of stakes (that is, assumptions about the combination of wagers), your betting policy is coherent only if your fair odds are probabilities. The central question posed here is the following one: Besides providing an operational test of coherent betting, does the "Book" argument also provide for adequate measurement (elicitation) of the agents degrees of beliefs? That is, are an agent's fair odds also his/her personal probabilities for those events? We argue the answer is "No!" The problem is caused by the possibility of state dependent utilities.