Opinion dynamics and social influence
How do agents change their opinions dependent on external influences or the opinion of others? In contrast to strategies in game theory which are characterized by a payoff dependent on the strategic choice of the counterparty, opinions are assumed to have no intrinsic value. Hence, the emergence of collective opinions in a multiagent system is the question of interest. In most cases, the formation of (partial) consensus among agents can lead to such collective opinions. Noticeably, different collective opinions can coexist, for example as opinions of a majority and a minority, or in different spatial domains. Studying formal multiagent models, we are mostly interested in the interaction rules between agents which may foster the emergence of consensus. Two model classes are analysed based on either binary opinions (voter models), or continuous opinions (bounded confidence models). Interactions between agents are restricted either to their neighborhood, or to agents with sufficiently similar opinions. We have proposed different mechanisms to enhance consensus formation, for example by considering the influence of the social network or other forms of local neighborhoods, by nonlinear response to the opinion of others, or by considering the agents heterogeneity. Particular emphasis was on the role of social influence, where agents became subject to the opinons of others in different ways. While social influence not necessarily hampers the formation of consensus, it can lead to the convergence to opinions that are far from the true value as investigations of the wisdom of crowds show.
Dissonance minimization as a microfoundation of social influence in models of opinion formation

[2014]

Groeber, Patrick;
Lorenz, Jan;
Schweitzer, Frank

The Journal of Mathematical Sociology,
pages: 147174,
volume: 38,
number: 3

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Abstract Models of opinion formation are used to investigate many collective phenomena. While social influence often constitutes a basic mechanism, its implementation differs between the models. In this paper, we provide a general framework of social influence inspired by the social psychological concept of cognitive dissonance.We only premise that individuals strive to minimize dissonance resulting from different opinions compared to neighbor individuals in a given social network. Within a game theoretic context, we show that our concept of dissonance reduction exhibits the basic properties of a coordination process. We further show that different models of opinion formation can be represented as best response dynamics within our general framework. Thus, we offer a unifying perspective on heterogeneous models and link them to rational choice theory.
Quantifying the effects of social influence

[2013]

Mavrodiev, Pavlin;
Tessone, Claudio Juan;
Schweitzer, Frank

Scientific Reports,
volume: 3,
number: 1360

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Abstract How do humans respond to indirect social influence when making decisions? We analysed an experiment where subjects had to repeatedly guess the correct answer to factual questions, while having only aggregated information about the answers of others. While the response of humans to aggregated information is a widely observed phenomenon, it has not been investigated quantitatively, in a controlled setting. We found that the adjustment of individual guesses depends linearly on the distance to the mean of all guesses. This is a remarkable, and yet surprisingly simple, statistical regularity. It holds across all questions analysed, even though the correct answers differ in several orders of magnitude. Our finding supports the assumption that individual diversity does not affect the response to indirect social influence. It also complements previous results on the nonlinear response in informationrich scenarios. We argue that the nature of the response to social influence crucially changes with the level of information aggregation. This insight contributes to the empirical foundation of models for collective decisions under social influence.
Measuring cultural dynamics through the Eurovision song contest

[2013]

Garcia, David;
Tanase, Dorian

ACS  Advances in Complex Systems,
pages: 33,
volume: 16,
number: 8

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Abstract Measuring culture and its dynamics through surveys has important limitations, but the emerging eld of computational social science allows us to overcome them by analyzing largescale datasets. In this article, we study cultural dynamics through the votes in the Eurovision song contest, which are decided by a crowdbased scheme in which viewers vote through mobile phone messages. Taking into account asymmetries and imperfect perception of culture, we measure cultural relations among European countries in terms of cultural anity. We propose the FriendorFoe coecient, a metric to measure voting biases among participants of a Eurovision contest. To validate how this metric represent cultural anity, we designed a model of a random, biased Eurovision contest. Simulations of this model show how our metrics can detect negative anities and serve as an estimator for positive anities. We apply this estimator to the historical set of Eurovision contests from 1975 to 2012, nding patterns of asymmetry and clustering in the resulting networks. Furthermore, we dene a measure of vote polarization that, when applied to empirical data, shows a sharp increase within countries of the EU during 2010 and 2011. As a result, we measure how the recent political decisions of EU states inuence the way their citizens relate to the culture of other EU members, leading to stronger cultural biases in the way they vote in the Eurovision song contest.
Enhancing consensus under opinion bias by means of hierarchical decision making

