Opinion Dynamics Model Research Articles

Effect of algorithmic bias and network structure on coexistence, consensus, and polarization of opinions.

Individuals of modern societies share ideas and participate in collective processes within a pervasive, variable, and mostly hidden ecosystem of content filtering technologies that determine what information we see online. Despite the impact of these algorithms on daily life and society, little is known about their effect on information transfer and opinion formation. It is thus unclear to what extent algorithmic bias has a harmful influence on collective decision-making, such as a tendency to polarize debate. Here we introduce a general theoretical framework to systematically link models of opinion dynamics, social network structure, and content filtering. We showcase the flexibility of our framework by exploring a family of binary-state opinion dynamics models where information exchange lies in a spectrum from pairwise to group interactions. All models show an opinion polarization regime driven by algorithmic bias and modular network structure. The role of content filtering is, however, surprisingly nuanced; for pairwise interactions it leads to polarization, while for group interactions it promotes coexistence of opinions. This allows us to pinpoint which social interactions are robust against algorithmic bias, and which ones are susceptible to bias-enhanced opinion polarization. Our framework gives theoretical ground for the development of heuristics to tackle harmful effects of online bias, such as information bottlenecks, echo chambers, and opinion radicalization.

Persuasion process on social networks

From the Rwandan genocide to the Arab Spring movement, it has been well known that social networks, offline or online, and mass media can collectively change and amplify public opinions, however there are few theoretical models to characterize the persuasion process. In this paper, we propose an opinion dynamics model based on invasion process with media effect and committed agents, and analytically obtain the fraction of each opinion at the steady state. We find that the relative proportion of committed agents plays a vital role in influencing corresponding opinion formation, and social networks can enhance the influence of committed agents through the interaction between individuals. Mass media can affect individuals not only directly due to exposure but indirectly due to social interactions. This paper reveals the influence of mass media and committed agents on the final distribution of opinions through a persuasion process, and lays the foundation for building more general models that consider individual heterogeneity and external influences.

Consensus, polarization, and coexistence in a continuous opinion dynamics model with quenched disorder.

A model of opinion dynamics is introduced in which each individual's opinion is measured on a bounded continuous spectrum. Each opinion is influenced heterogeneously by every other opinion in the population. It is demonstrated that consensus, polarization and a spread of moderate opinions are all possible within this model. Using dynamic mean-field theory, we are able to identify the statistical features of the interactions between individuals that give rise to each of the aforementioned emergent phenomena. The nature of the transitions between each of the observed macroscopic states is also studied. It is demonstrated that heterogeneity of interactions between individuals can lead to polarization, that mostly antagonistic or contrarian interactions can promote consensus at a moderate opinion, and that mostly reinforcing interactions encourage the majority to take an extreme opinion.

Managing public opinion in consensus-reaching processes for large-scale group decision-making problems

In a public-related decision-making event, some people whose interests are not consistent with the result of the event may post some false information on social media to guide others against the event. Without proper management, the public’s opposition may lead to the failure of the events, even causing social unrest and economic losses. In order to reduce the impact of false information on the evolution of people’s opinions, this paper develops two opinion dynamics models to investigate the evolution process of opinions of decision makers and other related people on social media. Then, in order to manage the public opinion formed by all related people’s opinions and ensure a smooth implementation of the result of these events in real life, a public opinion management-based consensus reaching process is proposed. Meanwhile, to improve the efficiency of management measures, people are divided into two categories based on their confidence levels. Eventually, an illustrative example and simulations are provided to demonstrate the feasibility and effectiveness of the proposed model for managing public opinion.

Opinion Dynamic Modeling of News Perception

During the last decade, the advent of the Web and online social networks rapidly changed the way we were used to search, gather and discuss information of any kind. These tools have given everyone the chance to become a news medium. While promoting more democratic access to information, direct and unfiltered communication channels may increase our chances to confront malicious/misleading behavior. Fake news diffusion represents one of the most pressing issues of our online society. In recent years, fake news has been analyzed from several perspectives; among such vast literature, an important theme is the analysis of fake news’ perception. In this work, moving from such observation, I propose a family of opinion dynamics models to understand the role of specific social factors on the acceptance/rejection of news contents. In particular, I model and discuss the effect that stubborn agents, different levels of trust among individuals, open-mindedness, attraction/repulsion phenomena, and similarity between agents have on the population dynamics of news perception. To discuss the peculiarities of the proposed models, I tested them on two synthetic network topologies thus underlying when/how they affect the stable states reached by the performed simulations.

