The noisy voter model under the influence of contrarians

The influence of contrarians on the noisy voter model is studied at the mean-field level. The noisy voter model is a variant of the voter model where agents can adopt two opinions, optimistic or pessimistic, and can change them by means of an imitation (herding) and an intrinsic (noise) mechanisms. An ensemble of noisy voters undergoes a finite-size phase transition, upon increasing the relative importance of the noise to the herding, form a bimodal phase where most of the agents shear the same opinion to a unimodal phase where almost the same fraction of agent are in opposite states. By the inclusion of contrarians we allow for some voters to adopt the opposite opinion of other agents (anti-herding). We first consider the case of only contrarians and show that the only possible steady state is the unimodal one. More generally, when voters and contrarians are present, we show that the bimodal-unimodal transition of the noisy voter model prevails only if the number of contrarians in the system is smaller than four, and their characteristic rates are small enough. For the number of contrarians bigger or equal to four, the voters and the contrarians can be seen only in the unimodal phase. Moreover, if the number of voters and contrarians, as well as the noise and herding rates, are of the same order, then the probability functions of the steady state are very well approximated by the Gaussian distribution

Opinion Optimization in Directed Social Networks

Shifting social opinions has far-reaching implications in various aspects, such as public health campaigns, product marketing, and political candidates. In this paper, we study a problem of opinion optimization based on the popular Friedkin-Johnsen (FJ) model for opinion dynamics in an unweighted directed social network with $n$ nodes and $m$ edges. In the FJ model, the internal opinion of every node lies in the closed interval $[0, 1]$, with 0 and 1 being polar opposites of opinions about a certain issue. Concretely, we focus on the problem of selecting a small number of $k\ll n$ nodes and changing their internal opinions to 0, in order to minimize the average opinion at equilibrium. We then design an algorithm that returns the optimal solution to the problem in $O(n^3)$ time. To speed up the computation, we further develop a fast algorithm by sampling spanning forests, the time complexity of which is $O(ln)$, with $l$ being the number of samplings. Finally, we execute extensive experiments on various real directed networks, which show that the effectiveness of our two algorithms is similar to each other, both of which outperform several baseline strategies of node selection. Moreover, our fast algorithm is more efficient than the first one, which is scalable to massive graphs with more than twenty million nodes

A review on trust propagation and opinion dynamics in social networks and group decision making frameworks

On-line platforms foster the communication capabilities of the Internet to develop large- scale influence networks in which the quality of the interactions can be evaluated based on trust and reputation. So far, this technology is well known for building trust and harness- ing cooperation in on-line marketplaces, such as Amazon (www.amazon.com) and eBay (www.ebay.es). However, these mechanisms are poised to have a broader impact on a wide range of scenarios, from large scale decision making procedures, such as the ones implied in e-democracy, to trust based recommendations on e-health context or influence and per- formance assessment in e-marketing and e-learning systems. This contribution surveys the progress in understanding the new possibilities and challenges that trust and reputation systems pose. To do so, it discusses trust, reputation and influence which are important measures in networked based communication mechanisms to support the worthiness of information, products, services opinions and recommendations. The existent mechanisms to estimate and propagate trust and reputation, in distributed networked scenarios, and how these measures can be integrated in decision making to reach consensus among the agents are analysed. Furthermore, it also provides an overview of the relevant work in opinion dynamics and influence assessment, as part of social networks. Finally, it identi- fies challenges and research opportunities on how the so called trust based network can be leveraged as an influence measure to foster decision making processes and recommen- dation mechanisms in complex social networks scenarios with uncertain knowledge, like the mentioned in e-health and e-marketing frameworks.The authors acknowledge the financial support from the EU project H2020-MSCA-IF-2016-DeciTrustNET-746398, FEDER funds provided in the National Spanish project TIN2016-75850-P , and the support of the RUDN University Program 5-100 (Russian Federation)

Analyzing the extremization of opinions in a general framework of bounded confidence and repulsion

In the bounded confidence framework, agents’ opinions evolve as a result of interactions with other agents having similar opinions. Thus, consensus or fragmentation of opinions can be reached, but not extremization (the evolution of opinions towards an extreme value). In contrast, when repulsion mechanisms are at work, agents with distant opinions interact and repel each other, leading to extremization. This work proposes a general opinion dynamics framework of bounded confidence and repulsion, which includes social network interactions and agent-independent time-varying rationality. We extensively analyze the performance of our model to show that the degree of extremization among a population can be controlled by the repulsion rule, and social networks promote extreme opinions. Agent-based rationality and time-varying adaptation also bear a strong impact on opinion dynamics. The high accuracy of our model is determined in a real-world social network well referenced in the literature, the Zachary Karate Club (with a known ground truth). Finally, we use our model to analyze the extremization of opinions in a real-world scenario, in Spain: a marketing action for the Netflix series “Narcos”