[2013]

Perony, Nicolas;
Pfitzner, Rene;
Scholtes, Ingo;
Tessone, Claudio Juan;
Schweitzer, Frank

ACS  Advances in Complex Systems,
pages: 1350020,
volume: 16

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Abstract We study the role of hierarchical structures in a simple model of collective consensus formation based on the bounded confidence model with continuous individual opinions. For the particular variation of this model considered in this paper, we assume that a bias towards an extreme opinion is introduced whenever two individuals interact and form a common decision. As a simple proxy for hierarchical social structures, we introduce a twostep decision making process in which in the second step groups of likeminded individuals are replaced by representatives once they have reached local consensus, and the representatives in turn form a collective decision in a downstream process. We find that the introduction of such a hierarchical decision making structure can improve consensus formation, in the sense that the eventual collective opinion is closer to the true average of individual opinions than without it. In particular, we numerically study how the size of groups of likeminded individuals being represented by delegate individuals affects the impact of the bias on the final populationwide consensus. These results are of interest for the design of organisational policies and the optimisation of hierarchical structures in the context of group decision making.
Hierarchical consensus formation reduces the influence of opinion bias

[2012]

Perony, Nicolas;
Pfitzner, Rene;
Scholtes, Ingo;
Schweitzer, Frank;
Tessone, Claudio Juan

In ECMS 2012  Proceedings of the 26th European Conference on Modelling and Simulation

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Abstract We study the role of hierarchical structures in a simple model of collective consensus formation based on the bounded confidence model with continuous individual opinions. For the particular variation of this model considered in this paper, we assume that a bias towards an extreme opinion is introduced whenever two individuals interact and form a common decision. As a simple proxy for hierarchical social structures, we introduce a twostep decision making process in which in the second step groups of likeminded individuals are replaced by representatives once they have reached local consensus, and the representatives in turn form a collective decision in a downstream process. We find that the introduction of such a hierarchical decision making structure can improve consensus formation, in the sense that the eventual collective opinion is closer to the true average of individual opinions than without it. In particular, we numerically study how the size of groups of likeminded individuals being represented by delegate individuals affects the impact of the bias on the final populationwide consensus. These results are of interest for the design of organisational policies and the optimisation of hierarchical structures in the context of group decision making.
Noiseinduced volatility of collective dynamics

[2012]

Harras, Georges;
Tessone, Claudio Juan;
Sornette, Didier

Physical Review E,
pages: 011150,
volume: 85,
number: 1

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Abstract Noiseinduced volatility refers to a phenomenon of increased level of fluctuations in the collective dynamics of bistable units in the presence of a rapidly varying external signal, and intermediate noise levels. The archetypical signature of this phenomenon is that –beyond the increase in the level of fluctuations– the response of the system becomes uncorrelated with the external driving force, making it different from stochastic resonance. Numerical simulations and an analytical theory of a stochastic dynamical version of the Ising model on regular and random networks demonstrate the ubiquity and robustness of this phenomenon, which is argued to be a possible cause of excess volatility in financial markets, of enhanced effective temperatures in a variety of outofequilibriumsystems and of strong selective responses of immune systems of complex biological organisms. Extensive numerical simulations are compared with a meanfield theory for different network topologies.
Effects of social influence on the wisdom of crowds

[2012]

Mavrodiev, Pavlin;
Tessone, Claudio Juan;
Schweitzer, Frank

In Proceedings of the conference on Collective Intelligence 2012

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Abstract Wisdom of crowds refers to the phenomenon that the aggregate prediction or forecast of a group of individuals can be surprisingly more accurate than most individuals in the group, and sometimes  than any of the individuals comprising it. This article models the impact of social influence on the wisdom of crowds. We build a minimalistic representation of individuals as Brownian particles coupled by means of social influence. We demonstrate that the model can reproduce results of a previous empirical study. This allows us to draw more fundamental conclusions about the role of social influence: In particular, we show that the question of whether social influence has a positive or negative net effect on the wisdom of crowds is illdefined. Instead, it is the starting configuration of the population, in terms of its diversity and accuracy, that directly determines how beneficial social influence actually is. The article further examines the scenarios under which social influence promotes or impairs the wisdom of crowds.
How social influence can undermine the wisdom of crowd effect

