Binary Opinion Research Articles

Modeling public opinion control by a charismatic leader

We study the average long-time behavior of the binary opinions of a social group with peer-to-peer interactions under the influence of an external bias and a persuadable leader, a strongly-biased agent with a dynamic opinion with the intention of spreading it across the system. We use a generalized, fully-connected Ising model, with each spin representing the binary opinion of an agent at a given time and a single, super spin representing the opinion of the leader. External fields and interaction constants model the opinion bias and peer-to-peer interactions, respectively, while the temperature T models an idealized social climate, representing an authoritarian regime if T is low or a liberal one if T is high. We derive a mean-field solution for the average magnetization m, the “social mood”, and investigate how m and the super spin magnetization vary as a function of T. We find that, depending on the initial conditions, due to the presence of metastable states, the sign of the average magnetization depends on the temperature. Finally, we verify that this effect is also present even if we consider only nearest-neighbor interactions within the social group.

Kinetic modeling of a Sznajd opinion model on social networks

In this paper, we study a kinetic modeling of opinion formation on social networks in which the distribution function depends on both the opinion and the connectivity of the agents. The opinion exchange process is governed by a Sznajd-type model with three opinions, [Formula: see text], 0, and the social network is represented statistically with connectivity denoting the number of contacts of a given individual. It is commonly accepted that, in social networks, the opinion of the agents with a higher connectivity, i.e. a larger number of followers, is more convincing than that of the agents with a lower number of followers. By the kinetic modeling approach, we derived the asymptotic mean opinion of a social network in terms of the initial opinion and the connectivity of the agents. The present work extends the result in [N. Loy, M. Raviola and A. Tosin, Opinion polarisation in social networks, Phil. Trans. R. Soc. A 380, 20210158 (2021)] where only binary opinions, [Formula: see text], were considered, that indecisive people who cannot make a clear choice between [Formula: see text] are allowed in this study.

Opinion dynamics under double thresholds

In this letter, we introduce a double threshold model to investigate opinion formation in social networks, considering bi-directional binary opinion changes. We derive the law of motion for opinion evolution analytically and explore the conditions for achieving oscillation, convergence, and even consensus comprehensively. Our findings demonstrate that under asymmetric thresholds with synchronous updating, the initial fraction of both opinions tends to approach the respective switching thresholds, facilitating rapid opinion convergence. Additionally, we observe that both lower and higher levels of connectivity promote consensus formation, while moderate connectivity can lead to opinion oscillations. Furthermore, network structures with longer connections or hubs expedite consensus emergence. However, under synchronous updating, both asymmetric and symmetric double thresholds may induce opinion oscillations, impeding stable state attainment. Conversely, with asynchronous updating, opinions consistently converge. Overall, our study enhances understanding of opinion dynamics, providing insights into consensus formation and offering a theoretical foundation to address socio-political issues in diverse communities.

[formula omitted]-player game formulation of the majority-vote model of opinion dynamics

From a self-centered perspective, it can be assumed that people only hold opinions that can benefit them. If opinions have no intrinsic value, and acquire their value when held by the majority of individuals in a discussion group, then we have a situation that can be modeled as an N-player game. Here we explore the dynamics of (binary) opinion formation using a game-theoretic framework to study an N-player game version of Galam’s local majority-vote model. The opinion dynamics is modeled by a stochastic imitation dynamics in which the individuals copy the opinion of more successful peers. In the infinite population limit, this dynamics is described by the classical replicator equation of evolutionary game theory. The equilibrium solution shows a threshold separating the initial frequencies that lead to the fixation of one opinion or the other. A comparison with Galam’s deterministic model reveals contrasting results, especially in the presence of inflexible individuals, who never change their opinions. In particular, the N-player game predicts a polarized equilibrium consisting only of extremists. Using finite-size scaling analysis, we evaluate the critical exponents that determine the population size dependence of the opinion’s fixation probability and mean fixation times near the threshold. The results underscore the usefulness of combining evolutionary game theory with opinion dynamics and the importance of statistical physics tools to summarize the results of Monte Carlo simulations.

