Three degrees of influence

Three Degrees of Influence is a theory in the realm of social networks, proposed by Nicholas A. Christakis and James H. Fowler in 2007. Christakis and Fowler found that social networks have great influence on individuals' behavior. But social influence does not end with the people to whom a person is directly tied. We influence our friends, who in their turn influence their friends, and so our actions can influence people we have never met, to whom we are only indirectly tied. They posit that diverse phenomena "ripple through our network, having an impact on our friends (one degree), our friends’ friends (two degrees), and even our friends’ friends’ friends (three degrees). Our influence gradually dissipates and ceases to have a noticeable effect on people beyond the social frontier that lies at three degrees of separation".

This argument is basically that peer effects need not stop at one degree, and that, if we can affect our friends, then we can (in many cases) affect our friends' friends, and so on. However, across a broad set of empirical settings, using both observational and experimental methods, they observed that the effect seems, in many cases, to no longer be meaningful at a social horizon of three degrees.

Christakis and Fowler examined phenomena from various domains, such as obesity, happiness, cooperation, and voting. Investigations by other groups have subsequently explored many other phenomena in this way (including crime, social learning, etc.).

Influence dissipates after three degrees (to and from friends’ friends’ friends) for three reasons, Christakis and Fowler propose:

Initial studies using observational data by Christakis and Fowler suggested that a variety of attributes (like obesity, smoking, and happiness), rather than being individualistic, are casually correlated by contagion mechanisms that transmit such phenomena over long distances within social networks. Certain subsequent analyses explored limitations to these analyses (subject to different statistical assumptions); or expressed concern that the statistical methods employed in these analyses could not fully control for other environmental factors; or resulted in statistical estimates without straightforward interpretations; or did not fully account for homophily processes in the creation and retention of relationships over time.

But other scholarship using sensitivity analysis has found that the basic estimates regarding the transmissibility of obesity and smoking cessation, for example, are robust, or has otherwise replicated or supported the findings. Additional, detailed modeling work published in 2016 showed that the GEE modeling approach used by Christakis and Fowler (and others) was quite effective at estimating social contagion effects and in distinguishing them from homophily. This paper concluded, "For network influence, we find that the approach appears to have excellent sensitivity, and quite good specificity with regard to distinguishing the presence or absence of such a 'network effect,' regardless of whether or not homophily is present in network formation. This was true for small cohorts (n = 30) and larger cohorts (n = 1000), and for cohorts that displayed lesser and greater realism in their distribution of friendships." Another methodological paper, by physicists ver Steeg and Galstyan, suggests it is indeed possible to bound estimates of peer effects even given the modeling constraints faced by Christakis and Fowler and even if parametric assumptions are otherwise required to identify such effects using observational data (if substantial unobserved homophily is thought to be present).

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