[2011]

Lorenz, Jan;
Rauhut, Heiko;
Schweitzer, Frank;
Helbing, Dirk

Proceedings of the National Academy of Sciences (PNAS),
pages: 90209025,
volume: 108,
number: 22

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Abstract Social groups can be remarkably smart and knowledgeable when their averaged judgements are compared with the judgements of individuals. Already Galton [Galton F (1907) Nature 75:7] found evidence that the median estimate of a group can be more accurate than estimates of experts. This wisdom of crowd effect was recently supported by examples from stock markets, political elections, and quiz shows [Surowiecki J (2004) The Wisdom of Crowds]. In contrast, we demonstrate by experimental evidence (N = 144) that even mild social influence can undermine the wisdom of crowd effect in simple estimation tasks. In the experiment, subjects could reconsider their response to factual questions after having received average or full information of the responses of other subjects. We compare subjects’ convergence of estimates and improvements in accuracy over five consecutive estimation periods with a control condition, in which no information about others’ responses was provided. Although groups are initially “wise,” knowledge about estimates of others narrows the diversity of opinions to such an extent that it undermines the wisdom of crowd effect in three different ways. The “social influence effect” diminishes the diversity of the crowd without improvements of its collective error. The “range reduction effect” moves the position of the truth to peripheral regions of the range of estimates so that the crowd becomes less reliable in providing expertise for external observers. The “confidence effect” boosts individuals’ confidence after convergence of their estimates despite lack of improved accuracy. Examples of the revealed mechanism range from misled elites to the recent global financial crisis.
Reply to Farrell: Improved individual estimation success can imply collective tunnel vision

[2011]

Rauhut, Heiko;
Lorenz, Jan;
Schweitzer, Frank;
Helbing, Dirk

Proceedings of the National Academy of Sciences (PNAS),
pages: E626,
volume: 108,
number: 36

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Abstract Analyzing the data of the wisdom of crowd experiment by Lorenz et al. (1), Farrell (2) points out that information exchange improves individual estimates of answers to factual questions. He furthermore suggests that information exchange increases individual rewards and that this comes with an increase in confidence in their estimates. However, it has to be noted that individual rewards were revealed only after subjects specified their confidence. [This also shows that the reference to Danchin et al. (3) is not fitting, because in the foraging example, subjects were constantly aware of the external metric, namely the success of the foraging activities of other individuals.] Moreover, although the original experiment was designed to study social interaction effects, Farrell applies a psychological perspective. In fact, Farrell's commentary (2) focuses on individuallevel effects, whereas Lorenz et al. (1) concentrated on grouplevel effects and show how aggregating microoutcomes can lead to unexpected macrolevel effects.
The wisdom of crowds in one mind : How individuals can simulate the knowledge of diverse societies to reach better decisions

[2011]

Rauhut, Heiko;
Lorenz, Jan

Journal of Mathematical Psychology,
pages: 191197,
volume: 55,
number: 2

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Abstract The joint knowledge of many diverse individuals can outperform experts in estimation and decisionmaking problems. This wisdom of the crowd has been demonstrated in different societal areas such as internet search engines, political elections or stock markets. Recently, psychologists argued that humans may even simulate a diverse society in their own minds by drawing different answers from their brain (Vul & Pashler, 2008). The underlying idea is that individuals can access different knowledge areas in their brain, whose joint evaluation yields better estimates than their separate consideration. This article presents a mathematical treatment of the wisdom of crowds and two potential mechanisms to quantify the wisdom of crowds in one mind. The implications of both methods are analyzed and applied to new experimental data (N = 144), which contain five consecutive estimates from the same individuals. The theoretical and empirical analysis demonstrates limitations of the wisdom of crowds in one mind: Asking oneself several times is on average less powerful than asking only one other individual. This is due to the smaller diversity of estimates of similar individuals and the larger average bias to which they converge. Further, individuals cannot perform independent draws from an ‘‘internal distribution’’. Hence, there may be other mechanisms at work such as talking oneself into believing initial guesses or eliciting progressively wilder ones. ©2010
Does ignorance promote norm compliance?

