Discrete Opinion Research Articles

How Does a Minority Opinion Spread?

In this paper, we propose a discrete opinion model in which two beliefs models compete. One opinion is endorsed bythe vast majority of agents, but this majority remains silent and rarely expresses its opinion. Conversely, the other beliefmodel is supported by a small minority that is very committed and does not hesitate to be loud. We observe that a very smallnumber of individuals is necessary for the minority opinion to become the majority. However, the presence of so-called ”inflexible” and ”super propagators” agents can counteract this phenomenon and prevent the loud minority from propagatingits view.

Mesoscopic analytical approach in a three state opinion model with continuous internal variable

Analytical approaches in models of opinion formation have been extensively studied either for an opinion represented as a discrete or a continuous variable. In this paper, we analyze a model which combines both approaches. The state of an agent is represented with an internal continuous variable (the leaning or propensity), that leads to a discrete public opinion: pro, against or neutral. This model can be described by a set of master equations which are a nonlinear coupled system of first order differential equations of hyperbolic type including non-local terms and non-local boundary conditions, which cannot be solved analytically. We developed an approximation to tackle this difficulty by deriving a set of master equations for the dynamics of the average leaning of agents with the same opinion, under the hypothesis of a time scale separation in the dynamics of the variables. We show that this simplified model accurately predicts the expected transition between a neutral consensus and a bi-polarized state, and also gives an excellent approximation for the dynamics of the average leaning of agents with the same opinion, even when the time separation scale hypothesis is not completely fulfilled.

AI in breast screening mammography: breast screening readers' perspectives.

This study surveyed the views of breast screening readers in the UK on how to incorporate Artificial Intelligence (AI) technology into breast screening mammography. An online questionnaire was circulated to the UK breast screening readers. Questions included their degree of approval of four AI implementation scenarios: AI as triage, AI as a companion reader/reader aid, AI replacing one of the initial two readers, and AI replacing all readers. They were also asked to rank five AI representation options (discrete opinion; mammographic scoring; percentage score with 100% indicating malignancy; region of suspicion; heat map) and indicate which evidence they considered necessary to support the implementation of AI into their practice among six options offered. The survey had 87 nationally accredited respondents across the UK; 73 completed the survey in full. Respondents approved of AI replacing one of the initial two human readers and objected to AI replacing all human readers. Participants were divided on AI as triage and AI as a reader companion. A region of suspicion superimposed on the image was the preferred AI representation option. Most screen readers considered national guidelines (77%), studies using a nationally representative dataset (65%) and independent prospective studies (60%) as essential evidence. Participants' free-text comments highlighted concerns and the need for additional validation. Overall, screen readers supported the introduction of AI as a partial replacement of human readers and preferred a graphical indication of the suspected tumour area, with further evidence and national guidelines considered crucial prior to implementation.

Non-equilibrium kinetic Biswas–Chatterjee–Sen model on complex networks

The phase transition of a discrete version of the non-equilibrium Biswas–Chatterjee–Sen model, defined on Erdös–Rényi random graphs (ERRGs) and directed ERRGs random graphs (DERRGs), has been studied. The mutual interactions (or affinities) can be both positive and negative, depending on the noise parameter value. Through extensive Monte Carlo simulations and finite-size scaling analysis, the continuous phase transitions and the corresponding critical exponent ratios have been obtained for several values of the average connectivity z. The effective dimensionality of the system has been found to be Deff≈1.0 for all values of z, which is similar to the one obtained on Barabási–Albert networks. The present results show that kinetic models of discrete opinion dynamics belong to a different universality class as the corresponding equilibrium Ising and Potts, and non-equilibrium majority-vote models on the same ERRGs and DERRGs. It is also noticed that the kinetic model here studied on ERRGs and DERRGs is in different universality classes for connectivities z<20, while for z≥20 the critical exponents are the same for both random graphs.

An opinion dynamics model for unrelated discrete opinions

Unrelated discrete opinions can be generally found in social media-based data about a certain topic, which cannot be well measured and analyzed using existing opinion dynamics models. To fill this gap, this study proposes a new discrete opinion dynamics model based on the sentiment–opinion transformation mechanism. In the model, a matrix formulating the transformation relationship between sentiments and opinions is considered. In addition, the model is initialized based on an initial-sentiment matrix of the information instead of a certain mathematical distribution. Subsequently, we design the simulation experiments using different values of parameters and different network topologies to study four effects on sentiment and opinion dynamics, namely, the effects of the threshold, the effects of the initial-sentiment matrix, the effects of the sentiment–opinion matrix, and the effects of the second piece of information. The results highlight the importance of transformation relation between sentiment and opinion.

