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The formulation and numerical scheme for solving the problem of filtering estimates of the informational impact of mass media on the electorate, allowing with a high degree of accuracy at a given observation interval to estimate the number of individuals in society who prefer a certain political subject (opinion), are proposed in the article. A mathematical model for assessing the information impact on the electorate during election campaigns, which boils down to solving a stochastic differential equation – the equation of state, forms the basis of the formulation of the problem. When compiling a model for filtering information impact estimates, it is proposed to reduce the study of the equation of state to a numerical solution of the Duncan–Mortensen–Zakai equation by introducing an additional observation equation, which is obtained from the equation of state when evaluating its stochastic components (observed agitation intensities) by methods of polyspectral analysis. In the projection formulation of the Galerkin method, when reducing to a system of linear differential equations and obtaining its solution in a recursive estimation scheme when sampling the analysis interval into subintervals and using the matrix exponential method, the Duncan–Mortensen–Zakai equation is solved. For a visual comparison of the effectiveness of the generated numerical solution to the problem of filtering information impact assessments, calculations were carried out on test examples.

This paper introduces a constructive definition of an informational community, which agrees with formal models of opinion dynamics for bounded rational agents in social networks. As is shown below, uncertainty can be taken into account when detecting informational communities. An example of a stable informational community is given. A control problem for informational communities is stated, and its solution is presented within the DeGroot model.

Many micro-level models of information processes in social networks consider either a change in the information-psychological state of agents (opinions, beliefs, attitudes) or a change in their observable behavior (actions). The goal in this paper is to develop and analyze a complex agent-based model of opinion dynamics that describes the dynamics of agents’ beliefs and the process of performing actions by agents. The issues of reaching consensus and polarizing opinions of agents are investigated.

The flow of information reaching us via the online media platforms is optimized not by the information content or relevance but by popularity and proximity to the target. This is typically performed in order to maximise platform usage. As a side effect, this introduces an algorithmic bias that is believed to enhance polarization of the societal debate. To study this phenomenon, we modify the well-known continuous opinion dynamics model of bounded confidence in order to account for the algorithmic bias and investigate its consequences. In the simplest version of the original model the pairs of discussion participants are chosen at random and their opinions get closer to each other if they are within a fixed tolerance level. We modify the selection rule of the discussion partners: there is an enhanced probability to choose individuals whose opinions are already close to each other, thus mimicking the behavior of online media which suggest interaction with similar peers. As a result we observe: a) an increased tendency towards polarization, which emerges also in conditions where the original model would predict convergence, and b) a dramatic slowing down of the speed at which the convergence at the asymptotic state is reached, which makes the system highly unstable. Polarization is augmented by a fragmented initial population.

Both classical social psychological theories and recent formal models of opinion differentiation and bi-polarization assign a prominent role to negative social influence. Negative influence is defined as shifts away from the opinion of others and hypothesized to be induced by discrepancy with or disliking of the source of influence. There is strong empirical support for the presence of positive social influence (a shift towards the opinion of others), but evidence that large opinion differences or disliking could trigger negative shifts is mixed. We examine positive and negative influence with controlled exposure to opinions of other individuals in one experiment and with opinion exchange in another study. Results confirm that similarities induce attraction, but results do not support that discrepancy or disliking entails negative influence. Instead, our findings suggest a robust positive linear relationship between opinion distance and opinion shifts.

By a simple extension of the bounded confidence model, it is possible to model the in uence of a radical group, or a charismatic leader on the opinion dynamics of 'normal' agents that update their opinions under both, the in uence of their normal peers, and the additional in uence of the radical group or a charismatic leader. From a more abstract point of view, we model the in uence of a signal, that is constant, may have different intensities, and is 'heard' only by agents with opinions, that are not too far away. For such a dynamic a Constant Signal Theorem is proven. In the model we get a lot of surprising effects. For instance, the more intensive signal may have less effect; more radicals may lead to less radicalization of normal agents. The model is an extremely simple conceptual model. Under some assumptions the whole parameter space can be analyzed. The model inspires new possible explanations, new perspectives for empirical studies, and new ideas for prevention or intervention policies.

Unlike many complex networks studied in the literature, social networks
rarely exhibit regular unanimous behavior, or consensus of opinions. This
requires a development of mathematical models that are sufficiently simple to
be examined and capture, at the same time, the complex behavior of real social
groups, where opinions and the actions related to them may form clusters of
different sizes. One such model, proposed in [1], deals with scalar opinions
and extends the idea in [2] of iterative pooling to take into account the
actors' prejudices, caused by some exogenous factors and leading to
disagreement in the final opinions. In this paper, we offer a novel
multidimensional extension, which represents the dynamics of agents' opinions
on several topics, and those topic-specific opinions are interdependent. As
soon as opinions on several topics are affected simultaneously by the same
influence networks, they automatically become related. However, we introduce an
additional relation, interdependent topics, by which the opinions being formed
on one topic are functions of the opinions held on other topics. We examine
rigorous convergence properties of the proposed model and find explicitly the
steady opinions of the agents. Although our model assumes synchronous
communication among the agents, we show that the same final opinion may be
reached "on average" via asynchronous gossip-based protocols.

