The exposure response function, while aggregated over all users, does not describe the behavior of any individual Digg or Twitter user – even the hypothetical “typical” user. In fact, there is no “typical” Twitter (or Digg) user. Twitter users are extremely heterogeneous. Separating them into more homogeneous sub-populations reveals a more regular pattern. Figure 2 shows the exposure response function for different populations of Twitter users, separated according to the number of friends they follow (large fluctuations are the result of small sample size). Why number of friends? This is explained in more detail in our papers [Hodas & Lerman 2012, 2013], but in short, we found it useful to separate users according to their cognitive load, i.e., the volume of information they receive, which is (on average) proportional to the number of friends they follow [Hodas et al, 2013]. Now, the probability that a user within each population will become infected increases monotonically with the number of infected, very similar to the predictions of the independent cascade model.
Figure 2 has a different, more significant interpretation, with consequences for information diffusion. It suggests that highly connected users, i.e., those who follow many others, are less susceptible to becoming infected. Their decreased susceptibility in fact explains Figure 1: as one moves to the right of the exposure response curve, only the better connected, and less sensitive, users contribute to that portion of the response. However, despite their reduced susceptibility, highly connected users respond positively to repeated exposures, like all other users. You do not inhibit response by repeatedly exposing people to information. Instead, the reason that these users are less susceptible hinges on the human brain’s limited bandwidth. There are only so many tweets any one can read, the more tweets you receive (on average proportional to the number of friends you follow), the less likely you are to see – and retweet – any specific tweet. If it was not for recognizing heterogeneity, we would not have found this far more interesting explanation.
 Vaupel, J. W. and Yashin, A. I. (1985). Heterogeneity’s ruses: some surprising effects of selection on population dynamics. The American Statistician, 39(3):176-185.
 Hodas, N. O. and Lerman, K. (2013). The simple rules of social contagion.
 Hodas, N. O., Kooti, F., and Lerman, K. (2013). Friendship paradox redux: Your friends are more interesting than you. In Proceedings of 7th International Conference on Weblogs and Social Media.
 Steeg, G. V., Ghosh, R., and Lerman, K. (2011). What stops social epidemics? In Proceedings of the 5th International AAAI Conference on Weblogs and Social Media.
 Romero, D. M., Meeder, B., and Kleinberg, J. (2011). Differences in the mechanics of information Diffusion Across topics: Idioms, political hashtags, and Complex Contagion on twitter. In Proceedings of World Wide Web Conference.
Kristina Lerman is a Project Leader at the University of Southern California Information Sciences Institute and holds a joint appointment as a Research Associate Professor in the USC Computer Science Department. After a brief stint as a theoretical roboticist, she found her calling in blending together methods from physics, computer science and social science to address problems in social computing and social media analysis. She writes many papers that are greatly enjoyed by all of their twenty readers.
Copyright @ 2013, Kristina Lerman, All rights reserved.