Consensus from group interactions: An adaptive voter model on hypergraphs.

We study the effect of group interactions on the emergence of consensus in a spin system. Agents with discrete opinions {0,1} form groups. They can change their opinion based on their group's influence (voter dynamics), but groups can also split and merge (adaptation). In a hypergraph, these groups are represented by hyperedges of different sizes. The heterogeneity of group sizes is controlled by a parameter β. To study the impact of β on reaching consensus, we provide extensive computer simulations and compare them with an analytic approach for the dynamics of the average magnetization. We find that group interactions amplify small initial opinion biases, accelerate the formation of consensus, and lead to a drift of the average magnetization. The conservation of the initial magnetization, known for basic voter models, is no longer obtained.

Modeling the nonlinear effects of opinion kinematics in elections: A simple Ising model with random field based study

Inspired by partisan competitions and contentious elections in democratic countries, we numerically explore the effect of campaign strategies and related factors on the opinion of an electorate. The nature of the electorate is modeled through agents with different behaviors, such as, being conformist, contrarian or inflexible. The agents are assumed to take discrete opinion values that depend on both internal and external influences. The inhomogeneity of external influence on individuals is modeled as a random field. Two types of electorates have been considered. In an electorate with only conformist agents short-duration high impact campaigns are highly effective. These are, however, also sensitive to perturbations at the local level modeled as inflexibles and/or absentees. In electorates with both conformist and contrarian agents and varying level of dominance due to local factors, short-term campaigns are effective only in the case of fragile dominance of a single party. Strong local dominance is relatively difficult to influence and long term campaigns with strategies aimed to impact local level politics are seen to be more effective.

Phase Transition in the Social Impact Model of Opinion Formation in Log-Normal Networks

People may change their opinions as a consequence of interacting with others. In the literature, this phenomenon is expressed as opinion formation and has a wide range of applications, including predicting social movements, predicting political voting results, and marketing. The interactions could be face-to-face or via online social networks. The social opinion phases are categorized into consensus, majority, and non-majority. In this research, we study phase transitions due to interactions between connected people with various noise levels using agent-based modeling and a computational social science approach. Two essential factors affect opinion formations: the opinion formation model and the network topology. We assumed the social impact model of opinion formation, a discrete binary opinion model, appropriate for both face-to-face and online interactions for opinion formation. For the network topology, scale-free networks have been widely used in many studies to model real social networks, while recent studies have revealed that most social networks fit log-normal distributions, which we considered in this study. Therefore, the main contribution of this study is to consider the log-normal distribution network topology in phase transitions in the social impact model of opinion formation. The results reveal that two parameters affect the phase transition: noise level and segregation. A non-majority phase happens in equilibrium in high enough noise level, regardless of the network topology, and a majority phase happens in equilibrium in lower noise levels. However, the segregation, which depends on the network topology, affects opinion groups’ population. A comparison with the scale-free network topology shows that in the scale-free network, which have a more segregated topology, resistance of segregated opinion groups against opinion change causes a slightly different phase transition at low noise levels. EI (External-Internal) index has been used to measure segregations, which is based on the difference between between-group (External) links and within-group (Internal) links.

Non-equilibrium BCS model on Apollonian networks

We study the phase transition in a discrete opinion dynamics model on an Apollonian network, where mutual interactions can be both positive and negative depending on the noise parameter q. We have characterized the critical exponents of the phase transitions through the Monte Carlo simulations and finite-size scaling analysis. Our finds attest that different from the equilibrium models, such as Ising and Potts on Apollonian network that do not present phase transition, the kinetic model report does. Moreover, we have included one additional aspect on the Apollonian network, the effect of redirecting a fraction of p of the network’s links. On this redirected network, we obtained the exponents ratio β∕ν, γ∕ν, and 1∕ν for several values of rewiring probability p. Similar to this model’s results on free-scale networks, the effective dimensionality of the system found was Deff≈1.0 for all values of p. The results presented here demonstrate that kinetic models of discrete opinion dynamics belong to a different universality class as the equilibrium Ising Model on Apollonian networks. It is noticed that the kinetic model study here and the majority-vote model on Apollonian networks are in the same universality class, for a rewiring probability lower than 0.5. Above p=0.5, the critical exponents are different from those found in the majority-vote model on Apollonian networks.

