We study learning and influence in networks where agents communicate according to an arbitrary social network and naively update their beliefs by repeatedly taking a weighted average of their neighbors’ opinions. A complete characterization is given of the social networks for which there is a convergence of beliefs. Comparative statics are derived to determine how social influence changes when some agents redistribute their weights. We also provide conditions under which beliefs of all agents in large societies converge to the truth, despite their naïve updating. Finally, we survey some recent structural results on the speed of convergence and relate these to issues of polarization and propaganda.
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