P. Ghirardato et M. Marinacci, The impossibility of compromise: some uniqueness properties of expected utility preferences, ECON THEORY, 16(2), 2000, pp. 245-258
We focus on the following uniqueness property of expected utility preferenc
es: Agreement of two preferences on one interior indifference class implies
their equality. We show that, besides expected utility preferences under (
objective) risk, this uniqueness property holds for subjective expected uti
lity preferences in Anscombe-Aumann's (partially subjective) and Savage's (
fully subjective) settings, while it does not hold for subjective expected
utility preferences in settings without rich state spaces. Indeed, when it
holds the uniqueness property is even stronger than described above, as it
needs only agreement on binary acts. The extension of the uniqueness proper
ty to the subjective case is possible because beliefs in the mentioned sett
ings are shown to satisfy an analogous property: If two decision makers agr
ee on a likelihood indifference class, they must have identical beliefs.