From social interactions to private environmental behaviours: The case of consumer food waste

Consumer food waste, like many environmental behaviours, takes place in private, and is not directly subject to social monitoring. Nevertheless, social interactions can affect private opinions and behaviours. This paper builds an agent-based model of interactions between consumers heterogeneous in their sociability, their initial opinions and behaviours related to food waste, and their willingness to consider different opinions, in order to assess how social interactions can affect private behaviours. Compared to existing models of opinion dynamics, we innovate by including a range of “cognitive dissonance” between stated opinions and actual behaviours that consumers are willing to accept before changing one of the two. We calibrate the model using questionnaire data on household food waste in Italy. We find that a limited degree of mixing between different socio-demographic groups, namely adult and young consumers, is enough to trigger change, but a certain openness of mind is required from more wasteful individuals. Equally, a small group of environmentally committed consumers can attract a sizeable share of the population towards low-waste behaviours if they show a certain variability of opinions and are willing to compromise with individuals in their close neighbourhood in terms of opinions. These findings can help design effective interventions to promote pro-environmental behaviours, taking advantage of the beneficial network effects while anticipating negative externalities.

Contrarian effect in opinion forming: Insights from Greta Thunberg phenomenon

ABSTRACT In recent months, the figure of Greta Thunberg and the theme of climate changings quickly became the focus of the debate. This has led to a polarization effect in opinion forming about the climate subject. Starting from the analysis of this phenomenon, we develop an opinion dynamics model in which several types of contrarian agents are considered. Each agent is supposed to have an opinion on several topics related to each other; thus, the opinions being formed on these topics are also mutually dependent. The aim of the paper is to investigate the indirect effects of contrarian agents on the collective opinion about these topics. Several numerical tests are presented in order to highlight the main features of the model.

A framework of opinion dynamics using fuzzy linguistic 2-tuples

Opinion dynamics investigate the spreading and evolution of opinions among a set of individuals. This is especially relevant in decision-making — the process of selecting an alternative from a set of possible options —, that is commonly based on personal opinions which may evolve along time. In this work, we present a model of opinion dynamics where opinions are represented using fuzzy linguistic 2-tuples, a realistic representation of imprecise information. In our framework, the propagation of opinions in the communication is divided into three independent sub-processes. Additionally, we use a social network to represent agents’ interactions and an awareness deactivation mechanism to model the awareness dynamics in the system (i.e., options for which agents have opinions). Our opinion dynamics model can be easily integrated into an agent-based system to how opinions spread and evolve. Experimental results show the impact of the communication processes, the social network topology, the awareness deactivation mechanism, and the agents’ influence on the opinion dynamics of others. Furthermore, we present two case studies of our opinion dynamics model applied to marketing and politics.

A Shared Control Framework for Human-Multirobot Foraging With Brain-Computer Interface

With the rapid development of multi-robot systems (MRSs), they can be widely used to perform various tasks in typical environments. However, the inevitable disadvantages of onboard sensor errors, communication delays, and underspecified environmental factors seriously affect the operation of MRSs. Therefore, this letter considers a shared control framework suitable for human-multirobot foraging with a brain-computer interface (BCI) as a means of allowing a human operator to express opinions, permitting the robots to rely on human experience and knowledge to improve cooperation. An opinion dynamics model is used to find the consensus opinion of the MRS, which, however, is likely not accurate due to the biased nature of the available environmental information. When the human operator learns the opinion of the robots, he/she can then either accept it or reject it and express his/her own opinion via the BCI. Of course, this human judgment may also be incorrect, or the BCI may suffer from false detections. Thus, the MRS does not directly follow the human operator's opinion; instead, it is added to the opinion dynamics model as a new node to generate the final consensus opinion. Extensive simulation results show that the proposed framework can markedly improve the efficiency of foraging compared with robot-only or human-only performance and traditional human-robot interaction methods.

Mean-field and graph limits for collective dynamics models with time-varying weights

In this paper, we study a model for opinion dynamics where the influence weights of agents evolve in time via an equation which is coupled with the opinions' evolution. We explore the natural question of the large population limit with two approaches: the now classical mean-field limit and the more recent graph limit. After establishing the existence and uniqueness of solutions to the models that we will consider, we provide a rigorous mathematical justification for taking the graph limit in a general context. Then, establishing the key notion of indistinguishability , which is a necessary framework to consider the mean-field limit, we prove the subordination of the mean-field limit to the graph one in that context. This actually provides an alternative proof for the mean-field limit. We conclude by showing some numerical simulations to illustrate our results.

