SignificanceSocial media sites are often blamed for exacerbating political polarization by creating “echo chambers” that prevent people from being exposed to information that contradicts their preexisting beliefs. We conducted a field experiment that offered a large group of Democrats and Republicans financial compensation to follow bots that retweeted messages by elected officials and opinion leaders with opposing political views. Republican participants expressed substantially more conservative views after following a liberal Twitter bot, whereas Democrats’ attitudes became slightly more liberal after following a conservative Twitter bot—although this effect was not statistically significant. Despite several limitations, this study has important implications for the emerging field of computational social science and ongoing efforts to reduce political polarization online.

There is widespread concern that Russia and other countries have launched social-media campaigns designed to increase political divisions in the United States. Though a growing number of studies analyze the strategy of such campaigns, it is not yet known how these efforts shaped the political attitudes and behaviors of Americans. We study this question using longitudinal data that describe the attitudes and online behaviors of 1,239 Republican and Democratic Twitter users from late 2017 merged with nonpublic data about the Russian Internet Research Agency (IRA) from Twitter. Using Bayesian regression tree models, we find no evidence that interaction with IRA accounts substantially impacted 6 distinctive measures of political attitudes and behaviors over a 1-mo period. We also find that interaction with IRA accounts were most common among respondents with strong ideological homophily within their Twitter network, high interest in politics, and high frequency of Twitter usage. Together, these findings suggest that Russian trolls might have failed to sow discord because they mostly interacted with those who were already highly polarized. We conclude by discussing several important limitations of our study—especially our inability to determine whether IRA accounts influenced the 2016 presidential election—as well as its implications for future research on social media influence campaigns, political polarization, and computational social science.

Many studies that gather social network data use survey methods that lead to censored, missing, or otherwise incomplete information. For example, the popular fixed rank nomination (FRN) scheme, often used in studies of schools and businesses, asks study participants to nominate and rank at most a small number of contacts or friends, leaving the existence of other relations uncertain. However, most statistical models are formulated in terms of completely observed binary networks. Statistical analyses of FRN data with such models ignore the censored and ranked nature of the data and could potentially result in misleading statistical inference. To investigate this possibility, we compare Bayesian parameter estimates obtained from a likelihood for complete binary networks with those obtained from likelihoods that are derived from the FRN scheme, and therefore accommodate the ranked and censored nature of the data. We show analytically and via simulation that the binary likelihood can provide misleading inference, particularly for certain model parameters that relate network ties to characteristics of individuals and pairs of individuals. We also compare these different likelihoods in a data analysis of several adolescent social networks. For some of these networks, the parameter estimates from the binary and FRN likelihoods lead to different conclusions, indicating the importance of analyzing FRN data with a method that accounts for the FRN survey design.

The information-theoretic limits of community detection have been studied extensively for network models with high levels of symmetry or homogeneity. The contribution of this paper is to study a broader class of network models that allow for variability in the sizes and behaviors of the different communities, and thus better reflect the behaviors observed in real-world networks. Our results show that the ability to detect communities can be described succinctly in terms of a matrix of effective signal-to-noise ratios that provides a geometrical representation of the relationships between the different communities. This characterization follows from a matrix version of the I-MMSE relationship and generalizes the concept of an effective scalar signal-to-noise ratio introduced in previous work. We provide explicit formulas for the asymptotic per-node mutual information and upper bounds on the minimum mean-squared error. The theoretical results are supported by numerical simulations. * G. Reeves is with the

There is mounting concern that social media sites contribute to political polarization by creating "echo chambers" that insulate people from opposing views about current events. We surveyed a large sample of Democrats and Republicans who visit Twitter at least three times each week about a range of social policy issues. One week later, we randomly assigned respondents to a treatment condition in which they were offered financial incentives to follow a 1 Twitter bot for one month that exposed them to messages produced by elected officials, organizations, and other opinion leaders with opposing political ideologies. Respondents were re-surveyed at the end of the month to measure the effect of this treatment, and at regular intervals throughout the study period to monitor treatment compliance. We find that Republicans who followed a liberal Twitter bot became substantially more conservative post-treatment, and Democrats who followed a conservative Twitter bot became slightly more liberal post-treatment. These findings have important implications for the interdisciplinary literature on political polarization as well as the emerging field of computational social science.Political polarization in the United States has become a central focus of social scientists in recent decades (1-7). Americans remain deeply divided on controversial issues such as inequality, race, and immigration. According to the 2016 National Election Study, 59.3% of Clinton voters believe federal aid to the poor should be increased compared to only 20.2% of Trump voters. 77.7% of Clinton voters express favorable attitudes towards the Black Lives Matter movement, whereas 31.2% of Trump voters do the same. 68.9% of Trump voters believe immigration to the United States should be decreased, compared to 21.9% of Clinton voters.Longstanding divides about these and many other issues have far-reaching consequences for the design and implementation of social policies as well as the effective function of democracy more broadly (8-12).America's deep partisan divides are often attributed to "echo chambers," or patterns of information sharing that reinforce pre-existing political beliefs by limiting exposure to heterogeneous ideas and perspectives (13)(14)(15)(16)(17). Concern about selective exposure to information and political polarization has increased in the age of social media (13,(18)(19)(20). The vast majority of Americans now visit a social media site at least once each day, and a rapidly growing number 2 of them list social media as their primary source of news (21). Despite initial optimism that social media might enable people to consume more heterogeneous sources of information about current events, there is growing concern that such forums exacerbate political polarization because of social network homophily, or the well-documented tendency of people to form social network ties to those who are similar to themselves (22, 23). The endogenous relationship between social network formation and political attitudes also creates formidable challenges f...

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Missing observations are pervasive throughout empirical research, especially in the social sciences. Despite multiple approaches to dealing adequately with missing data, many scholars still fail to address this vital issue. In this paper, we present a simple-to-use method for generating multiple imputations using a Gaussian copula. The Gaussian copula for multiple imputation (Hoff, 2007) allows scholars to attain estimation results that have good coverage and small bias. The use of copulas to model the dependence among variables will enable researchers to construct valid joint distributions of the data, even without knowledge of the actual underlying marginal distributions. Multiple imputations are then generated by drawing observations from the resulting posterior joint distribution and replacing the missing values. Using simulated and observational data from published social science research, we compare imputation via Gaussian copulas with two other widely used imputation methods: MICE and Amelia II. Our results suggest that the Gaussian copula approach has a slightly smaller bias, higher coverage rates, and narrower confidence intervals compared to the other methods. This is especially true when the variables with missing data are not normally distributed. These results, combined with theoretical guarantees and ease-of-use suggest that the approach examined provides an attractive alternative for applied researchers undertaking multiple imputations.

In the learning-to-match framework for causal inference, a parameterized distance metric is trained on a holdout train set so that the matching yields accurate estimated conditional average treatment effects. This way, the matching can be as accurate as other black box machine learning techniques for causal inference. We use a new learning-to-match algorithm called Matching-After-Learning-To-Stretch (MALTS) (Parikh et al., 2018) to study an observational dataset from the Atlantic Causal Inference Challenge. Other than providing estimates for (conditional) average treatment effects, the MALTS procedure allows practitioners to evaluate matched groups directly, understand where more data might need to be collected and gain an understanding of when estimates can be trusted.