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Individualization as driving force of clustering phenomena in humans.

Mäs M, Flache A, Helbing D - PLoS Comput. Biol. (2010)

Bottom Line: Small perturbations of individual opinions trigger social influence cascades that inevitably lead to monoculture, while larger noise disrupts opinion clusters and results in rampant individualism without any social structure.Our solution to the puzzle builds on recent empirical research, combining the integrative tendencies of social influence with the disintegrative effects of individualization.In summary, the new model can explain cultural clustering in human societies.

View Article: PubMed Central - PubMed

Affiliation: Department of Sociology, Interuniversity Center for Social Science Theory and Methodology, University of Groningen, Groningen, The Netherlands. m.maes@rug.nl

ABSTRACT
One of the most intriguing dynamics in biological systems is the emergence of clustering, in the sense that individuals self-organize into separate agglomerations in physical or behavioral space. Several theories have been developed to explain clustering in, for instance, multi-cellular organisms, ant colonies, bee hives, flocks of birds, schools of fish, and animal herds. A persistent puzzle, however, is the clustering of opinions in human populations, particularly when opinions vary continuously, such as the degree to which citizens are in favor of or against a vaccination program. Existing continuous opinion formation models predict "monoculture" in the long run, unless subsets of the population are perfectly separated from each other. Yet, social diversity is a robust empirical phenomenon, although perfect separation is hardly possible in an increasingly connected world. Considering randomness has not overcome the theoretical shortcomings so far. Small perturbations of individual opinions trigger social influence cascades that inevitably lead to monoculture, while larger noise disrupts opinion clusters and results in rampant individualism without any social structure. Our solution to the puzzle builds on recent empirical research, combining the integrative tendencies of social influence with the disintegrative effects of individualization. A key element of the new computational model is an adaptive kind of noise. We conduct computer simulation experiments demonstrating that with this kind of noise a third phase besides individualism and monoculture becomes possible, characterized by the formation of metastable clusters with diversity between and consensus within clusters. When clusters are small, individualization tendencies are too weak to prohibit a fusion of clusters. When clusters grow too large, however, individualization increases in strength, which promotes their splitting. In summary, the new model can explain cultural clustering in human societies. Strikingly, model predictions are not only robust to "noise"-randomness is actually the central mechanism that sustains pluralism and clustering.

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Comparison of the (A) Durkheimian model and (B) the noisy BC-model.Figures plot the size of the biggest cluster versus the number of clusters and compare it to the case of random fragmentation in all simulation runs that resulted in more than one and less than 32 clusters. Fig. 4A is based on the simulation experiment with the Durkheimian model underlying Fig. 3. Fig. 4B is based on an experiment with the BC-model [33] where we varied the bounded-confidence level  between 0.01 and 0.15 in steps of 0.02 and the noise level  between 5 and 50 in steps of 5. We conducted 100 replications per parameter combination and measured the number of clusters and the size of the biggest cluster after 250,000 iterations. White solid lines represent the average size of the biggest cluster. The dark blue area shows the respective interquartile range and the light blue area the complete value range. For comparison, we generated randomly fragmented opinion distributions of  agents where  agents hold random opinions () and the remaining  agents hold opinion  and form one big cluster. We varied the value of  between 0 and 100 in steps of 1 and generated 1000 distributions per condition. The average size of the biggest cluster of the resulting distributions is shown by the thin yellow-black line. (The curve stops at 22, since this is the highest number of clusters generated.) The bold yellow-black lines represent the related interquartile range. We find that the value range of the Durkheimian model (blue area) hardly overlaps with the interquartile range of the fragmented distributions (yellow area). This demonstrates that the Durkheimian model shows clustering rather than fragmentation. In contrast, Fig. 4B illustrates that the distributions of the noisy BC-model and the results for random fragmentation overlap.
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pcbi-1000959-g004: Comparison of the (A) Durkheimian model and (B) the noisy BC-model.Figures plot the size of the biggest cluster versus the number of clusters and compare it to the case of random fragmentation in all simulation runs that resulted in more than one and less than 32 clusters. Fig. 4A is based on the simulation experiment with the Durkheimian model underlying Fig. 3. Fig. 4B is based on an experiment with the BC-model [33] where we varied the bounded-confidence level between 0.01 and 0.15 in steps of 0.02 and the noise level between 5 and 50 in steps of 5. We conducted 100 replications per parameter combination and measured the number of clusters and the size of the biggest cluster after 250,000 iterations. White solid lines represent the average size of the biggest cluster. The dark blue area shows the respective interquartile range and the light blue area the complete value range. For comparison, we generated randomly fragmented opinion distributions of agents where agents hold random opinions () and the remaining agents hold opinion and form one big cluster. We varied the value of between 0 and 100 in steps of 1 and generated 1000 distributions per condition. The average size of the biggest cluster of the resulting distributions is shown by the thin yellow-black line. (The curve stops at 22, since this is the highest number of clusters generated.) The bold yellow-black lines represent the related interquartile range. We find that the value range of the Durkheimian model (blue area) hardly overlaps with the interquartile range of the fragmented distributions (yellow area). This demonstrates that the Durkheimian model shows clustering rather than fragmentation. In contrast, Fig. 4B illustrates that the distributions of the noisy BC-model and the results for random fragmentation overlap.

