Minimizing Polarization and Disagreement in Social Networks

The rise of social media and online social networks has been a disruptive force in society. Opinions are increasingly shaped by interactions on online social media, and social phenomena including disagreement and polarization are now tightly woven into everyday life. In this work we initiate the study of the following question: given $n$ agents, each with its own initial opinion that reflects its core value on a topic, and an opinion dynamics model, what is the structure of a social network that minimizes {\em polarization} and {\em disagreement} simultaneously? This question is central to recommender systems: should a recommender system prefer a link suggestion between two online users with similar mindsets in order to keep disagreement low, or between two users with different opinions in order to expose each to the other's viewpoint of the world, and decrease overall levels of polarization? Our contributions include a mathematical formalization of this question as an optimization problem and an exact, time-efficient algorithm. We also prove that there always exists a network with $O(n/\epsilon^2)$ edges that is a $(1+\epsilon)$ approximation to the optimum. For a fixed graph, we additionally show how to optimize our objective function over the agents' innate opinions in polynomial time. We perform an empirical study of our proposed methods on synthetic and real-world data that verify their value as mining tools to better understand the trade-off between of disagreement and polarization. We find that there is a lot of space to reduce both polarization and disagreement in real-world networks; for instance, on a Reddit network where users exchange comments on politics, our methods achieve a $\sim 60\,000$-fold reduction in polarization and disagreement.Comment: 19 pages (accepted, WWW 2018

The role of bot squads in the political propaganda on Twitter

Social Media are nowadays the privileged channel for information spreading and news checking. Unexpectedly for most of the users, automated accounts, also known as social bots, contribute more and more to this process of news spreading. Using Twitter as a benchmark, we consider the traffic exchanged, over one month of observation, on a specific topic, namely the migration flux from Northern Africa to Italy. We measure the significant traffic of tweets only, by implementing an entropy-based null model that discounts the activity of users and the virality of tweets. Results show that social bots play a central role in the exchange of significant content. Indeed, not only the strongest hubs have a number of bots among their followers higher than expected, but furthermore a group of them, that can be assigned to the same political tendency, share a common set of bots as followers. The retwitting activity of such automated accounts amplifies the presence on the platform of the hubs' messages.Comment: Under Submissio

Time evolution of the behaviour of Brazilian legislative Representatives using a complex network approach

The follow up of Representative behavior after elections is imperative for a democratic Representative system, at the very least to punish betrayal with no re-election. Our goal was to show how to follow Representatives' and how to show behavior in real situations and observe trends in political crises including the onset of game changing political instabilities. We used correlation and correlation distance matrices of Brazilian Representative votes during four presidential terms. Re-ordering these matrices with Minimal Spanning Trees displays the dynamical formation of clusters for the sixteen year period, which includes one Presidential impeachment. The reordered matrices, colored by correlation strength and by the parties clearly show the origin of observed clusters and their evolution over time. When large clusters provide government support cluster breaks, political instability arises, which could lead to an impeachment, a trend we observed three years before the Brazilian President was impeached. We believe this method could be applied to foresee other political storms.Comment: 11 pages, 4 Figure

Ideological and Temporal Components of Network Polarization in Online Political Participatory Media

Political polarization is traditionally analyzed through the ideological stances of groups and parties, but it also has a behavioral component that manifests in the interactions between individuals. We present an empirical analysis of the digital traces of politicians in politnetz.ch, a Swiss online platform focused on political activity, in which politicians interact by creating support links, comments, and likes. We analyze network polarization as the level of intra- party cohesion with respect to inter-party connectivity, finding that supports show a very strongly polarized structure with respect to party alignment. The analysis of this multiplex network shows that each layer of interaction contains relevant information, where comment groups follow topics related to Swiss politics. Our analysis reveals that polarization in the layer of likes evolves in time, increasing close to the federal elections of 2011. Furthermore, we analyze the internal social network of each party through metrics related to hierarchical structures, information efficiency, and social resilience. Our results suggest that the online social structure of a party is related to its ideology, and reveal that the degree of connectivity across two parties increases when they are close in the ideological space of a multi-party system.Comment: 35 pages, 11 figures, Internet, Policy & Politics Conference, University of Oxford, Oxford, UK, 25-26 September 201

Quantifying and minimizing risk of conflict in social networks

Controversy, disagreement, conflict, polarization and opinion divergence in social networks have been the subject of much recent research. In particular, researchers have addressed the question of how such concepts can be quantified given people’s prior opinions, and how they can be optimized by influencing the opinion of a small number of people or by editing the network’s connectivity. Here, rather than optimizing such concepts given a specific set of prior opinions, we study whether they can be optimized in the average case and in the worst case over all sets of prior opinions. In particular, we derive the worst-case and average-case conflict risk of networks, and we propose algorithms for optimizing these. For some measures of conflict, these are non-convex optimization problems with many local minima. We provide a theoretical and empirical analysis of the nature of some of these local minima, and show how they are related to existing organizational structures. Empirical results show how a small number of edits quickly decreases its conflict risk, both average-case and worst-case. Furthermore, it shows that minimizing average-case conflict risk often does not reduce worst-case conflict risk. Minimizing worst-case conflict risk on the other hand, while computationally more challenging, is generally effective at minimizing both worst-case as well as average-case conflict risk

The effect of candidate quality on electoral equilibrium: An experimental study

When two candidates of different quality compete in a one-dimensional policy space, the equilibrium outcomes are asymmetric and do not correspond to the median. There are three main effects. First, the better candidate adopts more centrist policies than the worse candidate. Second, the equilibrium is statistical, in the sense that it predicts a probability distribution of outcomes rather than a single degenerate outcome. Third, the equilibrium varies systematically with the level of uncertainty about the location of the median voter. We test these three predictions using laboratory experiments and find strong support for all three. We also observe some biases and show that they can be explained by quantal response equilibrium