All agreed: Aumann meets DeGroot

Abstract

28:192-200, 1982). We thus provide a concrete and plausible Bayesian rationalization of consensus through iterated pooling. The link clarifies the conditions under which iterated pooling can be rationalized from a Bayesian perspective, and offers an understanding of iterated pooling in terms of higher-order beliefs.

An Interpretation of Weights in Linear Opinion Pooling

“…There are other bodies of literature that can fruitfully be related to linear pooling through its Bayesian reconstruction. A good example is provided by Romeijn and Roy (2018), who construct a relation between iterative linear pooling (DeGroot 1974;Lehrer and Wagner 1981) and Aumann's well-known agreement theorem (Aumann 1976;Geanakoplos and Polemarchakis 1982). That result and the current one invite further research into pooling as a particular form of information sharing.…”

Support for Geometric Pooling

“…6 To wit, we will assume that each agent i is equipped with an information partition E i over Ω, that any piece of private information E i (ω) she might receive is taken from that partition E i , and that the information partitions {E i } i∈N are known by all the agents. This allows us to work only with the primitive space of states of nature Ω, instead of having to introduce (like in, e.g., Romeijn and Roy, 2018) an additional space of epistemic states corresponding to the possible probability announcements.…”

“…This implies the following. Assume that (unlike in, e.g.,Romeijn and Roy, 2018) one chooses not to explicitly model an additional algebra B for the probabilistic reports over A. This permits zooming in on the simplest implications of supra-Bayesianism, i.e., those reflected within the basic algebra A.…”