[2010]

Groeber, Patrick;
Rauhut, Heiko

Computational and Mathematical Organization Theory,
pages: 128,
volume: 16,
number: 1

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Abstract A large extent of undetected norm violations may have positive effects for society. If many norm violations are hidden, society seems to be in good order so that actors are more willing to comply with the norms themselves. In this sense, ignorance promotes norm compliance.We challenge this view by arguing that in scenarios, in which norms are controlled and enforced by third parties who receive rewards for their success, the opposite is true: Ignorance promotes norm violations. The reason is that unsuspicious inspectors who believe that little hidden norm violations are committed will spend less effort for detection, some formerly detected norm violations will go undetected, norm targets will be less deterred from the lower detection probability and will commit more norm violations over time. This article develops a respective mathematical model and confirms the above described intuition.
Heterogeneous bounds of confidence: Meet, discuss and find consensus!

[2010]

Lorenz, Jan

Inter Science Complexity,
pages: 4352,
volume: 15,
number: 4

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Abstract Models of continuous opinion dynamics under bounded confidence show a sharp transition between a consensus and a polarization phase at a critical global bound of confidence. In this paper, heterogeneous bounds of confidence are studied. The surprising result is that a society of agents with two different bounds of confidence (openminded and closedminded agents) can find consensus even when both bounds of confidence are significantly below the critical bound of confidence of a homogeneous society. The phenomenon is shown by examples of agentbased simulation and by numerical computation of the time evolution of the agents density. The result holds for the bounded confidence model of Deffuant, Weisbuch and others (Weisbuch, G. et al; Meet, discuss, and segregate!, Complexity, 2002, 7, 55 63), as well as for the model of Hegselmann and Krause (Hegselmann, R., Krause, U.; Opinion Dynamics and Bounded Confidence, Models, Analysis and Simulation, Journal of Artificial Societies and Social Simulation, 2002, 5, 2). Thus, given an average level of confidence, diversity of bounds of confidence enhances the chances for consensus. The drawback of this enhancement is that opinion dynamics becomes suspect to severe drifts of clusters, where openminded agents can pull closedminded agents towards another cluster of closedminded agents. A final consensus might thus not lie in the center of the opinion interval as it happens for uniform initial opinion distributions under homogeneous bounds of confidence. It can be located at extremal locations. This is demonstrated by example. This also show that the extension to heterogeneous bounds of confidence enriches the complexity of the dynamics tremendously.
Tipping diffusivity in information accumulation systems: More links, less consensus

[2010]

Shin, J. K.;
Lorenz, Jan

Journal of Statistical Mechanics: Theory and Experiment,
pages: P06005P06020,
volume: 2010,
number: 06

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Abstract Assume two different communities each of which maintain their respective opinions mainly because of the weak interaction between them. In such a case, it is an interesting problem to find the necessary strength of intercommunity interaction in order for the two communities to reach a consensus. In this paper, the information accumulation system (IAS) model is applied to investigate the problem. With the application of the IAS model, the opinion dynamics of the twocommunity problem is found to belong to a wider class of twospecies problems appearing in population dynamics or in the competition of two languages, for all of which the governing equations can be described in terms of coupled logistic maps. Tipping diffusivity is defined as the maximal intercommunity interaction such that the two communities maintain different opinions. For a problem with a simple community structure and homogeneous individuals, the tipping diffusivity is calculated theoretically. As a conclusion of the paper, the convergence of the two communities to the same value is less possible the more overall interaction, intracommunity and intercommunity, takes place. This implies, for example, that the increase in the interaction between individuals caused by the development of modern communication tools, such as Facebook and Twitter, does not necessarily improve the tendency towards global convergence between different communities. If the number of internal links increases by a factor, the number of intercommunity links must be increased by an even higher factor, in order for consensus to be the only stable attractor.
On conditions for convergence to consensus

[2010]

Lorenz, Jan;
Lorenz, Dirk A.

