People don't coincide in their priors, don't have access to the same evidence and aren't running off the same epistemology, and can't settle epistemologiical debates non-circularly......

Threr's a lot wrong with Aumannn, or at least the way some people use it.

What actually happens is that the reasons for the summary judgements are examined.

Really? My understanding was that

Between each iteration of the questionnaire, the facilitator or monitor team (i.e., the person or persons administering the procedure) informs group members of the opinions of their anonymous colleagues. Often this “feedback” is presented as a simple statistical summary of the group response, usually a mean or median value, such as the average group estimate of the date before which an event will occur. As such, the feedback comprises the opinions and judgments of all group members and not just the most vocal. At the end of the polling of participants (after several rounds of questionnaire iteration), the facilitator takes the group judgment as the statistical average (mean or median) of the panelists’ estimates on the final round.

(From Rowe & Wright's "Expert opinions in forecasting: the role of the Delphi technique", in the usual Armstrong anthology.) From the sound of it, the feedback is often purely statistical in nature, and if it wasn't commonly such restricted feedback, it's hard to see why Rowe & Wright would criticize Delphi studies for this:

The use of feedback in the Delphi procedure is an important feature of the technique. However, research that has compared Delphi groups to control groups in which no feedback is given to panelists (i.e., non-interacting individuals are simply asked to re-estimate their judgments or forecasts on successive rounds prior to the aggregation of their estimates) suggests that feedback is either superfluous or, worse, that it may harm judgmental performance relative to the control groups (Boje and Murnighan 1982; Parenté, et al. 1984). The feedback used in empirical studies, however, has tended to be simplistic, generally comprising means or medians alone with no arguments from panelists whose estimates fall outside the quartile ranges (the latter being recommended by the classical definition of Delphi, e.g., Rowe et al. 1991). Although Boje and Murnighan (1982) supplied some written arguments as feedback, the nature of the panelists and the experimental task probably interacted to create a difficult experimental situation in which no feedback format would have been effective.