Mentions: Populations consist of agents. Opinions vary between −250 and 250. Initial opinions are uniformly distributed. For visualization, the opinion scale is divided into 50 bins of equal size. Color coding indicates the relative frequency of agents in each bin. (A) Dynamics of the BC-model without noise [33] over 10 iterations (Each iteration consists of simulation events .). At each simulation event, one agent's opinion is replaced by the average opinion of those other agents who hold opinions within the focal agent's confidence interval (). For , one finds several homogeneous clusters, which stabilize when the distance between all clusters exceeds the confidence threshold . (B) Computer simulation of the same BC-model, but considering interaction noise. Agents that would otherwise not have been influential, now influence the focal agent's opinion with a probability of . This small noise is sufficient to eventually generate monoculture. (C) Simulation of the BC-model with opinion noise. After each opinion update, a random value drawn from a normal distribution with an average of zero and a standard deviation of (abbreviated by ) is added to the opinion. For weak opinion noise (), one cluster is formed, which carries out a random walk on the opinion scale. When the opinion noise is significantly increased (), there is still one big cluster, but many separated agents exist as well (cf. Fig. 4). With even stronger opinion noise (), the opinion distribution becomes completely random.


Individualization as driving force of clustering phenomena in humans.

Mäs M, Flache A, Helbing D - PLoS Comput. Biol. (2010)

Comparison of the (A) Durkheimian model and (B) the noisy BC-model.Figures plot the size of the biggest cluster versus the number of clusters and compare it to the case of random fragmentation in all simulation runs that resulted in more than one and less than 32 clusters. Fig. 4A is based on the simulation experiment with the Durkheimian model underlying Fig. 3. Fig. 4B is based on an experiment with the BC-model [33] where we varied the bounded-confidence level  between 0.01 and 0.15 in steps of 0.02 and the noise level  between 5 and 50 in steps of 5. We conducted 100 replications per parameter combination and measured the number of clusters and the size of the biggest cluster after 250,000 iterations. White solid lines represent the average size of the biggest cluster. The dark blue area shows the respective interquartile range and the light blue area the complete value range. For comparison, we generated randomly fragmented opinion distributions of  agents where  agents hold random opinions () and the remaining  agents hold opinion  and form one big cluster. We varied the value of  between 0 and 100 in steps of 1 and generated 1000 distributions per condition. The average size of the biggest cluster of the resulting distributions is shown by the thin yellow-black line. (The curve stops at 22, since this is the highest number of clusters generated.) The bold yellow-black lines represent the related interquartile range. We find that the value range of the Durkheimian model (blue area) hardly overlaps with the interquartile range of the fragmented distributions (yellow area). This demonstrates that the Durkheimian model shows clustering rather than fragmentation. In contrast, Fig. 4B illustrates that the distributions of the noisy BC-model and the results for random fragmentation overlap.
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Related In: Results  -  Collection

