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July 11, 2004
Network Influence Matters
Bernardo Huberman of HP Labs who developed their decision markets and Fang Wu of Stanford, published a study on Social Structure and Opinion Formation. Bernardo noted in an email to Howard Rheingold that: “the notion of a tipping point in opinion formation does not seem very sound,” although the results do support the notion that highly-connected individuals can speed the spread of opinions through social networks.
…These opinions can be either the result of serious reflection or, as is often the case when information is hard to process or obtain, formed through interactions with others that hold views on given issues. This reliance on others to form opinions lies at the heart of advertising through social cues, efforts to make people aware of societal and health related issues, fads that sweep social groups and organizations, and attempts at capturing the votes and minds of people in election years…
In this paper we propose a theory of opinion formation that explicitly takes into account the structure of the social network in which individuals are embedded. The theory assumes asynchronous choices by individuals among two or three opinions and it predicts the time evolution of the set of opinions from any arbitrary initial condition. We show that under very general conditions a martingale property ensues, i.e. that the expected weighted fraction of the population that holds a given opinion is constant in time. By weighted fraction we mean the fraction of individuals holding a given opinion, averaged over their social connectivity. Most importantly, this weighted fraction of opinions is not either zero or one, but corresponds to a non-trivial distribution of opinions in the long time limit. This coexistence of opinions within a social network is in agreement with the often observed locality effect, in which an opinion or a fad is localized to given groups without infecting the whole society.
Our theory further predicts that a relatively small number of individuals with high social rank can have a larger effect on opinion formation than individuals with low rank. By high rank we mean people with a large number of social connections. This also explains the fragility phenomenon, whereby an opinion that seems to be held by a rather large group of people can become nearly extinct in a very short time, a mechanism that is at the heart of fads.
Opinions don’t just tip when they cross a threshold, they are influenced, connection by connection.
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