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« Commercial friends | Main | Cost Per Influence »

July 11, 2004

Network Influence Matters

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Posted by Ross Mayfield

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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1. Lawrence Krubner on July 12, 2004 12:36 PM writes...

This theory is still a little flat and static. It would be more interesting if it included a prediction about why some people are more socially networked that others. When I think of social network interaction I think of multiple feedback loops - for instance, perhaps people with status help determine what the markers of status will be in the near future. People with aspirations and talent but no status pick up those markers like a sponge and adapt themselves to the landscape they find themselves in. Those with status are forced by the logic of their own status to grant status to the best adapters. Some young people (or people, not necessarily young, new to a field, or a group, or a niche) shine like stars because they pick up the local markers of status so well. Granted status they start to define status.

That's just one of the possible ways of explaining the dynamic nature that I'm sure we all see when we look at social networks. Another, opposite theory might argue that those without status sometimes gain influence by condensing in a shouting mob, an audience, which doles out status with its applause. The stars are only as big as the last wave of applause they managed to win.

I imagine there are many differnent environments in which people compete for status. I should think that in some status is easy to defend and hard to lose, but in others things change fast.

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