IEEE Transactions on Automatic Control,
pages: 16511656,
volume: 55,
number: 7

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Abstract A new theorem on conditions for convergence to consensus of a multiagent timedependent timediscrete dynamical system is presented. The theorem is build up on the notion of averaging maps. We compare this theorem to results by Moreau (IEEE Transactions on Automatic Control, vol. 50, no. 2, 2005) about setvalued Lyapunov theory and convergence under switching communication topologies. We give examples that point out differences of approaches including examples where Moreau's theorem is not applicable but ours is. Further on, we give examples that demonstrate that the theory of convergence to consensus is still not complete.
Nonlinear voter models: The transition from invasion to coexistence

[2009]

Schweitzer, Frank;
Behera, Laxmidhar

The European Physical Journal B,
pages: 301318,
volume: 67,
number: 3

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Abstract In nonlinear voter models the transitions between two states depend in a nonlinear manner on the frequencies of these states in the neighborhood. We investigate the role of these nonlinearities on the global outcome of the dynamics for a homogeneous network where each node is connected to $m = 4$ neighbors. The paper unfolds in two directions. We first develop a general stochastic framework for frequency dependent processes from which we derive the macroscopic dynamics for key variables, such as global frequencies and correlations. Explicite expressions for both the meanfield limit and the pair approximation are obtained. We then apply these equations to determine a phase diagram in the parameter space that distinguishes between different dynamic regimes. The pair approximation allows us to identify three regimes for nonlinear voter models: (i) complete invasion, (ii) random coexistence, and most interestingly (iii) correlated coexistence. These findings are contrasted with predictions from the meanfield phase diagram and are confirmed by extensive computer simulations of the microscopic dynamics.
Universality in movie rating distributions

[2009]

Lorenz, Jan

The European Physical Journal B,
pages: 251258,
volume: 71,
number: 2

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Abstract In this paper histograms of user ratings for movies (1,...,10) are analysed. The evolving stabilised shapes of histograms follow the rule that all are either doubleor triplepeaked. Moreover, at most one peak can be on the central bins 2,...,9 and the distribution in these bins looks smooth `Gaussianlike’ while changes at the extremes (1 and 10) often look abrupt. It is shown that this is well approximated under the assumption that histograms are confined and discretised probability density functions of L'evy skew $α$stable distributions. These distributions are the only stable distributions which could emerge due to a generalized central limit theorem from averaging of various independent random variables as which one can see the initial opinions of users. Averaging is also an appropriate assumption about the social process which underlies the process of continuous opinion formation. Surprisingly, not the normal distribution achieves the best fit over histograms observed on the web, but distributions with fat tails which decay as powerlaws with exponent –(1 + $α$) . The scale and skewness parameters of the L'evy skew $α$stable distributions seem to depend on the deviation from an average movie (with mean about 7.6). The histogram of such an average movie has no skewness and is the most narrow one. If a movie deviates from average the distribution gets broader and skew. The skewness pronounces the deviation. This is used to construct a one parameter fit which gives some evidence of universality in processes of continuous opinion dynamics about taste.
How groups can foster consensus: The case of local cultures

[2009]

Groeber, Patrick;
Schweitzer, Frank;
Press, Kerstin

Journal of Aritifical Societies and Social Simulation,
pages: 122,
volume: 12,
number: 2

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Abstract A local culture denotes a commonly shared behaviour within a cluster of firms. Similar to social norms or conventions, it is an emergent feature resulting from the firms' interaction in an economic network. To model these dynamics, we consider a distributed agent population, representing e.g. firms or individuals. Further, we build on a continuous opinion dynamics model with bounded confidence ($ epsilon$), which assumes that two agents only interact if differences in their behaviour are less than $ epsilon$. Interaction results in more similarity of behaviour, i.e. convergence towards a common mean. This framework is extended by two major concepts: (i) The agent's ingroup consisting of acquainted interaction partners is explicitly taken into account. This leads to an effective agent behaviour reflecting that agents try to continue to interact with past partners and thus to keep sufficiently close to them. (ii) The ingroup network structure changes over time, as agents can form new links to other agents with sufficiently close effective behaviour or delete links to agents no longer close in behaviour. Thus, our model provides a feedback mechanism between the agents' behaviour and their ingroup structure. Studying its consequences by means of agentbased computer simulations, we find that for narrowminded agents (low $ epsilon$) the additional feedback helps to find consensus more often, whereas for openminded agents (high $ epsilon$) this does not hold. This counterintuitive result is explained by simulations of the network evolution.
Diversityinduced resonance in a model for opinion formation

