This paper shows that an opinion pooling process following the rules laid down by Morris DeGroot, and later developed by Lehrer and Wagner, can be represented in the context of Aumann’s famous agreement theorem. For any opinion pooling process there is a common prior such that the approach to agreement, as described by Genneakoplos and Polymarchakis, coincides with the opinion pooling process. This equivalence can then be employed to analyse the notion of trust from DeGroot opinion pooling. It turns out that this notion comes down to a natural constraint on the likelihoods that appear in Genneakoplos and Polymarchakis’s dynamic approach to agreement. The paper thereby makes precise Aumann’s hunch, expressed in his seminal paper, that “the Harsanyi doctrine is implicit in much of this [DeGroot-based] literature”.
This paper is joint work with Olivier Roy (Bayreuth).