Consensus Expectations and Conventions
summary
Shows that iterated expectations x_i^n (taken as Cesàro averages) converge to a nonrandom consensus under a joint connectedness condition and that consensus equals the stationary distribution of an explicit Markov matrix B built from the interaction matrix Γ and conditional type beliefs. Decomposes each type weight into an agent eigenvector centrality times a type share r_ik, recovers complete‑information and common‑prior cases, and proves that a relatively less informed agent can determine outcomes. Tools: finite‑type linear algebra, Markov chains and the tree lemma.
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