Quantified Beliefs and Believed Quantities

It is shown that probabilistic beliefs and est imation of quanti t ies give rise to the same model, that of a type spacer and can be viewed as the two sides of the same coin. We s tudy the axiom of correct est imation, which s ta tes tha t an agent 's est imation of his own est imation is correct, showing it to be weaker than the introspection axiom, according to which an agent is certain of his own probabilistic beliefs. The correct es t imation axiom implies, however, tha t the agent is certain tha t he is introspective, and it is equivalent to the axioms of averaging and conditioning, which are expressed in te rms of probabilistic beliefs.