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LIT-999: Naïve Learning in Social Networks and the Wisdom of Crowds

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Properties5
StatusActive — read 2026-10-14 (NOTE-840) in full; worth reading for QUESTION-047 as a proved case in which members share one updating rule and the network alone decides whether the group belief is right: a growing society of DeGroot averagers converges to the truth if and only if the largest influence weight vanishes. Read it knowing that its agents are naïve, not sound (they ignore repeated information), that weights are fixed and signals independent, and that the result is asymptotic and about a model, not data.
Version2
Tagsnetwork-science, social-science, epistemology
Cited as “paper” byNOTE-840 — Golub & Jackson — Naïve Learning in Social Networks and the Wisdom of Crowds
Cited as “source” byTHEORY-321 — Under repeated DeGroot averaging in a strongly connected society, the consensus converges to the truth as the society grows if and only if the largest influence weight vanishes, so network structure alone, not the members' common updating rule, decides whether the group belief is right

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Benjamin Golub, Matthew O. Jackson (2010), American Economic Journal: Microeconomics 2(1), 112–149.

Key takeaways

From the reading, NOTE-840.

  • Consensus as an eigenvector average. For a convergent interaction matrix T, every agent in a closed group ends at s·p(0), s the unit left eigenvector of T; an agent’s influence is the trust-weighted influence of those who listen to it.
  • Wisdom ⇔ no dominant influence (Proposition 2). A growing society’s limit beliefs converge in probability to the truth iff the largest influence weight → 0, for all independent signal distributions with mean μ and variance bounded below, or for none.
  • Equal reciprocal weights (Corollary 1). Wisdom ⇔ max degree / total degree → 0.
  • Obstruction (Proposition 3). A finite group that everyone attends to, directly or within t steps, with weight bounded below, prevents wisdom. Indirect position can give an agent near-total influence (Example 4).
  • Sufficient conditions (Theorems 1, 4). Balance plus minimal out- or in-dispersion.
  • Speed is separate (§V). Fast or slow consensus can be right or wrong.
  • The agents are naïve. They ignore repetition and correlation of what they hear; only the first round is Bayesian.

Standing in the record

Filed 2026-10-12 for QUESTION-047 and read in full on 2026-10-14 (NOTE-840). It is a proved case of the question’s form: members share one updating rule, and whether the community settles on the truth is fixed by the influence structure. The filing called the members sound; they are naïve, which narrows what the case shows to uniform members, not sound ones. THEORY-321, filed from it, answers QUESTION-047 in part, in a model. It sits beside THEORY-143 and THEORY-148, adding concentration of influence as a structural variable.

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