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We study social learning in which agents weight neighbors’ opinions
differently based on their degrees, capturing situations in
which agents place more trust in well-connected individuals or,
conversely, discount their influence. We derive asymptotic properties
of learning outcomes in large stochastic networks and analyze
how the weighting rule affects societal wisdom and convergence
speed. We find that assigning greater weight to higher-degree
neighbors harms wisdom but has a non-monotonic effect on convergence
speed, depending on the diversity of views within highand
low-degree groups, highlighting a potential trade-off between
convergence speed and wisdom.
