As Figure 2B demonstrates, bounded confidence dynamics can in particular also imply that a whole population of initial moderates can be driven to one extreme, despite an equal initial distribution of extremists at both extremes of the opinion spectrum. This pattern, and the others, have been systematically studied for different variants of the bounded confidence model, particularly ones in which the tolerances are also modified during the interactions, different types of networks and different values of the model parameters Amblard and Deffuant ; Deffuant ; Deffuant et al.
As shown in Deffuant and Weisbuch the single extreme convergence happens if moderates first concentrate in the center of the opinion spectrum where they can get outside of the range of influence of one of the extremes because of random fluctuations. Then the moderates drift to the other extreme.
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This pattern is more likely to take place when the extremists are not too numerous, because when they are, they attract the moderates to both extremes. Morever, under the original bounded confidence model with constant tolerances , a pattern in which, the opinions of the moderate agents keep fluctuating all the time also can take place Mathias, Huet and Deffuant This is because moderate agents with large tolerances keep strong interactions with opinions of opposed "stubborn" extremists and this prevents them from creating stabilized clusters.
This does not occur in the variants of the model with changing tolerances, because the tolerances of the moderates decrease with interactions with extremists which leads finally extremist agents to stop interacting with one or both extremes. Recent work by Hegselmann and Krause used a combination of simulations and analytical tools to derive many of these phenomena from a general model in which a population following bounded confidence dynamics is exposed to an external signal as additional source of influence, sent for example by charismatic leaders, radical groups or — in a scientific discourse — by empirical evidence of the "truth" about a real-world phenomenon under discussion by scientists.
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They showed that the exact effects of the intensity of signals on the degree of extremization in a population interact sensitively and in sometimes counterintuitive ways with the distribution of confidence levels and initial opinions in the population. Resonating earlier results discussed above, they find for example that more intensive signals may decrease rather than increase convergence on extreme positions advocated by the signal.
This happens if those agents moving towards the position of the signal move too quickly, so that they drop out of the confidence range of a majority of population members who do not "hear" the signal. This majority is then "left behind" and stays at moderate positions, because it can no longer be influenced by those who hear the signal. Bounded confidence models have become a hugely influential modelling class implementing similarity biased social influence with continuous opinions. A large literature has evolved on extensions, modifications and analytical treatments of these models, often using tools of statistical physics.
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It is impossible to give a complete overview here. Comprehensive reviews can be found in Lorenz or Castellano et al. Like for models of assimilative influence, an important distinction is between models assuming a continuous opinion space Bounded Confidence-models and models assuming distinct nominal opinion categories. Models with nominal opinion spaces combine social influence with homophily, implemented as a lack of interaction if dissimilarity exceeds a critical threshold.
In these models the agents have a vector including several discrete opinions or cultural traits and the similarity is computed between such vectors. Drawing on Carley , Axelrod modelled spatially local interaction with a regular bounded lattice. The likelihood for an agent to select a particular neighbor for interaction is equal to the proportion of opinion dimensions called features by Axelrod in which they have the same trait modelling homophily.
If an agent interacts with a neighbor, then on a feature in which they still disagree, the trait of the neighbor is copied modelling influence so that the agents become more alike as a result. Most importantly for model behavior, interaction and thus influence becomes impossible if two neighbors have nothing in common.
In areas of the spatial network where agents locally happen to be relatively similar to each other, they influence each other more and thus agree on an increasing number of opinion dimensions while differentiating from neighbors at the same time. Eventually spatially connected "cultural regions" emerge and stabilize with maximal consensus within and disagreement on all features between neighboring regions.
Modelling symbolic interactionism, Mark proposed a model with essentially similar behavior, but representing opinions as a set of "facts" actors can learn from each other when interacting. The more facts two actors share in their knowledge base, the more likely they interact with each other and thus communicate more facts to each other. Again, interaction is impossible if agents have no facts in common. This is possible because in an interaction, actors cannot only share known facts, but also create with some probability new unique facts. This models the assumption of symbolic interactionism that individuals can create in social interactions new symbols with unique meaning for them, like "cool" new words members of a youth-clique invent to distinguish themselves.
New unique facts further spread through social influence primarily to those who are similar to their initial creators and so further differentiate the recipients from other agents in the system. Castellano et al. One problem that received particular attention is the sensitivity of cultural differentiation to noise. Addressing these sources of error, Klemm et al. Random changes of traits can generate new cultural overlap between otherwise dissimilar neighbors, thereby breaching through emergent cultural boundaries. Further studies explored mechanisms explaining opinion clustering despite noise.
One is that homophily extends to "network homophily" Centola et al. Recently, Ulloa et al. Other authors have moved towards integrating and comparing continuous and nominal models of similarity-biased social influence. The study of this model in the case of completely connected populations showed a frequent convergence to a large majority opinion cluster and several minority opinion clusters.
These studies further highlighted the similarity of conclusions arising from different modelling frameworks. Across different models of similarity-biased influence, several similar critical conditions for opinion clustering emerge. Most importantly, the more similarity is needed to make social influence possible between structurally connected agents, the smaller and more numerous are emergent opinion clusters. In bounded confidence models, this condition is governed by the width of confidence intervals.
The more features, the more likely it is that neighboring agents agree by random chance on at least one feature and thus can interact, while more different possible traits per feature make it less likely to agree by random chance and thus have the opposite effect on the likelihood of interaction Axelrod ; Klemm et al.
