Naive Learning in Social Networks: Convergence, Influence and Wisdom of Crowds

46 Pages Posted: 19 Jun 2007

See all articles by Matthew O. Jackson

Matthew O. Jackson

Stanford University - Department of Economics; Santa Fe Institute; Canadian Institute for Advanced Research (CIFAR)

Benjamin Golub

Stanford Graduate School of Business

Date Written: June 1, 2007

Abstract

We study learning and influence in a setting where agents communicate according to an arbitrary social network and naively update their beliefs by repeatedly taking weighted averages of their neighbors' opinions. A focus is on conditions under which beliefs of all agents in large societies converge to the truth, despite their naive updating. We show that this happens if and only if the influence of the most influential agent in the society is vanishing as the society grows. Using simple examples, we identify two main obstructions which can prevent this. By ruling out these obstructions, we provide general structural conditions on the social network that are sufficient for convergence to truth. In addition, we show how social influence changes when some agents redistribute their trust, and we provide a complete characterization of the social networks for which there is a convergence of beliefs. Finally, we survey some recent structural results on the speed of convergence and relate these to issues of segregation, polarization and propaganda.

Keywords: Social Networks, Learning, Diffusion, Bounded Rationality

JEL Classification: D85, D83, A14, L14, Z13

Suggested Citation

Jackson, Matthew O. and Golub, Benjamin, Naive Learning in Social Networks: Convergence, Influence and Wisdom of Crowds (June 1, 2007). FEEM Working Paper No. 64.2007. Available at SSRN: https://ssrn.com/abstract=994312 or http://dx.doi.org/10.2139/ssrn.994312

Matthew O. Jackson (Contact Author)

Stanford University - Department of Economics ( email )

Landau Economics Building
579 Serra Mall
Stanford, CA 94305-6072
United States
1-650-723-3544 (Phone)

HOME PAGE: http://www.stanford.edu/~jacksonm

Santa Fe Institute

1399 Hyde Park Road
Santa Fe, NM 87501
United States

Canadian Institute for Advanced Research (CIFAR) ( email )

180 Dundas Street West, Suite 1400
Toronto, Ontario
Canada

Benjamin Golub

Stanford Graduate School of Business ( email )

655 Knight Way
Stanford, CA 94305-5015
United States

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