In this work, we focus on strategies to influence the opinion dynamics of a well-connected society. We propose a generalization of the popular voter model. This variant of the voter model can capture a wide range of individuals including strong-willed individuals whose opinion evolution is independent of their neighbors as well as conformist/rebel individuals who tend to adopt the opinion of the majority/minority. Motivated by political campaigns which aim to influence opinion dynamics by the end of a fixed deadline, we focus on influencing strategies for finite time horizons. We characterize the nature of optimal influencing strategies as a function of the nature of individuals forming the society. Using this, we show that for a society consisting of predominantly strong-willed/rebel individuals, the optimal strategy is to influence towards the end of the finite time horizon, whereas, for a society predominantly consisting of conformist individuals who try to adopt the opinion of the majority, it could be optimal to influence in the initial phase of the finite time horizon.
The focus of this work is on designing influencing strategies to shape the collective opinion of a network of individuals. We consider a variant of the voter model where opinions evolve in one of two ways. In the absence of external influence, opinions evolve via interactions between individuals in the network, while, in the presence of external influence, opinions shift in the direction preferred by the influencer. We focus on a finite time-horizon and an influencing strategy is characterized by when it exerts influence in this time-horizon given its budget constraints. Prior work on this opi…
We study the problem of optimally investing in nodes of a social network in a competitive setting, where two camps aim to maximize adoption of their opinions by the population. In particular, we consider the possibility of campaigning in multiple phases, where the final opinion of a node in a phase acts as its initial biased opinion for the following phase. Using an extension of the popular DeGroot-Friedkin model, we formulate the utility functions of the camps, and show that they involve what can be interpreted as multiphase Katz centrality. Focusing on two phases, we analytically derive Nash…
Most previous works on opinion modeling lack the simultaneous study of individual mental activity and group behavior. This paper is motivated to propose an agent-based online opinion formation model based on attitude change theory, group behavior theory and evolutionary game theory in the perspective of sociology and psychology. In this model, there are three factors influencing the persuasion process, including credibility of the leaders, characteristic of the recipient, and group environment. The proposed model is applied to Twitter to analyze the influence of topic type, parameter changing,…
Social network based information campaigns can be used for promoting beneficial health behaviours and mitigating polarisation (e.g. regarding climate change or vaccines). Network-based intervention strategies typically rely on full knowledge of network structure. It is largely not possible or desirable to obtain population-level social network data due to availability and privacy issues. It is easier to obtain information about individuals' attributes (e.g. age, income), which are jointly informative of an individual's opinions and their social network position. We investigate strategies for i…
Agent-based models of opinion dynamics allow one to examine the spread of opinions between entities and to study phenomena such as consensus, polarization, and fragmentation. By studying a model of opinion dynamics on a social network, one can explore the effects of network structure on these phenomena. In social networks, some individuals share their ideas and opinions more frequently than others. These disparities can arise from heterogeneous sociabilities, heterogeneous activity levels, different prevalences to share opinions when engaging in a social-media platform, or something else. To e…
As an important factor governing opinion dynamics, stubbornness strongly affects various aspects of opinion formation. However, a systematically theoretical study about the influences of heterogeneous stubbornness on opinion dynamics is still lacking. In this paper, we study a popular opinion model in the presence of inhomogeneous stubbornness. We show analytically that heterogeneous stubbornness has a great impact on convergence time, expressed opinion of every node, and the overall expressed opinion. We provide an explanation of the expressed opinion in terms of stubbornness-dependent spanni…
The heterogeneity of the influence processes is an important feature of social systems: how we perceive social influence and how we influence other individuals is heavily influenced by our opinion and non-opinion attributes. The latter include demographic, cultural, and structural (how we are embedded in social networks) characteristics. Furthermore, the results of the influence processes may also depend on how similar the interacting individuals are in terms of their features. This paper addresses this issue and elaborates on an agent-based model that is sensitive to the individual characteri…
We consider a class of opinion dynamics on networks where at each time-step, each node in the network disregards the opinions of a certain number of its most extreme neighbors and updates its own opinion as a weighted average of the remaining opinions. When all nodes disregard the same number of extreme neighbors, previous work has shown that consensus will be reached if and only if the network satisfies certain topological properties. In this paper, we consider the implications of allowing each node to have a personal threshold for the number of extreme neighbors to ignore. We provide graph c…
