Advances in Complex Systems

We expect that democracy enables us to utilize collective intelligence such that our collective decisions build and enhance social welfare, and such that we accept their distributive and normative consequences. Collective decisions are produced by voting procedures which aggregate individual preferences and judgments. Before and after, individual preferences and judgments change as their underlying attitudes, values, and opinions change through discussion and deliberation. In large groups, these dynamics naturally go beyond the scope of the individual and consequently might show unexpected self-driven macroscopic systems dynamics following socio-physical laws. On the other hand, aggregated information and preferences as communicated through media, polls, political parties, or interest groups, also play a large role in the individual opinion formation process. Further on, actors are also capable of strategic opinion formation in the light of a pending referendum, election or other collective decision. Opinion dynamics and collective decision should thus not only be tackled by social choice, game theory, political and social psychology, but also from a systems dynamics and sociophysics perspective.

Social issues are generally discussed by highly-involved and less-involved people to build social norms defining what has to be thought and done about them. As self-involved agents share different attitude dynamics to other agents [Wood, W., Pool, G., Leck, K. and Purvis, D., Self-definition, defensive processing, and influence: The normative impact of majority and minority groups, J. Pers. Soc. Psychol. (1996) 1181–1193], we study the emergence and evolution of norms through an individual-based model involving these two types of agents. The dynamics of self-involved agents is drawn from [Huet, S. and Deffuant, G., Openness leads to opinion stability and narrowness to volatility, Adv. Complex Syst. 13 (2010) 405–423], and the dynamics of others, from [Deffuant, G., Neau, D., Amblard, F. and Weisbuch, G., Mixing beliefs among interacting agents, Adv. Complex Syst. 3 (2001) 87–98]. The attitude of an agent is represented as a segment on a continuous attitudinal space. Two agents are close if their attitude segments share sufficient overlap. Our agents discuss two different issues, one of which, called main issue, is more important for the self-involved agents than the other, called secondary issue. Self-involved agents are attracted to both issues if they are close to the main issue, but shift away from their peer’s opinion if they are only close on the secondary issue. Differently, non-self-involved agents are attracted by other agents when they are close on both the main and secondary issues. We observe the emergence of various types of extreme minor clusters. In one or different groups of attitudes, they can lead to an already-built moderate norm or a norm polarized on secondary and/or main issues. They can also push disagreeing agents gathered in different groups to a global moderate consensus.

Rumor spreading is a good sample of spreading in which human beings are the main players in the spreading process. Therefore, in order to have a more realistic model of rumor spreading on online social networks, the influence of psycho-sociological factors particularly those which affect users’ reactions toward rumor/anti-rumor should be considered. To this aim, we present a new model that considers the influence of dissenting opinions on those users who have already believed in rumor/anti-rumor but have not spread the rumor/anti-rumor yet. We hypothesize that influence is a motive for the believers to spread their beliefs in rumor/anti-rumor. We derive the stochastic equations of the new model and evaluate it by using two real datasets of rumor spreading on Twitter. The evaluation results support the new hypothesis and show that the novel model which is relied on the new hypothesis is able to better represent rumor spreading.

The advantages of groups over individuals in complex decision-making have long interested scientists across disciplinary divisions. Averaging over a collection of individual judgments proves a reliable strategy for aggregating information, particularly in diverse groups in which statistically independent beliefs fall on both sides of the truth and contradictory biases are cancelled out. Social influence, some have said, narrows variation in individual opinions and undermines this wisdom-of-crowds effect in continuous estimation tasks. Researchers, however, neglected to study social-influence effects on voting in discrete choice tasks. Using agent-based simulation, we show that under voting — the most widespread social decision rule — social influence contributes to information aggregation and thus strengthens collective judgment. Adding to our knowledge about complex systems comprised of adaptive agents, this finding has important ramifications for the design of collective decision-making in both public administration and private firms.

Given a system where the real-valued states of the agents are aggregated by a function to a real-valued state of the entire system, we are interested in the influence or importance of different agents for that function. This generalizes the notion of power indices for binary voting systems to decisions over interval policy spaces and has applications in economics, engineering, security analysis, and other disciplines. Here, we study the question of importance in systems with interval decisions. Based on the classical Shapley–Shubik and Penrose–Banzhaf index, from binary voting, we motivate and analyze two importance measures. Additionally, we present some results for parametric classes of aggregation functions.

