Eliciting Subjective Probabilities in Anscombe and Aumann's Model

In this note, we propose an alternative version of Anscombe and Aumann's Subjective Expected Utilities (SEU) representation theorem. In Anscombe and Aumann's model, a randomizing device with objective probabilities is available. As pointed out by Sarin and Wakker, when such a randomizing device is available, there is a natural and direct method to elicit subjective probabilities. Anscombe and Aumann did not use this method, but employed an indirect way to derive subjective probabilities. We investigate what happens if we use this direct method to elicit subjective probabilities in Anscombe and Aumann's model.