Minority Becomes Majority in Social Networks

It is often observed that agents tend to imitate the behavior of their neighbors in a social network. This imitating behavior might lead to the strategic decision of adopting a public behavior that differs from what the agent believes is the right one and this can subvert the behavior of the population as a whole. In this paper, we consider the case in which agents express preferences over two alternatives and model social pressure with the majority dynamics: at each step an agent is selected and its preference is replaced by the majority of the preferences of her neighbors. In case of a tie, the agent does not change her current preference. A profile of the agents' preferences is stable if the preference of each agent coincides with the preference of at least half of the neighbors (thus, the system is in equilibrium). We ask whether there are network topologies that are robust to social pressure. That is, we ask if there are graphs in which the majority of preferences in an initial profile always coincides with the majority of the preference in all stable profiles reachable from that profile. We completely characterize the graphs with this robustness property by showing that this is possible only if the graph has no edge or is a clique or very close to a clique. In other words, except for this handful of graphs, every graph admits at least one initial profile of preferences in which the majority dynamics can subvert the initial majority. We also show that deciding whether a graph admits a minority that becomes majority is NP-hard when the minority size is at most 1/4-th of the social network size.Comment: To appear in WINE 201

Non-consensus opinion model on directed networks

Dynamic social opinion models have been widely studied on undirected networks, and most of them are based on spin interaction models that produce a consensus. In reality, however, many networks such as Twitter and the World Wide Web are directed and are composed of both unidirectional and bidirectional links. Moreover, from choosing a coffee brand to deciding who to vote for in an election, two or more competing opinions often coexist. In response to this ubiquity of directed networks and the coexistence of two or more opinions in decision-making situations, we study a non-consensus opinion model introduced by Shao et al. \cite{shao2009dynamic} on directed networks. We define directionality $\xi$ as the percentage of unidirectional links in a network, and we use the linear correlation coefficient $\rho$ between the indegree and outdegree of a node to quantify the relation between the indegree and outdegree. We introduce two degree-preserving rewiring approaches which allow us to construct directed networks that can have a broad range of possible combinations of directionality $\xi$ and linear correlation coefficient $\rho$ and to study how $\xi$ and $\rho$ impact opinion competitions. We find that, as the directionality $\xi$ or the indegree and outdegree correlation $\rho$ increases, the majority opinion becomes more dominant and the minority opinion's ability to survive is lowered

Coupled dynamics of node and link states in complex networks: A model for language competition

Inspired by language competition processes, we present a model of coupled evolution of node and link states. In particular, we focus on the interplay between the use of a language and the preference or attitude of the speakers towards it, which we model, respectively, as a property of the interactions between speakers (a link state) and as a property of the speakers themselves (a node state). Furthermore, we restrict our attention to the case of two socially equivalent languages and to socially inspired network topologies based on a mechanism of triadic closure. As opposed to most of the previous literature, where language extinction is an inevitable outcome of the dynamics, we find a broad range of possible asymptotic configurations, which we classify as: frozen extinction states, frozen coexistence states, and dynamically trapped coexistence states. Moreover, metastable coexistence states with very long survival times and displaying a non-trivial dynamics are found to be abundant. Interestingly, a system size scaling analysis shows, on the one hand, that the probability of language extinction vanishes exponentially for increasing system sizes and, on the other hand, that the time scale of survival of the non-trivial dynamical metastable states increases linearly with the size of the system. Thus, non-trivial dynamical coexistence is the only possible outcome for large enough systems. Finally, we show how this coexistence is characterized by one of the languages becoming clearly predominant while the other one becomes increasingly confined to "ghetto-like" structures: small groups of bilingual speakers arranged in triangles, with a strong preference for the minority language, and using it for their intra-group interactions while they switch to the predominant language for communications with the rest of the population.Comment: 21 pages, 15 figure

Community structure and ethnic preferences in school friendship networks

Recently developed concepts and techniques of analyzing complex systems provide new insight into the structure of social networks. Uncovering recurrent preferences and organizational principles in such networks is a key issue to characterize them. We investigate school friendship networks from the Add Health database. Applying threshold analysis, we find that the friendship networks do not form a single connected component through mutual strong nominations within a school, while under weaker conditions such interconnectedness is present. We extract the networks of overlapping communities at the schools (c-networks) and find that they are scale free and disassortative in contrast to the direct friendship networks, which have an exponential degree distribution and are assortative. Based on the network analysis we study the ethnic preferences in friendship selection. The clique percolation method we use reveals that when in minority, the students tend to build more densely interconnected groups of friends. We also find an asymmetry in the behavior of black minorities in a white majority as compared to that of white minorities in a black majority.Comment: submitted to Physica

Growth aspirations and social capital: Young firms in a post-conflict environnment

We explore the social determinants of growth aspirations of young firms’ owners and managers in a post-conflict economy. We focus on social capital, which we treat as a multi-dimensional phenomenon, studying not only the effect of owners’ and managers’ personal networks on growth aspirations, but also other facets that facilitate cooperation such as trust in institutions and generalised trust in people. We posit that that the generalised trust amplifies the beneficial effects of personal business networks, explaining how this conclusion diverges from earlier literature. We argue that in a post-conflict country, preservation of ethnic diversity is indicative of tolerance and low communication barriers and social capital appropriable for entrepreneurship. Our empirical counterpart and hypotheses testing rely on survey of young businesses in Bosnia and Herzegovina

Can extremism guarantee pluralism?

Many models have been proposed to explain opinion formation in groups of individuals; most of these models study opinion propagation as the interaction between nodes/agents in a social network. Opinion formation is a complex process and a realistic model should also take into account the important feedbacks that the opinions of the agents have on the structure of the social networks and on the characteristics of the opinion dynamics. In this paper we will show that associating to different agents different kinds of interconnections and different interacting behaviours can lead to interesting scenarios, like the coexistence of several opinion clusters, namely pluralism. In our model agents have opinions uniformly and continuously distributed between two extremes. The social network is formed through a social aggregation mechanism including the segregation process of the extremists that results in many real communities. We show how this process affects the opinion dynamics in the whole society. In the opinion evolution we consider the different predisposition of single individuals to interact and to exchange opinion with each other; we associate to each individual a different tolerance threshold, depending on its own opinion: extremists are less willing to interact with individuals with strongly different opinions and to change significantly their ideas. A general result is obtained: when there is no interaction restriction, the opinion always converges to uniformity, but the same is happening whenever a strong segregation process of the extremists occurs. Only when extremists are forming clusters but these clusters keep interacting with the rest of the society, the survival of a wide opinion range is guaranteed.Comment: 20 pages, 10 figure