Saturday, November 3, 2007

Social Networks

I attended Matthew Jackson's talk today on modeling social networks. Besides the obvious shortcomings of using models to simulate real-world phenomenon, it seems that there are some lessons to be learned after applying certain analysis techniques to real-world networks.

More specifically, the structure of a social network (connections and their weights) determines the speed of convergence for opinions (at least as abstracted by the model). This has some interesting ramifications in the two examples that Matthew provided.

In the first example (managers in a small firm), the influence (characterized by the final convergent opinion if only that individual had that opinion initially) of individuals varied significantly, and actually corresponding quite closely to the actual hierarchy of executives within the company (the CEO and vice-presidents all had high influences).

In the second example (teenagers in a high school), the visual representation clearly showed the a segregation of groups (mostly on the basis of race, at least that's what the coloring of the graph seemed to portray). This segregation seemed to limit the overall convergence, as the analysis indicated that the second-largest eigenvalue was 0.98. (in other words, in each cycle of opinion updating, the error for convergence decreased by 2%)

Matthew also discussed the conditions under which social networks could converge "wisely". Basically, if each individual had some initial state of belief that was randomly distributed but centered around the "truth", under what conditions would the social network converge to an "accurate" value of belief?

Essentially, the answer is: true democracy (surprised?). A key requirement is that no one individual has strong influence (otherwise the error in that individual's belief would propagate), and that large groups of people pay attention to a majority of individuals in the social network.

If we believe that this method of modeling real-life social networks approximates the ways in which actual social networks work, this poses a number of problems for disseminating accurate information. For example, if we take the case of HIV denialism, clearly the group of HIV denialists is not swayed by a majority of the world (who accurately believe it when *ALL* medical doctors agree that HIV causes AIDS). Moreover, this group includes some highly influential people, including some musical artists.

However, there may be some hope yet: given that real-life social networks are "flawed" in this manner, it only makes sense to use the tools we have rather than trying to dramatically alter the way in which society forms opinions. Wikipedia accomplishes this rather well, by establishing itself as a highly influential source of information, that maintains accuracy by receiving input from any and all users, thus allowing it to converge to an "accurate" state. In fact, since Wikipedia requires external sources to verify information, it removes the need for contributers to be randomly distributed with respect to their "accuracy". As individuals, we can seek to benefit society by establishing ourselves with high influence via maintaining popular blogs...

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