An imitation model based on the majority

In the voter model, agents possess binary opinions. At each time step, an agent is selected along with a social neighbor and adopts the opinion of that neighbor at the next time step. In this paper, we delve into a variant of the voter model known as an imitation model based on the majority. This model represents a network opinion framework where individuals, situated on the vertex set of a finite connected graph interpreted as a social network, exhibit one of two competing opinions labeled as +1 and −1. The agent alters its opinion solely when the count of social neighbors holding opposing viewpoints exceeds those aligning with the agent’s opinion. We explore the conditions leading to a consensus and investigate the probability of consensus on a finite connected social graph.

Phase Diagram for Social Impact Theory in Initially Fully Differentiated Society

The study of opinion formation and dynamics is one of the core topics in sociophysics. In this paper, the results of computer simulation of opinion dynamics based on social impact theory are presented. The simulations are based on Latané theory in its computerised version proposed by Nowak, Szamrej and Latané. The active parameters of the model describe the volatility of the actors (social temperature T) and the effective range of interaction (governed by an exponent α in a scaling function of distance between actors). Initially, every actor i has his/her own opinion. Our results indicate that ultimately at least 90% of the initial opinions available are removed from the society. For a low social temperature and a long range of interaction, only one opinion survives. Also, a rough sketch of the system phase diagram is presented. It indicates a set of (α,T) leading either to (1) the dominance of the unanimity of the opinions or (2) mixtures of unanimity and polarisation, or (3) taking random opinions by actors, or (4) a mixture of the final fates of the systems. The drastic reduction of finally observed opinions vs. their initial variety may be generic for many sociophysical models of opinions formation but masked by assuming an initially small pool of available opinions (in the worst case, in models with only binary opinions).

The effect of iterativity on adversarial opinion forming

Consider the following model to study adversarial effects on opinion forming. A set of initially selected experts form their binary opinion while being influenced by an adversary, who may convince some of them of the falsehood. All other participants in the network then take the opinion of the majority of their neighboring experts. Can the adversary influence the experts in such a way that the majority of the network believes the falsehood? Alon et al. [2] conjectured that in this context an iterative dissemination process will always be beneficial to the adversary. In this note we provide a counterexample to that conjecture.

Shifting from climate change denial to acceptance: a mixed-method, semester long case study in an undergraduate first-year experience course

Climate change denial is often treated as a binary opinion. However, an individual can express acceptance of climate change, while still denying other aspects of the field such as its causation by humans, impacts, or our ability to mitigate these impacts. Here, we conduct a semester long survey and discourse analysis of a class of first-year undergraduates as they complete a course on climate change to assess changes in their attitudes on climate denial verse acceptance across these more specific factors. Our results suggest that acceptance of the scientific facts about climate change is higher than acceptance of its impacts and solutions. However, acceptance that personal and societal changes can mitigate climate change increased throughout the term. These results can help create course curriculum with more effectively targeted content to assist in shifting perspectives on climate change in young undergraduates.

Ising model on clustered networks: A model for opinion dynamics

We study opinion dynamics on networks with a nontrivial community structure, assuming individuals can update their binary opinion as the result of the interactions with an external influence with strength $h\in [0,1]$ and with other individuals in the network. To model such dynamics, we consider the Ising model with an external magnetic field on a family of finite networks with a clustered structure. Assuming a unit strength for the interactions inside each community, we assume that the strength of interaction across different communities is described by a scalar $\epsilon \in [-1,1]$, which allows a weaker but possibly antagonistic effect between communities. We are interested in the stochastic evolution of this system described by a Glauber-type dynamics parameterized by the inverse temperature $\beta$. We focus on the low-temperature regime $\beta\rightarrow\infty$, in which homogeneous opinion patterns prevail and, as such, it takes the network a long time to fully change opinion. We investigate the different metastable and stable states of this opinion dynamics model and how they depend on the values of the parameters $\epsilon$ and $h$. More precisely, using tools from statistical physics, we derive rigorous estimates in probability, expectation, and law for the first hitting time between metastable (or stable) states and (other) stable states, together with tight bounds on the mixing time and spectral gap of the Markov chain describing the network dynamics. Lastly, we provide a full characterization of the critical configurations for the dynamics, i.e., those which are visited with high probability along the transitions of interest.

