Social pressure in opinion dynamics

Motivated by privacy and security concerns in online social networks, we study the role of social pressure in opinion dynamics. These are dynamics, introduced in economics and sociology literature, that model the formation of opinions in a social network. We enrich one of the most classical opinion dynamics, by introducing the pressure, increasing with time, to reach an agreement. We prove that for clique social networks, the dynamics always converges to consensus (no matter the level of noise) if the social pressure is high enough. Moreover, we provide (tight) bounds on the speed of convergence; these bounds are polynomial in the number of nodes in the network provided that the pressure grows sufficiently fast. We finally look beyond cliques: we characterize the graphs for which consensus is guaranteed, and make some considerations on the computational complexity of checking whether a graph satisfies such a condition

Stochastic Opinion Dynamics under Social Pressure in Arbitrary Networks

Social pressure is a key factor affecting the evolution of opinions on networks in many types of settings, pushing people to conform to their neighbors' opinions. To study this, the interacting Polya urn model was introduced by Jadbabaie et al., in which each agent has two kinds of opinion: inherent beliefs, which are hidden from the other agents and fixed; and declared opinions, which are randomly sampled at each step from a distribution which depends on the agent's inherent belief and her neighbors' past declared opinions (the social pressure component), and which is then communicated to their neighbors. Each agent also has a bias parameter denoting her level of resistance to social pressure. At every step, the agents simultaneously update their declared opinions according to their neighbors' aggregate past declared opinions, their inherent beliefs, and their bias parameters. We study the asymptotic behavior of this opinion dynamics model and show that agents' declaration probabilities converge almost surely in the limit using Lyapunov theory and stochastic approximation techniques. We also derive necessary and sufficient conditions for the agents to approach consensus on their declared opinions. Our work provides further insight into the difficulty of inferring the inherent beliefs of agents when they are under social pressure

Social Pressure in Opinion Games

Motivated by privacy and security concerns in online social networks, we study the role of social pressure in opinion games. These are games, important in economics and sociology, that model the formation of opinions in a social network. We enrich the definition of (noisy) best-response dynamics for opinion games by introducing the pressure, increasing with time, to reach an agreement. We prove that for clique social networks, the dynamics always converges to consensus (no matter the level of noise) if the social pressure is high enough. Moreover, we provide (tight) bounds on the speed of convergence; these bounds are polynomial in the number of players provided that the pressure grows sufficiently fast. We finally look beyond cliques: we characterize the graphs for which consensus is guaranteed, and make some considerations on the computational complexity of checking whether a graph satisfies such a condition

The role of homophily in the emergence of opinion controversies

Understanding the emergence of strong controversial issues in modern societies is a key issue in opinion studies. A commonly diffused idea is the fact that the increasing of homophily in social networks, due to the modern ICT, can be a driving force for opinion polariation. In this paper we address the problem with a modelling approach following three basic steps. We first introduce a network morphogenesis model to reconstruct network structures where homophily can be tuned with a parameter. We show that as homophily increases the emergence of marked topological community structures in the networks raises. Secondly, we perform an opinion dynamics process on homophily dependent networks and we show that, contrary to the common idea, homophily helps consensus formation. Finally, we introduce a tunable external media pressure and we show that, actually, the combination of homophily and media makes the media effect less effective and leads to strongly polarized opinion clusters.Comment: 24 pages, 10 figure

Expressed and Private Opinion Dynamics on Influence Networks with Asynchronous Updating

© 2020 IEEE. In this paper, an asynchronous discrete-time opinion dynamics model on a social influence network is considered. At each time instant, a single individual activates and updates two state variables simultaneously. The individual's new private opinion is a weighted average of her current private opinion, the expressed opinions of her neighbors, and a constant prejudice. Meanwhile, the individual's new expressed opinion is equal to her current private opinion, altered due to a pressure to conform to the public opinion as perceived by the individual, being the average expressed opinion among her neighbors. We analyze the system for social networks which are rooted, and show that if no individual holds a prejudice, then a mild assumption on the activation sequence of the individuals guarantees convergence. In particular, the expressed and private opinions of all individuals converge to the same value exponentially fast, with two lower bounds on convergence speeds based on two different assumptions on the network topology. Simulations are provided to illustrate the result, and provide support to the conjecture that the system dynamics may converge even if individuals hold an existing prejudice