Multidimensional Model of Opinion Dynamics in Social Networks: Polarization Indices

Multidimensional Model of Opinion Dynamics in Social Networks: Polarization Indices

Dynamics of Public Opinions in an Online and Offline Social Network

With the development of the information and Internet technology, the public opinions with big data will rapidly emerge in an online-offline social network, and an inefficient management of public opinions often will lead to the security crisis for either firms or governments. To unveil the interaction mechanism among a large number of agents between the online and offline social networks, in this paper we propose the public opinion dynamics model in an online-offline social network context. Next, in the theory aspect we investigate the analytical conditions to form a consensus in the public opinion dynamics model. Furthermore, we conduct the extensive simulations to investigate how the online agents impact the dynamics of public opinion formation, and unfold that the online agents shorten the steady-state time, decrease the number of opinion clusters, and smoothen the opinion changes in the opinion dynamics. The increase in the size of the online agents often enhances these effects. The results in this paper can provide a basis for the management of the public opinions in the Internet age.

An adaptive group decision making framework: Individual and local world opinion based opinion dynamics

Opinion dynamics (OD) models, which simulate individuals’ opinion evolution process on social network to analyze the final state of opinion distribution in a group, usually differ from each other due to the differences in social network evolution rules and opinion evolution rules. However, most existing social network evolution rules and opinion evolution rules usually cannot characterize the comprehensive influence of key factors such as neighbors and opinion differences in social relationships. To fully consider the properties of social network evolution and improve the efficiency of consensus reaching process in group decision making, this paper introduces the concept of local world opinion derived from individuals’ common friends, and then proposes an individual and local world opinion-based OD model. In the proposed model, social network evolution is jointly determined by the distance between individual opinions and network structure similarity. The pair of individuals with the largest consensus improvement space are then suggested to adjust their opinions by using an adaptive individual opinion adjustment mechanism. Finally, detailed simulation results are provided to demonstrate the convergence of the proposed model and analyze different parameters’ effects on the stabilized time steps and the number of stable state opinion clusters.

Synchronising institutions and value systems: A model of opinion dynamics mediated by proportional representation.

Individuals increasingly participate in online platforms where they copy, share and form they opinions. Social interactions in these platforms are mediated by digital institutions, which dictate algorithms that in turn affect how users form and evolve their opinions. In this work, we examine the conditions under which convergence on shared opinions can be obtained in a social network where connected agents repeatedly update their normalised cardinal preferences (i.e. value systems) under the influence of a non-constant reflexive signal (i.e. institution) that aggregates populations’ information using a proportional representation rule. We analyse the impact of institutions that aggregate (i) expressed opinions (i.e. opinion-aggregation institutions), and (ii) cardinal preferences (i.e. value-aggregation institutions). We find that, in certain regions of the parameter space, moderate institutional influence can lead to moderate consensus and strong institutional influence can lead to polarisation. In our randomised network, local coordination alone in the total absence of institutions does not lead to convergence on shared opinions, but very low levels of institutional influence are sufficient to generate a feedback loop that favours global conventions. We also show that opinion-aggregation may act as a catalyst for value change and convergence. When applied to digital institutions, we show that the best mechanism to avoid extremism is to increase the initial diversity of the value systems in the population.

An online multi-dimensional opinion dynamic model with misinformation diffusion in emergency events

Multiple opinions, including many that are negative, are produced in emergency events. These opinions are commonly formed asynchronously based on misinformation. However, most researches on opinion dynamics involving information neglect the asynchronous process of initial opinion formation due to information diffusion. Since online social networks like Sina Weibo act as major avenues for the expression, after analysing online behaviours, an opinion dynamic model is developed with consideration of misinformation diffusion of public opinion. In this model, schemes are developed for opinion interactions in multiple dimensions by introducing characteristics of online communication as another way of opinion interactions besides communication between neighbours. Subsequently, we investigate the impacts of network structure, diffusion rate, repost rate and other factors, which provide insights into understanding online opinion dynamics during emergency events. Furthermore, we conduct simulations to determine the intervention effects of different official responses. Results show that removing comments compulsively exhibits better performance in reducing negative opinion as well as increasing the density of Spreaders. Debunking misinformation by posting early results officially which indicates the probability of the existence of misinformation may lead public opinion in time if it takes a long time to finally confirm the misinformation.

On the steady state of continuous-time stochastic opinion dynamics with power-law confidence

AbstractThis paper introduces a non-linear and continuous-time opinion dynamics model with additive noise and state-dependent interaction rates between agents. The model features interaction rates which are proportional to a negative power of the opinion distances. We establish a non-local partial differential equation for the distribution of opinion distances and use Mellin transforms to provide an explicit formula for the stationary solution of the latter, when it exists. Our approach leads to new qualitative and quantitative results on this type of dynamics. To the best of our knowledge these Mellin transform results are the first quantitative results on the equilibria of opinion dynamics with distance-dependent interaction rates. The closed-form expressions for this class of dynamics are obtained for the two-agent case. However, the results can be used in mean-field models featuring several agents whose interaction rates depend on the empirical average of their opinions. The technique also applies to linear dynamics, namely with a constant interaction rate, on an interaction graph.

