Quantified Beliefs and Believed Quantities

Dov Samet

Faculty of Management, Tel Aviv University, Tel Aviv, Israel

Received August 11, 1999; final version received February 24, 2000 Journal of
Economic Literature

Beliefs about quantities are expressed by estimations. Beliefs are quantified by
ascribing to them probability numbers. It is, shown that beliefs about quantities
and quantified beliefs give rise to the same model, that of a type space. We study
the axiom that an agent's estimation coincides with the estimation of that estima-
tion, showing it to be weaker than the introspection axiom, according to which an
agent is certain of his own probabilistic beliefs. It implies, however, that the agent
is certain that he is introspective, and it is equivalent to the axioms of averaging
and conditioning, which are expressed in terms of probabilistic beliefs.