On the determination of subjective probability by choices

The paper explores the uniqueness properties of the subjective probabilities in two axiomatizations of state-dependent preferences. Karni, Schmeidler, and Vind's system depends on selecting an arbitrary auxiliary probability, and as such, does not guarantee the uniqueness of the derived subjective probability. However, an axiom system initially designed by Karni and Schmeidler (KS) and further elaborated upon here does guarantee the desired uniqueness as well as a useful property of ‘stability’ of the derived solution. When the preference relation displays state-independence, even the KS probabilities may not agree with those derived from the classic Anscombe–Aumann (AA) theorem. However, we claim that, in this case, the KS rather than the AA probabilities are the appropriate representation of the agent's beliefs.