Hiding opinions by minimizing disclosed information: an obfuscation-based opinion dynamics model

ABSTRACT In the field of opinion dynamics, the hiding of opinions is routinely modeled as staying silent. However, staying silent is not always feasible. In situations where opinions are indirectly expressed by one’s observable actions, people may however try to hide their opinions via a more complex and intelligent strategy called obfuscation, which minimizes the information disclosed to others. This study proposes a formal opinion dynamics model to study the hitherto unexplored effect of obfuscation on public opinion formation based on the recently developed Action-Opinion Inference Model. For illustration purposes, we use our model to simulate two cases with different levels of complexity, highlighting that the effect of obfuscation largely depends on the subtle relations between actions and opinions.

Hive geometry shapes the recruitment rate of honeybee colonies.

Honey bees make decisions regarding foraging and nest-site selection in groups ranging from hundreds to thousands of individuals. To effectively make these decisions, bees need to communicate within a spatially distributed group. However, the spatiotemporal dynamics of honey bee communication have been mostly overlooked in models of collective decisions, focusing primarily on mean field models of opinion dynamics. We analyze how the spatial properties of the nest or hive, and the movement of individuals with different belief states (uncommitted or committed) therein affect the rate of information transmission using spatially-extended models of collective decision-making within a hive. Honeybees waggle-dance to recruit conspecifics with an intensity that is a threshold nonlinear function of the waggler concentration. Our models range from treating the hive as a chain of discrete patches to a continuous line (long narrow hive). The combination of population-thresholded recruitment and compartmentalized populations generates tradeoffs between rapid information propagation with strong population dispersal and recruitment failures resulting from excessive population diffusion and also creates an effective colony-level signal-detection mechanism whereby recruitment to low quality objectives is blocked.

Opinion Dynamics Optimization by Varying Susceptibility to Persuasion via Non-Convex Local Search

A long line of work in social psychology has studied variations in people’s susceptibility to persuasion—the extent to which they are willing to modify their opinions on a topic. This body of literature suggests an interesting perspective on theoretical models of opinion formation by interacting parties in a network: in addition to considering interventions that directly modify people’s intrinsic opinions, it is also natural to consider interventions that modify people’s susceptibility to persuasion. In this work, motivated by this fact, we propose an influence optimization problem. Specifically, we adopt a popular model for social opinion dynamics, where each agent has some fixed innate opinion, and a resistance that measures the importance it places on its innate opinion; agents influence one another’s opinions through an iterative process. Under certain conditions, this iterative process converges to some equilibrium opinion vector. For the unbudgeted variant of the problem, the goal is to modify the resistance of any number of agents (within some given range) such that the sum of the equilibrium opinions is minimized; for the budgeted variant, in addition the algorithm is given upfront a restriction on the number of agents whose resistance may be modified. We prove that the objective function is in general non-convex. Hence, formulating the problem as a convex program as in an early version of this work (Abebe et al., KDD’18) might have potential correctness issues. We instead analyze the structure of the objective function, and show that any local optimum is also a global optimum, which is somehow surprising as the objective function might not be convex. Furthermore, we combine the iterative process and the local search paradigm to design very efficient algorithms that can solve the unbudgeted variant of the problem optimally on large-scale graphs containing millions of nodes. Finally, we propose and evaluate experimentally a family of heuristics for the budgeted variant of the problem.

Fuzzy inference based Hegselmann–Krause opinion dynamics for group decision-making under ambiguity

This paper considers a group decision-making mechanism for a group of social agents with ambiguous interactions. First, a fuzzy inference approach is introduced to describe bounded confidence based interaction rules among social agents for a certain object in a social network platform. Second, an influence graph is introduced to model the communication network topology associated with the group of agents. A fuzzy inference based opinion dynamics model is built when the defuzzified interaction weights among agents are used in the opinion update scheme for each agent. Third, the patterns of the collective final opinions are analyzed under the proposed fuzzy opinion dynamics model. The fuzziness of opinion gaps and interaction weights among agents are respectively investigated in the collective opinion evolution. Simulation results show the influence of fuzzy values of opinion gaps and interaction weights on the pattern of the collective final opinions and reveal the quantitative relationships of opinion gap and interaction weights between the original HK opinion dynamics model and the fuzzy HK opinion dynamics model.