Can consumers understand that there is more to palm oil than deforestation?

Environmental factors, such as climate change, with an array of social conflicts from labour conditions to land rights continue to refocus the spotlight on palm oil. Often depicted alongside deforestation, habitat destruction and biodiversity loss, palm oil tends to be viewed critically, especially by societies in palm oil importing countries. Oil palm cultivation, when poorly managed, can have severe ecological effects. However, the fact that it is the highest yielding vegetable oil complicates discussions around palm oil. Even if all palm oil was replaced with the second highest yielding vegetable oil, soybean oil, a six-fold amount of land would be required to make ends meet. Aspects such as these are not often at the forefront of consumers' minds. Using an online survey, this paper explores what German consumers (n = 1220) associate with palm oil and what they know about the geography of its production. Building on this, we investigate how society deals with the concept of indirect land use change and the role that information can play in encouraging a move away from a binary (good/bad) opinion of palm oil, and instead towards one that considers both the indirect effects related to oil palm cultivation and the feasibility of alternatives. Results show that while the effect size for different variables varies, the provision of information can especially influence how individuals understand issues of indirect land use change. However, when comparing the perceived sustainability of certified palm oil to other vegetable oils, it does not fare much better. Hence, while information can be useful to raise awareness about specific aspects, it alone is generally insufficient to encourage deeper thinking related to the complexity of different sustainability dimensions compared to more readily understandable aspects such as biodiversity loss. These findings are salient as they highlight the risk that perceptions of vegetable oil sustainability may not be in keeping with actual environmental sustainability, whereby alternatives are more glorified than their reality. This is especially important when considering which vegetable oil is capable of continuing to supply our increasing demands while doing so in the most environmentally- and socially benign way possible.

Link updating strategies influence consensus decisions as a function of the direction of communication.

Consensus decision-making in social groups strongly depends on communication links that determine to whom individuals send, and from whom they receive, information. Here, we ask how consensus decisions are affected by strategic updating of links and how this effect varies with the direction of communication. We quantified the coevolution of link and opinion dynamics in a large population with binary opinions using mean-field numerical simulations of two voter-like models of opinion dynamics: an incoming model (IM) (where individuals choose who to receive opinions from) and an outgoing model (OM) (where individuals choose who to send opinions to). We show that individuals can bias group-level outcomes in their favour by breaking disagreeing links while receiving opinions (IM) and retaining disagreeing links while sending opinions (OM). Importantly, these biases can help the population avoid stalemates and achieve consensus. However, the role of disagreement avoidance is diluted in the presence of strong preferences-highly stubborn individuals can shape decisions to favour their preferences, giving rise to non-consensus outcomes. We conclude that collectively changing communication structures can bias consensus decisions, as a function of the strength of preferences and the direction of communication.

Multi-opinion Markovian agent networks: Parametrization, second order moment and social power

This paper extends the theory of Markovian multi-agent opinion networks, previously studied in the binary opinion case, to the situation of multiple opinions. The first step is the definition of a suitable canonical representation of a multi-state Markov chain, to describe the behavior of any non-interacting agent in terms of its prejudice. Based on this parametrization, the time evolution of both first- and second-order moments of the opinion shares when the agents are connected in a social network is completely characterized, both in transient and at steady-state. The steady-state analysis allows one to introduce an appropriate notion of marginal social power, measuring the sensitivity of the average network opinion to the agents’ prejudices.

