An Agent-Based Model of Collective Emotions in Online Communities

We develop a agent-based framework to model the emergence of collective emotions, which is applied to online communities. Agents individual emotions are described by their valence and arousal. Using the concept of Brownian agents, these variables change according to a stochastic dynamics, which also considers the feedback from online communication. Agents generate emotional information, which is stored and distributed in a field modeling the online medium. This field affects the emotional states of agents in a non-linear manner. We derive conditions for the emergence of collective emotions, observable in a bimodal valence distribution. Dependent on a saturated or a superlinear feedback between the information field and the agent's arousal, we further identify scenarios where collective emotions only appear once or in a repeated manner. The analytical results are illustrated by agent-based computer simulations. Our framework provides testable hypotheses about the emergence of collective emotions, which can be verified by data from online communities.Comment: European Physical Journal B (in press), version 2 with extended introduction, clarification

Individualization as driving force of clustering phenomena in humans

One of the most intriguing dynamics in biological systems is the emergence of clustering, the self-organization into separated agglomerations of individuals. 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 clustering of opinions in human populations. The puzzle is particularly pressing if opinions vary continuously, such as the degree to which citizens are in favor of or against a vaccination program. Existing opinion formation models suggest that "monoculture" is unavoidable 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 did 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 of 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 simulation experiments to demonstrate 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.Comment: 12 pages, 4 figure

A relative approach to opinion formation

Formal models of opinion formation commonly represent an individual’s opinion by a value on a fixed opinion interval. We propose an alternative modeling method wherein interpretation is only provided to the relative positions of opinions vis-à-vis each other. This method is then considered in a similar setting as the discrete-time Altafini model (an extension of the well-known DeGroot model), but with more general influence weights. Even in a linear framework, the model can describe, in the long run, polarization, dynamics with a periodic pattern, and (modulus) consensus formation. In addition, in our alternative approach key characteristics of the opinion dynamic can be derived from real-valued square matrices of influence weights, which immediately allows one to transfer matrix theory insights to the field of opinion formation dynamics under more relaxed conditions than in the DeGroot or discrete-time Altafini models. A few specific themes are covered: (i) We demonstrate how stable patterns in relative opinion dynamics are identified which are hidden when opinions are considered in an absolute opinion framework. (ii) For the two-agent case, we provide an exhaustive closed-form description of the relative opinion model’s dynamic in the long run. (iii) We explore group dynamics analytically, in particular providing a non-trivial condition under which a subgroup’s asymptotic behavior carries over to the entire population

Manifesto of computational social science

The increasing integration of technology into our lives has created unprecedented volumes of data on society’s everyday behaviour. Such data opens up exciting new opportunities to work towards a quantitative understanding of our complex social systems, within the realms of a new discipline known as Computational Social Science. Against a background of financial crises, riots and international epidemics, the urgent need for a greater comprehension of the complexity of our interconnected global society and an ability to apply such insights in policy decisions is clear. This manifesto outlines the objectives of this new scientific direction, considering the challenges involved in it, and the extensive impact on science, technology and society that the success of this endeavour is likely to bring about

Cooperation, Norms, and Revolutions: A Unified Game-Theoretical Approach

Cooperation is of utmost importance to society as a whole, but is often challenged by individual self-interests. While game theory has studied this problem extensively, there is little work on interactions within and across groups with different preferences or beliefs. Yet, people from different social or cultural backgrounds often meet and interact. This can yield conflict, since behavior that is considered cooperative by one population might be perceived as non-cooperative from the viewpoint of another. To understand the dynamics and outcome of the competitive interactions within and between groups, we study game-dynamical replicator equations for multiple populations with incompatible interests and different power (be this due to different population sizes, material resources, social capital, or other factors). These equations allow us to address various important questions: For example, can cooperation in the prisoner's dilemma be promoted, when two interacting groups have different preferences? Under what conditions can costly punishment, or other mechanisms, foster the evolution of norms? When does cooperation fail, leading to antagonistic behavior, conflict, or even revolutions? And what incentives are needed to reach peaceful agreements between groups with conflicting interests? Our detailed quantitative analysis reveals a large variety of interesting results, which are relevant for society, law and economics, and have implications for the evolution of language and culture as well

Injecting complexity in simulation models:Do selection and social influence jointly promote cooperation?

This paper employs a simulation model to investigate the effectiveness of cooperation selection (“selecting similar others”) and social influence (“do as others do”), since both mechanisms promote cooperation in theoretical analyses and experimental studies. However, it is unclear how effective cooperation selection and social influence are in simulation models where both mechanisms operate simultaneously alongside additional social dynamics, such as reciprocity and transitivity. This paper relies on a model loosely based on an empirical case in which students selected others based on how cooperative they perceive the other. Using existing theoretical cooperation models as a benchmark, we insert relational, behavioral, and contextual assumptions into our model and build on data from 95 students when we vary the strength of cooperation selection and social influence relative to empirically observed levels. We take co-evolution stochastic actor-oriented models as basis because the model inherently accounts for the interdependence of behavior and network selection. Our simulations reveal that cooperation benefits most when cooperation selection and social influence are strongly positive. Through the combination of cooperation selection and social influence, the simulations show that cooperators form dense local clusters, influencing their peers to keep cooperating while insulating themselves from social influence from defectors. Robustness checks confirm the stability of these findings across diverse parameter configurations

A Bad Barrel Spoils a Good Apple:How Uncertainty and Networks Affect Whether Matching Rules Can Foster Cooperation

Meritocratic matching solves the problem of cooperation by ensuring that only prosocial agents group together while excluding proselfs who are less inclined to cooperate. However, matching is less effective when estimations of individual merit rely on group-level outcomes. Prosocials in uncooperative groups are unable to change the nature of the group and are themselves forced to defect to avoid exploitation. They are then indistinguishable from proselfs, preventing them from accessing cooperative groups. We investigate informal social networks as a potential solution. Interactions in dyadic network relations provide signals of individual cooperativeness which are easier to interpret. Network relations can thus help prosocials to escape from uncooperative groups. To test our intuitions, we develop an ABM modeling cooperative behavior based on a stochastic learning model with adaptive thresholds. We investigate both randomly and homophilously formed networks. We find that homophilous networks create conditions under which meritocratic matching can function as intended. Simulation experiments identify two underlying reasons. First, dyadic network interactions in homophilous networks differentiate more between prosocials and proselfs. Second, homophilous networks create groups of prosocial agents who are aware of each other’s behavior. The stronger this prosociality segregation is, the more easily prosocials cooperate in the group context. Further analyses also highlight a downside of homophilous networks. When prosocials successfully escape from uncooperative groups, non-cooperatives have fewer encounters with prosocials, diminishing their chances to learn to cooperate through those encounters