Adoption as a Social Marker: Innovation Diffusion with Outgroup Aversion

Social identities are among the key factors driving behavior in complex societies. Signals of social identity are known to influence individual behaviors in the adoption of innovations. Yet the population-level consequences of identity signaling on the diffusion of innovations are largely unknown. Here we use both analytical and agent-based modeling to consider the spread of a beneficial innovation in a structured population in which there exist two groups who are averse to being mistaken for each other. We investigate the dynamics of adoption and consider the role of structural factors such as demographic skew and communication scale on population-level outcomes. We find that outgroup aversion can lead to adoption being delayed or suppressed in one group, and that population-wide underadoption is common. Comparing the two models, we find that differential adoption can arise due to structural constraints on information flow even in the absence of intrinsic between-group differences in adoption rates. Further, we find that patterns of polarization in adoption at both local and global scales depend on the details of demographic organization and the scale of communication. This research has particular relevance to widely beneficial but identity-relevant products and behaviors, such as green technologies, where overall levels of adoption determine the positive benefits that accrue to society at large.Comment: 26 pages, 10 figure

Hipsters on Networks: How a Small Group of Individuals Can Lead to an Anti-Establishment Majority

The spread of opinions, memes, diseases, and "alternative facts" in a population depends both on the details of the spreading process and on the structure of the social and communication networks on which they spread. In this paper, we explore how \textit{anti-establishment} nodes (e.g., \textit{hipsters}) influence the spreading dynamics of two competing products. We consider a model in which spreading follows a deterministic rule for updating node states (which describe which product has been adopted) in which an adjustable fraction $p_{\rm Hip}$ of the nodes in a network are hipsters, who choose to adopt the product that they believe is the less popular of the two. The remaining nodes are conformists, who choose which product to adopt by considering which products their immediate neighbors have adopted. We simulate our model on both synthetic and real networks, and we show that the hipsters have a major effect on the final fraction of people who adopt each product: even when only one of the two products exists at the beginning of the simulations, a very small fraction of hipsters in a network can still cause the other product to eventually become the more popular one. To account for this behavior, we construct an approximation for the steady-state adoption fraction on $k$-regular trees in the limit of few hipsters. Additionally, our simulations demonstrate that a time delay $\tau$ in the knowledge of the product distribution in a population, as compared to immediate knowledge of product adoption among nearest neighbors, can have a large effect on the final distribution of product adoptions. Our simple model and analysis may help shed light on the road to success for anti-establishment choices in elections, as such success can arise rather generically in our model from a small number of anti-establishment individuals and ordinary processes of social influence on normal individuals.Comment: Extensively revised, with much new analysis and numerics The abstract on arXiv is a shortened version of the full abstract because of space limit

Holistic Influence Maximization: Combining Scalability and Efficiency with Opinion-Aware Models

The steady growth of graph data from social networks has resulted in wide-spread research in finding solutions to the influence maximization problem. In this paper, we propose a holistic solution to the influence maximization (IM) problem. (1) We introduce an opinion-cum-interaction (OI) model that closely mirrors the real-world scenarios. Under the OI model, we introduce a novel problem of Maximizing the Effective Opinion (MEO) of influenced users. We prove that the MEO problem is NP-hard and cannot be approximated within a constant ratio unless P=NP. (2) We propose a heuristic algorithm OSIM to efficiently solve the MEO problem. To better explain the OSIM heuristic, we first introduce EaSyIM - the opinion-oblivious version of OSIM, a scalable algorithm capable of running within practical compute times on commodity hardware. In addition to serving as a fundamental building block for OSIM, EaSyIM is capable of addressing the scalability aspect - memory consumption and running time, of the IM problem as well. Empirically, our algorithms are capable of maintaining the deviation in the spread always within 5% of the best known methods in the literature. In addition, our experiments show that both OSIM and EaSyIM are effective, efficient, scalable and significantly enhance the ability to analyze real datasets.Comment: ACM SIGMOD Conference 2016, 18 pages, 29 figure

Learning to be Biased

We simulate societal opinion dynamics when there is confirmation bias in information gathering and spread. If decision making is influenced by confirmation bias, the agent puts more weight on positive information to confirm hypothesis or reservation in the learning process, which renders selectivity in information gathering. If the utility discovered post purchase is low, it is externalized rather than internalized (i.e., self blame) for the selectivity of information. This causes the agent to outweigh the negative information. These two mechanisms are simulated to investigate the societal opinion dynamics and explain behavioral patterns such as overconfidence, stickiness of response and ``success breeds success" phenomenon.Confirmation bias; Opinion percolation and convergence; Selectivity in information search; Hypothesis testing

Dynamical Systems on Networks: A Tutorial

We give a tutorial for the study of dynamical systems on networks. We focus especially on "simple" situations that are tractable analytically, because they can be very insightful and provide useful springboards for the study of more complicated scenarios. We briefly motivate why examining dynamical systems on networks is interesting and important, and we then give several fascinating examples and discuss some theoretical results. We also briefly discuss dynamical systems on dynamical (i.e., time-dependent) networks, overview software implementations, and give an outlook on the field.Comment: 39 pages, 1 figure, submitted, more examples and discussion than original version, some reorganization and also more pointers to interesting direction

Opinion modeling on social media and marketing aspects

We introduce and discuss kinetic models of opinion formation on social networks in which the distribution function depends on both the opinion and the connectivity of the agents. The opinion formation model is subsequently coupled with a kinetic model describing the spreading of popularity of a product on the web through a social network. Numerical experiments on the underlying kinetic models show a good qualitative agreement with some measured trends of hashtags on social media websites and illustrate how companies can take advantage of the network structure to obtain at best the advertisement of their products

Role of social environment and social clustering in spread of opinions in co-evolving networks

Taking a pragmatic approach to the processes involved in the phenomena of collective opinion formation, we investigate two specific modifications to the co-evolving network voter model of opinion formation, studied by Holme and Newman [1]. First, we replace the rewiring probability parameter by a distribution of probability of accepting or rejecting opinions between individuals, accounting for the asymmetric influences in relationships among individuals in a social group. Second, we modify the rewiring step by a path-length-based preference for rewiring that reinforces local clustering. We have investigated the influences of these modifications on the outcomes of the simulations of this model. We found that varying the shape of the distribution of probability of accepting or rejecting opinions can lead to the emergence of two qualitatively distinct final states, one having several isolated connected components each in internal consensus leading to the existence of diverse set of opinions and the other having one single dominant connected component with each node within it having the same opinion. Furthermore, and more importantly, we found that the initial clustering in network can also induce similar transitions. Our investigation also brings forward that these transitions are governed by a weak and complex dependence on system size. We found that the networks in the final states of the model have rich structural properties including the small world property for some parameter regimes. [1] P. Holme and M. Newman, Phys. Rev. E 74, 056108 (2006)