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Social media are decentralized, interactive, and transformative, empowering users to produce and spread information to influence others. This has changed the dynamics of political communication that were previously dominated by traditional corporate news media. Having hundreds of millions of tweets collected over the 2016 and 2020 U.S. presidential elections gave us a unique opportunity to measure the change in polarization and the diffusion of political information. We analyze the diffusion of political information among Twitter users and investigate the change of polarization between these elections and how this change affected the composition and polarization of influencers and their retweeters. We identify "influencers" by their ability to spread information and classify them into those affiliated with a media organization, a political organization, or unaffiliated. Most of the top influencers were affiliated with media organizations during both elections. We found a clear increase from 2016 to 2020 in polarization among influencers and among those whom they influence. Moreover, 75% of the top influencers in 2020 were not present in 2016, demonstrating that such status is difficult to retain. Between 2016 and 2020, 10% of influencers affiliated with media were replaced by center- or right-orientated influencers affiliated with political organizations and unaffiliated influencers., Comment: 41 pages, 13 figures, 9 tables

Fads, product adoption, mobs, rumors, memes, and emergent norms are diverse social contagions that have been modeled as network cascades. Empirical study of these cascades is vulnerable to what we describe as the "opacity problem": the inability to observe the critical level of peer influence required to trigger an individual's behavioral change. Even with maximal information, network cascades reveal intervals that bound critical levels of peer exposure, rather than critical values themselves. Existing practice uses interval maxima, which systematically over-estimates the social influence required for behavioral change. Simulations reveal that the over-estimation is likely common and large in magnitude. This is confirmed by an empirical study of hashtag cascades among 3.2 million Twitter users: one in five hashtag adoptions suffers critical value uncertainty due to the opacity problem. Different assumptions about these intervals lead to qualitatively different conclusions about the role of peer reinforcement in diffusion. We introduce a solution that combines identifying tightly bounded intervals with predicting uncertain critical values using node-level information., Comment: 31 pages, 7 figures, 2 tables

Axelrod (1997) showed how local convergence in cultural influence can preserve cultural diversity. We argue that central implications of Axelrod's model may change profoundly, if his model is integrated with the assumption of social influence as assumed by an earlier generation of modelers. Axelrod and all follow up studies employed instead the assumption that influence is interpersonal (dyadic). We show how the combination of social influence with homophily allows solving two important problems. Our integration of social influence yields monoculture in small societies and diversity increasing in population size, consistently with empirical evidence but contrary to earlier models. The second problem was identified by Klemm et al.(2003a,b), an extremely narrow window of noise levels in which diversity with local convergence can be obtained at all. Our model with social influence generates stable diversity with local convergence across a much broader interval of noise levels than models based on interpersonal influence., Comment: 20 pages, 3 figures, Paper presented at American Sociological Association 103rd Annual Meeting, August 1-4, 2008, Boston, MA. Session on Mathematical Sociology

Recent extensions of the Axelrod model of cultural dissemination (Klemm et al 2003) showed that global diversity is extremely fragile with small amounts of cultural mutation. This seemed to undermine the original Axelrod theory that homophily preserves diversity. We show that cultural diversity is surprisingly robust if we increase the tendency towards homophily as follows. First, we raised the threshold of similarity below which influence is precluded. Second, we allowed agents to be influenced by all neighbors simultaneously, instead of only one neighbor as assumed in the orginal model. Computational experiments show how both modifications strongly increase the robustness of diversity against mutation. We also find that our extensions may reverse at least one of the main results of Axelrod. While Axelrod predicted that a larger number of cultural dimensions (features) reduces diversity, we find that more features may entail higher levels of diversity., Comment: 21 pages, 8 figures, Submitted for presentation in Mathematical Sociology Session, Annual Meeting of the American Sociological Association (ASA), 2007

We relax a simplification of Axelrod's (1997) model of cultural dissemination that has not yet been studied, the assumption that all cultural states are nominal. We integrate metric states into the original model. Computational experiments demonstrate that metric states undermine cultural diversity, even without noise, by creating sufficient overlap between agents for mutual influence. We then show how adding "bounded confidence" - a recent innovation in models of social influence - allows cultural diversity to persist. However, further experiments reveal that the solution is fragile. Diversity can be sustained only with a relatively small number of metric states, low levels of noise or narrow confidence intervals., Comment: 8 pages, 4 figures

Following Axelrod's model of cultural dissemination, formal computational studies of cultural influence have suggested that more contact between geographically distant regions may increase overall cultural homogeneity and reduce societal polarization. In the present paper, we show that two plausible modifications of Axelrod's original mechanism turn the effect of range of communication upside-down. We assume a continuous rather than a nominal state space and we add the negative side of social influence, heterophobia and rejection. Computational analyses of the resulting model demonstrate that now a larger range of contact can increase rather than decrease the extent of polarization in the population. Further experiments identify the window of conditions under which the effect obtains., Comment: 20 pages, 6 figures, Paper to be presented in the Mathematical Sociology Session of the 101st Annual Meeting of the American Sociological Association, Montreal August 11-14, 2006

Random links between otherwise distant nodes can greatly facilitate the propagation of disease or information, provided contagion can be transmitted by a single active node. However we show that when the propagation requires simultaneous exposure to multiple sources of activation, called multiplex propagation, the effect of random links is just the opposite: it makes the propagation more difficult to achieve. We calculate analytical and numerically critical points for a threshold model in several classes of complex networks, including an empirical social network., Comment: 4 pages, 5 figures, for similar work visit http://hsd.soc.cornell.edu and http://www.imedea.uib.es/physdept