[2009]

Tessone, Claudio Juan;
Toral, Raul

The European Physical Journal B,
pages: 549555,
volume: 71,
number: 4

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Abstract We study an opinion formation model that takes into account that individuals have diverse preferences when forming their opinion regarding a particular issue. We show that the system exhibits a phenomenon called "diversityinduced resonance"[Tessone et al. Phys. Rev. Lett. 97, 194101 (2006)], by which an external influence (for example advertising, or fashion trends) is better followed by populations having the right degree of diversity in their preferences, rather than others where the individuals are identical or have too different preferences. We support our findings by numerical simulations of the model and a meanfield type analytical theory.
Decelerating microdynamics can accelerate macrodynamics in the voter model

[2008]

Tessone, Claudio Juan;
Schweitzer, Frank

Physical Review Letters,
pages: 14,
volume: 101,
number: 1

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Abstract For the voter model, we study the effect of a memorydependent transition rate. We assume that the transition of a spin into the opposite state decreases with the time it has been in its current state. Counterintuitively, we find that the time to reach a macroscopically ordered state can be accelerated by slowing down the microscopic dynamics in this way. This holds for different network topologies, including fully connected ones. We find that the ordering dynamics is governed by two competing processes which either stabilize the majority or the minority state. If the first one dominates, it accelerates the ordering of the system. The conclusions of this Letter are not restricted to the voter model, but remain valid to many other spin systems as well.
Slower is faster: Fostering consensus formation by heterogeneous interia

[2008]

Tessone, Claudio Juan;
Schweitzer, Frank

ACS  Advances in Complex Systems,
pages: 551563,
volume: 11,
number: 4

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Abstract We investigate an extension of the voter model in which voters are equipped with an individual inertia to change their opinion. This inertia depends on the persistence time of a voter's current opinion (ageing). We focus on the case of only two different inertia values: zero if a voter just changed towards a new opinion and nu otherwise. We are interested in the average time to reach consensus, i.e. the state in which all voters have adopted the same opinion. Adding inertia to the system means to slow down the dynamics at the voter's level, which should presumably lead to a slower consensus formation. As an unexpected outcome of our inertial voter dynamics, there is a parameter region of nu where an increasing inertia leads to a faster consensus formation. These results rest on the heterogeneity of voters which evolves through the described ageing. In a control setting of homogeneous inertia values, we only find monotonously increasing consensus times. In the paper, we present dynamical equations for the meanfield case which allow for analytical insight into the observed slowerisfaster effect.
Opinion dynamics: The effect of the number of peers met at once

[2008]

Urbig, Diemo;
Lorenz, Jan

Journal of Artificial Societies and Social Simulation,
pages: 127,
volume: 11,
number: 2 4

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Abstract The opinion dynamics model introduced by Deffuant and Weisbuch as well as the one by Hegselmann and Krause are rather similar. In both models individuals are assumed to have opinions about an issue, they meet and discuss, and they may adapt their opinions towards the other agents` opinions or may ignore each other if their positions are too different. Both models differ with respect to the number of peers they meet at once. Furthermore the model by Deffuant and Weisbuch has a convergence parameter that controls how fast agents adapt their opinions. By defining the reversed parameter as selfsupport we can extend the applicability of this parameter to scenarios with more than one interaction partner. We investigate the effects of changing the number of peers met at once, which is done for different population sizes, and the effects of changing the selfsupport. For describing the dynamics we look at different statistics, i.e. number of cluster, number of major clusters, and Gini coefficient.
Continuous opinion dynamics under bounded confidence: A survey

[2007]

Lorenz, Jan

International Journal of Modern Physics C,
pages: 18191838,
volume: 18,
number: 12