A Survey on Nonstrategic Models of Opinion Dynamics

The paper presents a survey on selected models of opinion dynamics. Both discrete (more precisely, binary) opinion models as well as continuous opinion models are discussed. We focus on frameworks that assume non-Bayesian updating of opinions. In the survey, a special attention is paid to modeling nonconformity (in particular, anticonformity) behavior. For the case of opinions represented by a binary variable, we recall the threshold model, the voter and q-voter models, the majority rule model, and the aggregation framework. For the case of continuous opinions, we present the DeGroot model and some of its variations, time-varying models, and bounded confidence models.

Block size dependence of coarse graining in discrete opinion dynamics model: Application to the US presidential elections

The electoral college of voting system for the US presidential election is analogous to a coarse graining procedure commonly used to study phase transitions in physical systems. In a recent paper, opinion dynamics models manifesting a phase transition, were shown to be able to explain the cases when a candidate winning more number of popular votes could still lose the general election on the basis of the electoral college system. We explore the dependence of such possibilities on various factors like the number of states and total population (i.e., system sizes) and get an interesting scaling behavior. In comparison with the real data, it is shown that the probability of the minority win, calculated within the model assumptions, is indeed near the highest possible value. In addition, we also implement a two step coarse graining procedure, relevant for both opinion dynamics and information theory.

Discrete opinion dynamics with M choices

Here, I study how to obtain an opinion dynamics model for the case where there are $M$ possible discrete choices and there is need to model how strong each agent choice is. The new model is obtained as an extension of the Continuous Opinions and Discrete Actions (CODA) model. Technical difficulties with the choice of proper variables for a simple model are solved. For the symmetrical case, a dimensionless model is found. However, when analyzing the results, a change of variables seems to be required for ease of interpretation. Extremism is observed here as well, generated by the local reinforcement of opinions inside domains of agents with the same choice.

Kinetic Models of Discrete Opinion Dynamics on Directed Barabási–Albert Networks

Kinetic models of discrete opinion dynamics are studied on directed Barabási–Albert networks by using extensive Monte Carlo simulations. A continuous phase transition has been found in this system. The critical values of the noise parameter are obtained for several values of the connectivity of these directed networks. In addition, the ratio of the critical exponents of the order parameter and the corresponding susceptibility to the correlation length have also been computed. It is noticed that the kinetic model and the majority-vote model on these directed Barabási–Albert networks are in the same universality class.

Consensus emerging from the bottom-up: the role of cognitive variables in opinion dynamics

The study of opinions $-$ e.g., their formation and change, and their effects on our society $-$ by means of theoretical and numerical models has been one of the main goals of sociophysics until now, but it is one of the defining topics addressed by social psychology and complexity science. Despite the flourishing of different models and theories, several key questions still remain unanswered. The aim of this paper is to provide a cognitively grounded computational model of opinions in which they are described as mental representations and defined in terms of distinctive mental features. We also define how these representations change dynamically through different processes, describing the interplay between mental and social dynamics of opinions. We present two versions of the model, one with discrete opinions (voter model-like), and one with continuous ones (Deffuant-like). By means of numerical simulations, we compare the behaviour of our cognitive model with the classical sociophysical models, and we identify interesting differences in the dynamics of consensus for each of the models considered.

Modeling and Simulation of Polarization in Internet Group Opinions Based on Cellular Automata

Hot events on Internet always attract many people who usually form one or several opinion camps through discussion. For the problem of polarization in Internet group opinions, we propose a new model based on Cellular Automata by considering neighbors, opinion leaders, and external influences. Simulation results show the following: (1) It is easy to form the polarization for both continuous opinions and discrete opinions when we only consider neighbors influence, and continuous opinions are more effective in speeding the polarization of group. (2) Coevolution mechanism takes more time to make the system stable, and the global coupling mechanism leads the system to consensus. (3) Opinion leaders play an important role in the development of consensus in Internet group opinions. However, both taking the opinion leaders as zealots and taking some randomly selected individuals as zealots are not conductive to the consensus. (4) Double opinion leaders with consistent opinions will accelerate the formation of group consensus, but the opposite opinions will lead to group polarization. (5) Only small external influences can change the evolutionary direction of Internet group opinions.

Discrete opinion models as a limit case of the CODA model

Opinion Dynamics models can be, for most of them, divided between discrete and continuous. They are used in different circumstances and the relationship between them is not clear. Here we will explore the relationship between a model where choices are discrete but opinions are a continuous function (the Continuous Opinions and Discrete Actions, CODA, model) and traditional discrete models. I will show that, when CODA is altered to include reasoning about the influence one agent can have on its own neighbors, agreement and disagreement no longer have the same importance. The limit when an agent considers itself to be more and more influent will be studied and we will see that one recovers discrete dynamics, like those of the voter model in that limit.