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Generally, confidence levels and the number of features on which individuals are open to influence can be seen as representation of societal level characteristics, like the degree of tolerance, "broad-mindedness" or generalized trust in a society, but also as representation of individual trust, openness to discrepant views or connectedness with dissimilar people. Network density overall fosters the emergence of consensus in models with nominal opinions, mirroring some of the results obtained when network structures where integrated in bounded confidence models. The more facts agents can memorize, the more likely two agents can have at least one fact in common and thus interact with a positive probability.
Correspondingly, Mark finds that distinct subgroups become larger and less numerous if memory size increases.
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Noise is a second condition with similar effects across different models. The mechanism through which noise reduces diversity is essentially the same. In their models, agents adopt with a small probability any possible opinion on the opinion scale, while they otherwise follow a bounded confidence rule.
Agents adopting random positions in between emergent clusters can trigger influence cascades towards merging those clusters, because they fall into the confidence ranges of both of them. However, agents adopting random positions close to only one cluster join that cluster and thus stabilize its existence as a separate group in the opinion space. When noise rates are such that both dynamics are in balance, this form of noise can preserve diversity rather than destroy it.
This result resembles findings obtained in the Axelrod framework Klemm et al. At the same time, for many models in this class the opinion clustering generated by models with similarity-biased influence can be fragile against noise, and is limited to particular slices of the parameters space sufficiently restrictive confidence bounds, low numbers of features, etc.
Models with similarity-biased influence can explain why there is no influence between some agents and they thus fail to converge. The reason is that in nominal opinion spaces differences within one feature do not have a magnitude. Bounded Confidence models instead can show how a whole population can become extremist and possibly bi-polarized by adopting the opinions of its initially most extreme members.
Yet, in these models a population cannot become more extreme than its initial extremists. In these models of repulsive influence, assimilation was combined with its counterpart, differentiation — the assumption that some interactions lead individuals to adjust their opinions in such a way as to become more dissimilar to others they disagree with. Different terms have been used in the literature to denote repulsive influence, like rejection, negative influence, differentiation or reactance.
Hunter et al. We illustrate the implementation of this mechanism with a modification of our basic model of similarity-biased continuous opinion dynamics given in Equations 3 and 4, similar to the formalization given by Jager and Amblard Compared to similarity-biased influence, the only change concerns the way how influence weights are implemented.
Equation 5 describes that influence weights can become either positive or negative, depending on the opinion differences. Equations 3 and 5 jointly show how the direction of influence switches from a "pull" towards the opinion of the source towards a "push" away from it, as soon as the disagreement o jt -o it shifts above a critical level. This critical level is here set to 0.
In this basic form, Equations 2 and 5 allow interactions to push the opinion outside of the opinion interval [0,1]. In some models this is prevented by a smoothening Flache and Macy b or truncating function Feliciani, Flache and Tolsma ; in some others the opinion space is self-contained by the specification of the interaction dynamics Huet and Deffuant For the simulations shown in Figure 1c we used a simple truncation rule.
Different implementations of the weight function f have been proposed for models with repulsive influence on continuous opinions e. But this time these theories were interpreted as to not only imply that individuals want to be similar to people they like, or to accept the opinion of others when these are similar, but also that individuals strive to be dissimilar to people they dislike, and accentuate disagreement with others if these are too dissimilar. Additionally, several authors assume that social influence relations between individuals are not only modified by homophily, but also by xenophobia Baldassarri and Bearman ; Flache and Macy b ; Macy et al.
Xenophobia is the counterpart of the assumption that people are more open to influence from similar others: the larger the dissimilarity between two interacting individuals, the more they evaluate each other negatively Rosenbaum , triggering differentiation from the source. Other modelers Huet and Deffuant ; Huet, Deffuant, and Jager derived repulsive influence from a different psychological process.
In line with the social judgement theory Sherif and Hovland they assume that the degree of ego-involvement and self-relevance play a crucial role in social influence processes. In case of strong disagreement on a highly ego-involved issue represented as an opinion dimension , individuals may increase their opinion difference on a less ego-involved issue represented as another opinion dimension.
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This can occur in particular when issues are at stake that are central to the social identity of an individual. Building on research on intergroup dynamics Brewer ; Tajfel , further models Salzarulo ; Dykstra et al. Figure 1c describes a typical dynamic that has been generated with the model presented above. Starting from an opinion that is initially randomly uniformly distributed in the population, soon two clusters start to form at the opposite extremes of the spectrum, until eventually all agents have joined one of the two emergent factions. Due to their large distance from other members of the population, initial extremists "push" even moderate agents to differentiate from their extreme views and to thus shift towards the opposite pole.
The assimilation pressures of positive influence then "pulls" their "moderate friends" with them in the process, adjusting their opinions towards increasingly extreme positions on the opinion scale. This class of models offers a possible explanation of how bi-polarization can arise despite the presence of simultaneous assimilative influence, as well as how agents can adopt opinions that are more extreme than any of the initial opinions present in the population.
Like unconditional and similarity-biased influence, also repulsive influence has been implemented for both continuous as well as nominal opinion spaces.
bbmpay.veritrans.co.id/los-gigantes-conocer-gente-joven.php Different implementations of the same principle were proposed for continuous opinions. For instance, some models Jager and Amblard introduce threshold levels for the difference between opinions that determine whether an interaction triggers assimilation small differences , differentiation large differences , or has no effect intermediate range. These models exhibit opinion clustering, moderate and extreme consensus as well as bi-polarization.