| Popis: |
Prelec, Seung and McCoy (2017) proposed a crowd wisdom model where ideal Bayesian observers receive discrete i.i.d. signals si ∈ {s1,...,sn} conditional on an unknown ‘state,’ i.e., a possible world aj ∈ {a1,...,am}. Signals and worlds are presumed drawn from a distribution p(si,aj) known to observers, but unknown to the analyst. The paper asserted via an example but without formal proof that if ideal observers specify a belief matrix as conditional distributions p(aj|si), and a meta-knowledge matrix (beliefs about other observers’ signals) as p(si|sk) = ∑j p(si|aj)p(aj|sk), then the analyst can, in the large sample limit, derive p(si,aj) and identify the actual signal-generating world. Here we provide a proof based on computing the signal prior as the stationary distribution of the meta-knowledge matrix. |