DYNAMICS OF DISCRETE OPINIONS WITHOUT COMPROMISE

A new agent-based, bounded-confidence model for discrete one-dimensional opinion dynamics is presented. The agents interact if their opinions do not differ by more than a tolerance parameter. In pairwise interactions, one of the pair, randomly selected, converts to the opinion of the other. The model can be used to simulate cases where no compromise is possible, such as choices of substitute goods, or other exclusive choices. The homogeneous case with maximum tolerance is equivalent to the Gambler's Ruin problem. A homogeneous system always ends up in an absorbing state, which can have one or more surviving opinions. An upper bound for the final number of opinions is given. The distribution of absorption times fits the generalized extreme value distribution. The diffusion coefficient of an opinion increases linearly with the number of opinions within the tolerance parameter. A general master equation and specific Markov matrices are given. The software code developed for this study is provided as a supplement.

Opinion Dynamics with Disagreement and Modulated Information

Opinion dynamics concerns social processes through which populations or groups of individuals agree or disagree on specific issues. As such, modelling opinion dynamics represents an important research area that has been progressively acquiring relevance in many different domains. Existing approaches have mostly represented opinions through discrete binary or continuous variables by exploring a whole panoply of cases: e.g. independence, noise, external effects, multiple issues. In most of these cases the crucial ingredient is an attractive dynamics through which similar or similar enough agents get closer. Only rarely the possibility of explicit disagreement has been taken into account (i.e., the possibility for a repulsive interaction among individuals' opinions), and mostly for discrete or 1-dimensional opinions, through the introduction of additional model parameters. Here we introduce a new model of opinion formation, which focuses on the interplay between the possibility of explicit disagreement, modulated in a self-consistent way by the existing opinions' overlaps between the interacting individuals, and the effect of external information on the system. Opinions are modelled as a vector of continuous variables related to multiple possible choices for an issue. Information can be modulated to account for promoting multiple possible choices. Numerical results show that extreme information results in segregation and has a limited effect on the population, while milder messages have better success and a cohesion effect. Additionally, the initial condition plays an important role, with the population forming one or multiple clusters based on the initial average similarity between individuals, with a transition point depending on the number of opinion choices.

Role of conviction in nonequilibrium models of opinion formation

We analyze the critical behavior of a class of discrete opinion models in the presence of disorder. Within this class, each agent opinion takes a discrete value (± 1 or 0) and its time evolution is ruled by two terms, one representing agent-agent interactions and the other the degree of conviction or persuasion (a self-interaction). The mean-field limit, where each agent can interact evenly with any other, is considered. Disorder is introduced in the strength of both interactions, with either quenched or annealed random variables. With probability p (1-p), a pairwise interaction reflects a negative (positive) coupling, while the degree of conviction also follows a binary probability distribution (two different discrete probability distributions are considered). Numerical simulations show that a nonequilibrium continuous phase transition, from a disordered state to a state with a prevailing opinion, occurs at a critical point p(c) that depends on the distribution of the convictions, with the transition being spoiled in some cases. We also show how the critical line, for each model, is affected by the update scheme (either parallel or sequential) as well as by the kind of disorder (either quenched or annealed).

Connections between the Sznajd model with general confidence rules and graph theory

The Sznajd model is a sociophysics model that is used to model opinion propagation and consensus formation in societies. Its main feature is that its rules favor bigger groups of agreeing people. In a previous work, we generalized the bounded confidence rule in order to model biases and prejudices in discrete opinion models. In that work, we applied this modification to the Sznajd model and presented some preliminary results. The present work extends what we did in that paper. We present results linking many of the properties of the mean-field fixed points, with only a few qualitative aspects of the confidence rule (the biases and prejudices modeled), finding an interesting connection with graph theory problems. More precisely, we link the existence of fixed points with the notion of strongly connected graphs and the stability of fixed points with the problem of finding the maximal independent sets of a graph. We state these results and present comparisons between the mean field and simulations in Barabási-Albert networks, followed by the main mathematical ideas and appendices with the rigorous proofs of our claims and some graph theory concepts, together with examples. We also show that there is no qualitative difference in the mean-field results if we require that a group of size q>2, instead of a pair, of agreeing agents be formed before they attempt to convince other sites (for the mean field, this would coincide with the q-voter model).