Here we developed a new conceptual, stochastic Heterogeneous Opinion-Status model (HOpS model), which is adaptive network model. The HOpS model admits to identify the main attributes of dynamics on networks and to study analytically the relation between topological network properties and processes taking place on a network. Another key point of the HOpS model is the possibility to study network dynamics via the novel parameter of heterogeneity. We show that not only clear topological network properties, such as node degree, but also, the nodes' status distribution (the factor of network hetero…
We study discrete preference games in heterogeneous social networks. These games model the interplay between a player's private belief and his/her publicly stated opinion (which could be different from the player's belief) as a strategic game in which the players' strategies are the opinions and the cost of an opinion in a state is a convex combination through a parameter $α\in[0,1]$ of two factors: the disagreement between the player's opinion and his/her internal belief and the number of neighbors whose opinions differ from the one of the player. The parameter $α$ models how stubborn a playe…
In this work, we investigate a heterogeneous population in the modified Hegselmann-Krause opinion model on complex networks. We introduce the Shannon information entropy about all relative opinion clusters to characterize the cluster profile in the final configuration. Independent of network structures, there exists the optimal stubbornness of one subpopulation for the largest number of clusters and the highest entropy. Besides, there is the optimal bounded confidence (or subpopulation ratio) of one subpopulation for the smallest number of clusters and the lowest entropy. However, network stru…
We introduce an heterogeneous nonlinear $q$-voter model with zealots and two types of susceptible voters, and study its non-equilibrium properties when the population is finite and well mixed. In this two-opinion model, each individual supports one of two parties and is either a zealot or a susceptible voter of type $q_1$ or $q_2$. While here zealots never change their opinion, a $q_i$-susceptible voter ($i=1,2$) consults a group of $q_i$ neighbors at each time step, and adopts their opinion if all group members agree. We show that this model violates the detailed balance whenever $q_1 \neq q_…
In this paper, we consider a network of consumers who are under the combined influence of their neighbors and external influencing entities (the marketers). The consumers' opinion follows a hybrid dynamics whose opinion jumps are due to the marketing campaigns. By using the relevant static game model proposed recently in [1], we prove that although the marketers are in competition and therefore create tension in the network, the network reaches a consensus. Exploiting this key result, we propose a coopetition marketing strategy which combines the one-shot Nash equilibrium actions and a policy …
The dissemination of information and the development of public opinion are essential elements of most social media platforms and are often described as distinct, man-made occurrences. However, what is often disregarded is the interdependence between these two phenomena. Information dissemination serves as the foundation for the formation of public opinion, while public opinion, in turn, drives the spread of information. In our study, we model the co-evolutionary relationship between information and public opinion on heterogeneous multiplex networks. This model takes into account a minority of …
We study a rating system in which a set of individuals (e.g., the customers of a restaurant) evaluate a given service (e.g, the restaurant), with their aggregated opinion determining the probability of all individuals to use the service and thus its generated revenue. We explicitly model the influence relation by a social network, with individuals being influenced by the evaluation of their trusted peers. On top of that we allow a malicious service provider (e.g., the restaurant owner) to bribe some individuals, i.e., to invest a part of his or her expected income to modify their opinion, ther…
We investigate opinion spreading by a threshold model in a situation where the influence of people is heterogeneously distributed. We focus on the response of the average opinion as a function between the trend between out-degree (number of neighbors)---effectively the strength of influence of a node---and the threshold for adopting a new product or opinion. We find that if the coupling is very positive, the final state of the system will be a mix of different opinions otherwise it will it converges to a consensus state. We find that this cannot be simply explained as a phase transition, but e…
Beyond Polarization: Opinion Mixing and Social Influence in Deliberation
Stanford University（斯坦福大学）；Center on Democracy, Development, and the Rule of Law, Stanford University（斯坦福大学民主、发展与法治中心）；Generation Lab；Duke University（杜克大学）
We study the dynamics of the out-of-equilibrium nonlinear q-voter model with two types of susceptible voters and zealots, introduced in [EPL 113, 48001 (2016)]. In this model, each individual supports one of two parties and is either a susceptible voter of type $q_1$ or $q_2$, or is an inflexible zealot. At each time step, a $q_i$-susceptible voter ($i = 1,2$) consults a group of $q_i$ neighbors and adopts their opinion if all group members agree, while zealots are inflexible and never change their opinion. This model violates detailed balance whenever $q_1 \neq q_2$ and is characterized by tw…
Polarization of opinions about vaccination can have a negative impact on pandemic control. In this work we quantify this negative impact for the transmission of COVID-19, using an agent based simulation in an heterogeneous population with multi-type networks, representing different types of social interactions. We show that the clustering of unvaccinated individuals, associated with polarization of opinion, can lead to significant differences in the evolution of the pandemic compared to deterministic model predictions. Under our realistic baseline scenario these differences are a 33pc increase…