Influence maximization is a well-known problem in the social network analysis literature which is to find a small subset of seed nodes to maximize the diffusion or spread of information. The main application of this problem in the real-world is in viral marketing. However, the classic influence maximization is disabled to model the real-world viral marketing problem, since the effect of the marketing message content and nodes’ opinions have not been considered. In this paper, a modified version of influence maximization which is named as “opinion-aware influence maximization” (OAIM) problem is proposed to make the model more realistic. In this problem, the main objective is to maximize the spread of a desired opinion, by optimizing the message content, rather than the number of infected nodes, which leads to selection of the best set of seed nodes. A nonlinear bi-objective mathematical programming model is developed to model the considered problem. Some transformation techniques are applied to convert the proposed model to a linear single-objective mathematical programming model. The exact solution of the model in small datasets can be obtained by CPLEX algorithm. For the medium and large-scale datasets, a new genetic algorithm is proposed to cope with the size of the problem. Experimental results on some of the well-known datasets show the efficiency and applicability of the proposed OAIM model. In addition, the proposed genetic algorithm overcomes state-of-the-art algorithms.

We consider a simple model of agents modifying their opinion about themselves and about the others during random pair interactions. Two unexpected patterns emerge: (1) without gossips, starting from zero, agents’ opinions tend to grow and stabilize on average at a positive value; (2) when introducing gossips, this pattern is inverted; the opinions tend to decrease and stabilize on average at a negative value. We show that these patterns can be explained by the relative influence of a positive bias on self-opinions and of a negative bias on opinions about others. Without gossips, the positive bias on self-opinions dominates, leading to a positive average opinion. Gossips increase the negative bias about others, which can dominate the positive bias on self-opinions, leading to a negative average opinion.

The paper introduces a general sharing structure and presents sufficient and necessary conditions for the agents to approach by the dynamics of sharing an equal distribution of assets. For the special case of a ring structure with a uniform sharing rate, robustness is analyzed in case the rate does change during the process of sharing. The search for an equal distribution is similar to that for consensus in opinion dynamics and multiagent systems as a result of which tools from the latter are used in proving the results.

Polarization between groups is a major topic of contemporary societal debate and research. Formal models of opinion dynamics try to explain how intergroup polarization arises from simple first principles of social interaction. In existing models, intergroup attitudes affect social influence in the form of homophily or xenophobia, fixed tendencies of individuals to be more open to influence from ingroup members or distance themselves from attitudes of outgroup members. These models generate polarization between groups, but they neglect a central insight from empirical research. Intergroup attitudes are themselves subject to social influence in interactions with both in- and outgroup members. A model is proposed in which the attitude which is subject to social influence is also an intergroup attitude. It affects in turn the influence process itself. Furthermore, it is shown how this changes model predictions about process and conditions of polarization between groups. More complex patterns of intergroup relations emerge than in a model with fixed xenophobia. Especially, a renegade minority (‘outgroup lovers’) is found to have a key role in avoiding mutually negative intergroup relations and even elicit reversed polarization, resulting in a majority of individuals developing a negative attitude towards their ingroup and a positive one for the outgroup.

In Schelling’s segregation model, agents of two ethnic groups reside in a regular grid and aim to live in a neighborhood that matches the minimum desired fraction of members of the same ethnicity. The model shows that observed segregation can emerge from people interacting under spatial constraints following homophily preferences. Even mild preferences can generate high degrees of segregation at the macro level. In modern, ethnically diverse societies, people might not define similarity based on ethnicity. Instead, shared tolerance towards ethnic diversity might play a more significant role, impacting segregation and integration in societies. With this consideration, we extend Schelling’s model by dividing the population of agents into value-oriented and ethnicity-oriented agents. Using parameter sweeping, we explore the consequences that the mutual adaptation of these two types of agents has on ethnic segregation, value segregation, and population density in the neighborhood. We examine for equally sized ethnic groups and for majority–minority conditions. The introduction of value-oriented agents reduces total ethnic segregation compared to Schelling’s original model, but the new value segregation appears to be more pronounced than ethnic segregation. Due to spillover effects, stronger ethnic homophily preferences lead not only to greater ethnic segregation, but also to more value segregation. Stronger value-orientation of the tolerant agents similarly leads to increased ethnic segregation of the ethnicity-oriented agents. Also, value-oriented agents tend to live in neighborhoods with more agents than ethnicity-oriented agents. In majority–minority settings, such effects appear to be more drastic for the minority than the majority ethnicity.