Phase transitions in biased opinion dynamics with 2-choices rule

AbstractWe consider a model of binary opinion dynamics where one opinion is inherently “superior” than the other, and social agents exhibit a “bias” toward the superior alternative. Specifically, it is assumed that an agent updates its choice to the superior alternative with probability α > 0 irrespective of its current opinion and opinions of other agents. With probability $1-\alpha$, it adopts majority opinion among two randomly sampled neighbors and itself. We are interested in the time it takes for the network to converge to a consensus on the superior alternative. In a complete graph of size n, we show that irrespective of the initial configuration of the network, the average time to reach consensus scales as $\Theta(n\,\log n)$ when the bias parameter α is sufficiently high, that is, $\alpha \gt \alpha_c$ where αc is a threshold parameter that is uniquely characterized. When the bias is low, that is, when $\alpha \in (0,\alpha_c]$, we show that the same rate of convergence can only be achieved if the initial proportion of agents with the superior opinion is above certain threshold $p_c(\alpha)$. If this is not the case, then we show that the network takes $\Omega(\exp(\Theta(n)))$ time on average to reach consensus.

Patient Perspectives on Artificial Intelligence in Healthcare Decision Making: A Multi-Center Comparative Study.

Investigate the patient opinion on the use of Artificial Intelligence (AI) in Orthopaedics. 397 orthopaedic patients from a large urban academic center and a rural health system completed a 37-component survey querying patient demographics and perspectives on clinical scenarios involving AI. An average comfort score was calculated from thirteen Likert-scale questions (1, not comfortable; 10, very comfortable). Secondary outcomes requested a binary opinion on whether it is acceptable for patient healthcare data to be used to create AI (yes/no) and the impact of AI on: orthopaedic care (positive/negative); healthcare cost (increase/decrease); and their decision to refuse healthcare if cost increased (yes/no). Bivariate and multivariable analyses were employed to identify characteristics that impacted patient perspectives. The average comfort score across the population was 6.4, with significant bivariate differences between age (p = 0.0086), gender (p = 0.0001), education (p = 0.0029), experience with AI/ML (p < 0.0001), survey format (p < 0.0001), and four binary outcomes (p < 0.05). When controlling for age and education, multivariable regression identified significant relationships between comfort score and experience with AI/ML (p = 0.0018) and each of the four binary outcomes (p < 0.05). In the final multivariable model gender, survey format, perceived impact of AI on orthopaedic care, and the decision to refuse care if it were to increase cost remained significantly associated with the average AI comfort score (p < 0.05). Additionally, patients were not comfortable undergoing surgery entirely by a robot with distant physician supervision compared to close supervision. The orthopaedic patient appears comfortable with AI joining the care team.

Majority networks and local consensus algorithm

In this paper, we study consensus behavior based on the local application of the majority consensus algorithm (a generalization of the majority rule) over four-connected bi-dimensional networks. In this context, we characterize theoretically every four-vicinity network in its capacity to reach consensus (every individual at the same opinion) for any initial configuration of binary opinions. Theoretically, we determine all regular grids with four neighbors in which consensus is reached and in which ones not. In addition, in those instances in which consensus is not reached, we characterize statistically the proportion of configurations that reach spurious fixed points from an ensemble of random initial configurations. Using numerical simulations, we also analyze two observables of the system to characterize the algorithm: (1) the quality of the achieved consensus, that is if it respects the initial majority of the network; and (2) the consensus time, measured as the average amount of steps to reach convergence.

Disagreement and fragmentation in growing groups

The arise of disagreement is an emergent phenomenon that can be observed within a growing social group and, beyond a certain threshold, can lead to group fragmentation. To better understand how disagreement emerges, we introduce an analytically tractable model of group formation where individuals have multidimensional binary opinions and the group grows through a noisy homophily principle, i.e., like-minded individuals attract each other with exceptions occurring with some small probability. Assuming that the level of disagreement is correlated with the number of different opinions coexisting within the group, we find analytically and numerically that in growing groups disagreement emerges spontaneously regardless of how small the noise in the system is. Moreover, for groups of infinite size, fragmentation is inevitable. We also show that the model outcomes are robust under different group growth mechanisms.