Estimating True Beliefs from Declared Opinions

Social networks often exert social pressure, causing individuals to adapt their expressed opinions to conform to their peers. An agent in such systems can be modeled as having a (true and unchanging) inherent belief but broadcasts a declared opinion at each time step based on her inherent belief and the past declared opinions of her neighbors. An important question in this setting is parameter estimation: how to disentangle the effects of social pressure to estimate inherent beliefs from declared opinions. To address this, Jadbabaie et al. formulated the interacting P\'olya urn model of opinion dynamics under social pressure and studied it on complete-graph social networks using an aggregate estimator, and found that their estimator converges to the inherent beliefs unless majority pressure pushes the network to consensus. In this work, we study this model on arbitrary networks, providing an estimator which converges to the inherent beliefs even in consensus situations. Finally, we bound the convergence rate of our estimator in both consensus and non-consensus scenarios; to get the bound for consensus scenarios (which converge slower than non-consensus) we additionally found how quickly the system converges to consensus

Socio-Physical Approach to Consensus Building and the Occurrence of Opinion Divisions Based on External Efficacy

The proliferation of public networks has enabled instantaneous and interactive communication that transcends temporal and spatial constraints. The vast amount of textual data on the Web has facilitated the study of quantitative analysis of public opinion, which could not be visualized before. In this paper, we propose a new theory of opinion dynamics. This theory is designed to explain consensus building and opinion splitting in opinion exchanges on social media such as Twitter. With the spread of public networks, immediate and interactive communication that transcends temporal and spatial constraints has become possible, and research is underway to quantitatively analyze the distribution of public opinion, which has not been visualized until now, using vast amounts of text data. In this paper, we propose a model based on the Like Bounded Confidence Model, which represents opinions as continuous quantities. However, the Bounded Confidence mModel assumes that people with different opinions move without regard to their opinions, rather than ignoring them. Furthermore, our theory modeled the phenomenon in such a way that it can incorporate and represent the effects of external external pressure and dependence on surrounding conditions. This paper is a revised version of a paper submitted in December 2018(Opinion Dynamics Theory for Analysis of Consensus Formation and Division of Opinion on the Internet).Comment: Revised Paper:Opinion Dynamics Theory for Analysis of Consensus Formation and Division of Opinion on the Internet(2018

Culture Outsmarts Nature in the Evolution of Cooperation

A one dimensional cellular automata model describes the evolutionary dynamics of cooperation when grouping by cooperators provides protection against predation. It is used to compare the dynamics of evolution of cooperation in three settings. G: only vertical transmission of information is allowed, as an analogy of genetic evolution with heredity; H: only horizontal information transfer is simulated, through diffusion of the majority\'s opinion, as an analogy of opinion dynamics or social learning; and C: analogy of cultural evolution, where information is transmitted both horizontally (H) and vertically (V) so that learned behavior can be transmitted to offspring. The results show that the prevalence of cooperative behavior depends on the costs and benefits of cooperation so that: a- cooperation becomes the dominant behavior, even in the presence of free-riders (i.e., non-cooperative obtaining benefits from the cooperation of others), under all scenarios, if the benefits of cooperation compensate for its cost; b- G is more susceptible to selection pressure than H achieving a closer adaptation to the fitness landscape; c- evolution of cooperative behavior in H is less sensitive to the cost of cooperation than in G; d- C achieves higher levels of cooperation than the other alternatives at low costs, whereas H does it at high costs. The results suggest that a synergy between H and V is elicited that makes the evolution of cooperation much more likely under cultural evolution than under the hereditary kind where only V is present.Social Simulation, Interactions, Group Size, Selfish Heard, Cultural Evolution, Biological Evolution