An Axiomatic Theory of Non Bayesian Social Learning
summary
Proves one-step Bayesian updating on a network is NP-hard via reductions from subset-sum and exact-cover, then axiomatizes non‑Bayesian rules with four properties (including label neutrality and conditioning consistency) and shows the only memory‑one rule satisfying them is a log-linear update. Characterizes when learning occurs: spectral radius >1 polarizes, <1 depolarizes, =1 is required for consistent learning; positive homogeneous rules must have degree one and bounded curvature (normalized second derivative between −1 and 1) or learning fails.
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