In a consensus protocol an agreement among agents is achieved thanks to the collaborative efforts of all agents, expresses by a communication graph with nonnegative weights. The question we ask in this paper is the following: is it possible to achieve a form of agreement also in presence of antagonistic interactions, modeled as negative weights on the communication graph? The answer to this question is affirmative: on signed networks all agents can converge to a consensus value which is the same for all agents except for the sign. Necessary and sufficient conditions are obtained to describe cases in which this is possible. These conditions have strong analogies with the theory of monotone systems. Linear and nonlinear Laplacian feedback designs are proposed.

We present a model of opinion dynamics where agents adjust continuous opinions on the occasion of random binary encounters whenever their difference in opinion is below a given threshold. High thresholds yield convergence of opinions towards an average opinion, but low thresholds result in several opinion clusters: members of the same cluster share the same opinion but do not adjust any more with members of other clusters.

This article uses data from the American National Election Studies and national exit polls to test Fiorina's assertion that ideological polarization in the American public is a myth. Fiorina argues that twenty-first-century Americans, like the midtwentieth-century Americans described by Converse, “are not very well-informed about politics, do not hold many of their views very strongly, and are not ideological” (2006, 19). However, our evidence indicates that since the 1970s, ideological polarization has increased dramatically among the mass public in the United States as well as among political elites. There are now large differences in outlook between Democrats and Republicans, between red state voters and blue state voters, and between religious voters and secular voters. These divisions are not confined to a small minority of activists—they involve a large segment of the public and the deepest divisions are found among the most interested, informed, and active citizens. Moreover, contrary to Fiorina's suggestion that polarization turns off voters and depresses turnout, our evidence indicates that polarization energizes the electorate and stimulates political participation.

This paper focuses at the dynamics of attitude change in large groups. A multi-agent computer simulation has been developed as a tool to study hypothesis we take to study these dynamics. A major extension in comparison to earlier models is that Social Judgment Theory is being formalized to incorporate processes of assimilation and contrast in persuasion processes. Results demonstrate that the attitude structure of agents determines the occurrence of assimilation and contrast effects, which in turn cause a group of agents to reach consensus, to bipolarize, or to develop a number of subgroups sharing the same position. Subsequent experiments demonstrate the robustness of these effects for a different formalization of the social network, and the susceptibility for population size.

When does opinion formation within an interacting group lead to consensus, polarization or fragmentation? The article investigates various models for the dynamics of continuous opinions by analytical methods as well as by computer simulations. Section 2 develops within a unified framework the classical model of consensus formation, the variant of this model due to Friedkin and Johnsen, a time-dependent version and a nonlinear version with bounded confidence of the agents. Section 3 presents for all these models major analytical results. Section 4 gives an extensive exploration of the nonlinear model with bounded confidence by a series of computer simulations. An appendix supplies needed mathematical definitions, tools, and theorems.

Suppose that the authors are interested in the distribution of a set of characteristics over a population. They study a precise sense in which this distribution can be said to be polarized and provide a theory of measurement. Polarization, as conceptualized here, is closely related to the generation of social tensions, to the possibilities of revolution and revolt, and to the existence of social unrest in general. The authors take special care to distinguish their theory from the theory of inequality measurement. They derive measures of polarization that are easily applicable to distributions of characteristics such as income and wealth. Copyright 1994 by The Econometric Society.

In this paper, a rigorous mathematical analysis of the Krasnoshchekov model is presented. We have shown that in case a community does not contain any group of people having zero resistance to interpersonal influence, which are moreover isolated from the pressure of the rest of community, the Krasnoshchekov opinion readjustment procedure can be reduced to the Friedkin–Johnsen dynamics. In turn, if one repeats the Krasnoshchekov opinion updating rule, the corresponding dynamics forces individuals’ opinions to converge eventually to some terminal opinions, which are a consensus under the same conditions as in the French–Harary–DeGroot dynamics. Otherwise, the Krasnoshchekov dynamics exhibits patterns, which are much closer to the behavior of electrons in the superconductivity state.

[ I ALWAYS SHARE REQUESTED PAPERS ]
Studies concerning social patterns that appear as a result of propaganda and rumors generally tend to neglect considerations of
the behavior of individuals that constitute these patterns. This places obvious limitations upon the scope of research. We propose a dynamical model for the mechanics of the processes of polarization and formation
of echo chambers. This model is based on the Rashevsky neurological
scheme of decision-making

This paper considers an extension of the actional model of influence in online social networks. Within the framework of this model, the influence and influence levels of separate agents (users) and meta-agents (subsets of users) are calculated on the basis of their actions taking into account the goals of a control subject (a Principal). We study some properties of the influence function. An example illustrates how the actional model can be used to calculate the influence levels of users in a concrete social network under available initial data.

Breakthroughs have been made in algorithmic approaches to understanding how individuals in a group influence each other to reach a consensus. However, what happens to the group consensus if it depends on several statements, one of which is proven false? Here, we show how the existence of logical constraints on beliefs affect the collective convergence to a shared belief system and, in contrast, how an idiosyncratic set of arbitrarily linked beliefs held by a few may become held by many. © 2016, American Association for the Advancement of Science. All rights reserved.

This paper introduces a constructive approach to online social networks analysis. We suggest a conceptual model of a social network, formulate major problems of analysis and control in social networks, describe methods and algorithms for activity analysis in social networks, as well as technologies for social networks monitoring and analysis.

Reaching a consensus

- M H De Groot

Social Networks: Models of Information Influence, Control and Confrontation

- A G Chkhartishvili
- D A Gubanov
- D A Novikov

On the evaluation of a symmetry of political views and polarization of society

- F T Aleskerov
- M A Golubenko

Polarization in 2016

- M Gentzkow