Degree-Weighted Social Learning

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 high- and low-degree groups, highlighting a potential trade-off between convergence speed and wisdom.