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getmorefigures.php?uid=PMC2958804&req=5

pcbi-1000959-g004: Comparison of the (A) Durkheimian model and (B) the noisy BC-model.Figures plot the size of the biggest cluster versus the number of clusters and compare it to the case of random fragmentation in all simulation runs that resulted in more than one and less than 32 clusters. Fig. 4A is based on the simulation experiment with the Durkheimian model underlying Fig. 3. Fig. 4B is based on an experiment with the BC-model [33] where we varied the bounded-confidence level between 0.01 and 0.15 in steps of 0.02 and the noise level between 5 and 50 in steps of 5. We conducted 100 replications per parameter combination and measured the number of clusters and the size of the biggest cluster after 250,000 iterations. White solid lines represent the average size of the biggest cluster. The dark blue area shows the respective interquartile range and the light blue area the complete value range. For comparison, we generated randomly fragmented opinion distributions of agents where agents hold random opinions () and the remaining agents hold opinion and form one big cluster. We varied the value of between 0 and 100 in steps of 1 and generated 1000 distributions per condition. The average size of the biggest cluster of the resulting distributions is shown by the thin yellow-black line. (The curve stops at 22, since this is the highest number of clusters generated.) The bold yellow-black lines represent the related interquartile range. We find that the value range of the Durkheimian model (blue area) hardly overlaps with the interquartile range of the fragmented distributions (yellow area). This demonstrates that the Durkheimian model shows clustering rather than fragmentation. In contrast, Fig. 4B illustrates that the distributions of the noisy BC-model and the results for random fragmentation overlap.
Mentions: Populations consist of agents. Opinions vary between −250 and 250. Initial opinions are uniformly distributed. For visualization, the opinion scale is divided into 50 bins of equal size. Color coding indicates the relative frequency of agents in each bin. (A) Dynamics of the BC-model without noise [33] over 10 iterations (Each iteration consists of simulation events .). At each simulation event, one agent's opinion is replaced by the average opinion of those other agents who hold opinions within the focal agent's confidence interval (). For , one finds several homogeneous clusters, which stabilize when the distance between all clusters exceeds the confidence threshold . (B) Computer simulation of the same BC-model, but considering interaction noise. Agents that would otherwise not have been influential, now influence the focal agent's opinion with a probability of . This small noise is sufficient to eventually generate monoculture. (C) Simulation of the BC-model with opinion noise. After each opinion update, a random value drawn from a normal distribution with an average of zero and a standard deviation of (abbreviated by ) is added to the opinion. For weak opinion noise (), one cluster is formed, which carries out a random walk on the opinion scale. When the opinion noise is significantly increased (), there is still one big cluster, but many separated agents exist as well (cf. Fig. 4). With even stronger opinion noise (), the opinion distribution becomes completely random.

Bottom Line: Small perturbations of individual opinions trigger social influence cascades that inevitably lead to monoculture, while larger noise disrupts opinion clusters and results in rampant individualism without any social structure.Our solution to the puzzle builds on recent empirical research, combining the integrative tendencies of social influence with the disintegrative effects of individualization.In summary, the new model can explain cultural clustering in human societies.

View Article: PubMed Central - PubMed

Affiliation: Department of Sociology, Interuniversity Center for Social Science Theory and Methodology, University of Groningen, Groningen, The Netherlands. m.maes@rug.nl

ABSTRACT
One of the most intriguing dynamics in biological systems is the emergence of clustering, in the sense that individuals self-organize into separate agglomerations in physical or behavioral space. Several theories have been developed to explain clustering in, for instance, multi-cellular organisms, ant colonies, bee hives, flocks of birds, schools of fish, and animal herds. A persistent puzzle, however, is the clustering of opinions in human populations, particularly when opinions vary continuously, such as the degree to which citizens are in favor of or against a vaccination program. Existing continuous opinion formation models predict "monoculture" in the long run, unless subsets of the population are perfectly separated from each other. Yet, social diversity is a robust empirical phenomenon, although perfect separation is hardly possible in an increasingly connected world. Considering randomness has not overcome the theoretical shortcomings so far. Small perturbations of individual opinions trigger social influence cascades that inevitably lead to monoculture, while larger noise disrupts opinion clusters and results in rampant individualism without any social structure. Our solution to the puzzle builds on recent empirical research, combining the integrative tendencies of social influence with the disintegrative effects of individualization. A key element of the new computational model is an adaptive kind of noise. We conduct computer simulation experiments demonstrating that with this kind of noise a third phase besides individualism and monoculture becomes possible, characterized by the formation of metastable clusters with diversity between and consensus within clusters. When clusters are small, individualization tendencies are too weak to prohibit a fusion of clusters. When clusters grow too large, however, individualization increases in strength, which promotes their splitting. In summary, the new model can explain cultural clustering in human societies. Strikingly, model predictions are not only robust to "noise"-randomness is actually the central mechanism that sustains pluralism and clustering.

Show MeSH
Related in: MedlinePlus