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Abstract Models of continuous opinion dynamics under bounded confidence have been presented independently by Krause and Hegselmann and by Deffuant et al in 2000. They have raised a fair amount of attention in the communities of social simulation, sociophysics and complexity science. The researchers working on it come from disciplines as physics, mathematics, computer science, social psychology and philosophy. Agents hold continuous opinions which they can gradually adjust if they hear the opinions of others. The idea of bounded confidence is that agents only interact if they are close in opinion to each other. Usually, the models are analyzed with agentbased simulations in a MonteCarlo style, but they can also be reformulated on the agent's density in the opinion space in a masterequation style. This paper is to present the agentbased and densitybased modeling frameworks including the cases of multidimensional opinions and heterogeneous bounds of confidence; second, to give the bifurcation diagrams of cluster configuration in the homogeneous model with uniformly distributed initial opinions; third to review the several extensions and the evolving phenomena which have been studied so far; and fourth to state some basic open questions.
Coexistence of social norms based on inand outgroup interactions

[2007]

Groeber, Patrick;
Fent, Thomas;
Schweitzer, Frank

ACS  Advances in Complex Systems,
pages: 271286,
volume: 10,
number: 2

more» «less

Abstract The question how social norms can emerge from microscopic interactions between individuals is a key problem in social sciences to explain collective behavior. In this paper we propose an agentbased model to show that randomly distributed social behavior by way of local interaction converges to a state with a multimodal distribution of behavior. This can be interpreted as a coexistence of different social norms, a result that goes beyond previous investigations. The model is discrete in time and space, behavior is characterized in a continuous state space. The adaptation of social behavior by each agent is based on attractive and repulsive forces caused by friendly and adversary relations among agents. The model is analyzed both analytically and by means of spatiotemporal computer simulations. It provides conditions under which we find convergence towards a single norm, coexistence of two opposing norms, and coexistence of a multitude of norms. For the latter case, we also show the evolution of the spatiotemporal distribution of behavior.
On spatial consensus formation: Is the sznajd model different from a voter model?

[2003]

Behera, Laxmidhar;
Schweitzer, Frank

International Journal of Modern Physics C,
pages: 13311354,
volume: 14,
number: 10

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Abstract In this paper, we investigate the socalled ``Sznajd Model'' (SM) in one dimension, which is a simple cellular automata approach to consensus formation among two opposite opinions (described by spin up or down). To elucidate the SM dynamics, we first provide results of computer simulations for the spatiotemporal evolution of the opinion distribution $L(t)$, the evolution of magnetization $m(t)$, the distribution of decision times $P( tau)$ and relaxation times $P( mu)$. In the main part of the paper, it is shown that the SM can be completely reformulated in terms of a linear VM, where the transition rates towards a given opinion are directly proportional to frequency of the respective opinion of the secondnearest neighbors (no matter what the nearest neighbors are). So, the SM dynamics can be reduced to one rule, ``Just follow your secondnearest neighbor''. The equivalence is demonstrated by extensive computer simulations that show the same behavior between SM and VM in terms of $L(t)$, $m(t)$, $P( tau)$, $P( mu)$, and the final attractor statistics. The reformulation of the SM in terms of a VM involves a new parameter $ sigma$, to bias between antiand ferromagnetic decisions in the case of frustration. We show that $ sigma$ plays a crucial role in explaining the phase transition observed in SM. We further explore the role of synchronous versus asynchronous update rules on the intermediate dynamics and the final attractors. Compared to the original SM, we find three additional attractors, two of them related to an asymmetric coexistence between the opposite opinions.
Coordination of decisions in a spatial agent model

[2002]

Schweitzer, Frank;
Zimmermann, Joerg;
Muhlenbein, H.

Physica A: Statistical Mechanics and its Applications,
pages: 189216,
volume: 303,
number: 12

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Abstract For a binary choice problem, the spatial coordination of decisions in an agent community is investigated both analytically and by means of stochastic computer simulations. The individual decisions are based on different local information generated by the agents with a finite lifetime and disseminated in the system with a finite velocity. We derive critical parameters for the emergence of minorities and majorities of agents making opposite decisions and investigate their spatial organization. We find that dependent on two essential parameters describing the local impact and the spatial dissemination of information, either a definite stable minority/majority relation (singleattractor regime) or a broad range of possible values (multiattractor regime) occurs. In the latter case, the outcome of the decision process becomes rather diverse and hard to predict, both with respect to the share of the majority and their spatial distribution. We further investigate how a dissemination of information on different time scales affects the outcome of the decision process. We find that a more “efficient” information exchange within a subpopulation provides a suitable way to stabilize their majority status and to reduce “diversity” and uncertainty in the decision process.