From ‘tiaras and twirls’ to ‘action and adventure’. Eliciting children’s gendered perceptions of Disney characters through participatory visual methodology

ABSTRACT This study, based on interpretative phenomenological methodology, examines the influence Disney media and merchandise may have on children’s understandings of gender. Although there are various studies in this area, most focus on the Disney Princesses’ effects on girls’ gender development and few directly elicit the views of both girls and boys (Golden and Jacoby 2018). The current study attempts to address this gap by investigating how girls and boys, aged five to eight years, interpret messages circulated by Disney to make sense of the gendered norms and roles of its characters. Participatory visual methods used were a draw and talk exercise and an image-values line activity. Critical discourse analysis identified two key gender discourses: physical appearance and gendered behaviours, with children’s exclusionary binary opinions core to both. However, both boys and girls valued the more active traits portrayed by the contemporary princesses. Through adopting a feminist poststructuralist lens, this study contributes to the existing body of knowledge that informs of ways to deconstruct stereotypes with children to promote positive gender development in childhood.

Diffusion of binary opinions in a growing population with heterogeneous behaviour and external influence

&lt;abstract&gt;&lt;p&gt;We consider a growing population of individuals with binary opinions, namely, 0 or 1, that evolve in discrete time. The underlying interaction network is complete. At every time step, a fixed number of individuals are added to the population. The opinion of the new individuals may or may not depend on the current configuration of opinions in the population. Further, in each time step, a fixed number of individuals are chosen and they update their opinion in three possible ways: they organically switch their opinion with some probability and with some probability they adopt the majority or the minority opinion. We study the asymptotic behaviour of the fraction of individuals with either opinion and characterize conditions under which it converges to a deterministic limit. We analyze the behaviour of the limiting fraction as a function of the probability of new individuals having opinion 1 as well as with respect to the ratio of the number of people being added to the population and the number of people being chosen to update opinions. We also discuss the nature of fluctuations around the limiting fraction and study the transitions in scaling depending on the system parameters. Further, for this opinion dynamics model on a finite time horizon, we obtain optimal external influencing strategies in terms of when to influence to get the maximum expected fraction of individuals with opinion 1 at the end of the finite time horizon.&lt;/p&gt;&lt;/abstract&gt;

Multiscale voter model on real networks

We introduce the Multiscale Voter Model (MVM) to investigate clan influence at multiple scales—family, neighborhood, political party…—in opinion formation on real complex networks. Clans, consisting of similar nodes, are constructed using a coarse-graining procedure on network embeddings that allows us to control for the length scale of interactions. We ran numerical simulations to monitor the evolution of MVM dynamics in real and synthetic networks, and identified a transition between a final stage of full consensus and one with mixed binary opinions. The transition depends on the scale of the clans and on the strength of their influence. We found that enhancing group diversity promotes consensus while strong kinship yields to metastable clusters of same opinion. The segregated domains, which signal opinion polarization, are discernible as spatial patterns in the hyperbolic embeddings of the networks. Our multiscale framework can be easily applied to other dynamical processes affected by scale and group influence.

Game-theoretical approach for opinion dynamics on social networks.

Opinion dynamics on social networks have received considerable attentions in recent years. Nevertheless, just a few works have theoretically analyzed the condition in which a certain opinion can spread in the whole structured population. In this article, we propose an evolutionary game approach for a binary opinion model to explore the conditions for an opinion's spreading. Inspired by real-life observations, we assume that an agent's choice to select an opinion is not random but is based on a score rooted from both public knowledge and the interactions with neighbors. By means of coalescing random walks, we obtain a condition in which opinion A can be favored to spread on social networks in the weak selection limit. We find that the successfully spreading condition of opinion A is closely related to the basic scores of binary opinions, the feedback scores on opinion interactions, and the structural parameters including the edge weights, the weighted degrees of vertices, and the average degree of the network. In particular, when individuals adjust their opinions based solely on the public information, the vitality of opinion A depends exclusively on the difference of basic scores of A and B. When there are no negative (positive) feedback interactions between connected individuals, we find that the success of opinion A depends on the ratio of the obtained positive (negative) feedback scores of competing opinions. To complete our study, we perform computer simulations on fully connected, small-world, and scale-free networks, respectively, which support and confirm our theoretical findings.