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Increasing Peer Pressure on any Connected Graph Leads to Consensus

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      Abstract

      In this paper, we propose a novel generic model of opinion dynamics over a social network, in the presence of communication among the users leading to interpersonal influence i.e., peer pressure. Each individual in the social network has a distinct objective function representing a weighted sum of internal and external pressures. We prove conditions under which a connected group of users converges to a fixed opinion distribution, and under which conditions the group reaches consensus. Through simulation, we study the rate of convergence on large scale-free networks as well as the impact of user stubbornness on convergence in a simple political model.

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      The spread of obesity in a large social network over 32 years.

      The prevalence of obesity has increased substantially over the past 30 years. We performed a quantitative analysis of the nature and extent of the person-to-person spread of obesity as a possible factor contributing to the obesity epidemic. We evaluated a densely interconnected social network of 12,067 people assessed repeatedly from 1971 to 2003 as part of the Framingham Heart Study. The body-mass index was available for all subjects. We used longitudinal statistical models to examine whether weight gain in one person was associated with weight gain in his or her friends, siblings, spouse, and neighbors. Discernible clusters of obese persons (body-mass index [the weight in kilograms divided by the square of the height in meters], > or =30) were present in the network at all time points, and the clusters extended to three degrees of separation. These clusters did not appear to be solely attributable to the selective formation of social ties among obese persons. A person's chances of becoming obese increased by 57% (95% confidence interval [CI], 6 to 123) if he or she had a friend who became obese in a given interval. Among pairs of adult siblings, if one sibling became obese, the chance that the other would become obese increased by 40% (95% CI, 21 to 60). If one spouse became obese, the likelihood that the other spouse would become obese increased by 37% (95% CI, 7 to 73). These effects were not seen among neighbors in the immediate geographic location. Persons of the same sex had relatively greater influence on each other than those of the opposite sex. The spread of smoking cessation did not account for the spread of obesity in the network. Network phenomena appear to be relevant to the biologic and behavioral trait of obesity, and obesity appears to spread through social ties. These findings have implications for clinical and public health interventions. Copyright 2007 Massachusetts Medical Society.
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        A review of research on bullying and peer victimization in school: An ecological system analysis

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          Biased Assimilation, Homophily and the Dynamics of Polarization

          Are we as a society getting more polarized, and if so, why? We try to answer this question through a model of opinion formation. Empirical studies have shown that homophily results in polarization. However, we show that DeGroot's well-known model of opinion formation based on repeated averaging can never be polarizing, even if individuals are arbitrarily homophilous. We generalize DeGroot's model to account for a phenomenon well-known in social psychology as biased assimilation: when presented with mixed or inconclusive evidence on a complex issue, individuals draw undue support for their initial position thereby arriving at a more extreme opinion. We show that in a simple model of homophilous networks, our biased opinion formation process results in either polarization, persistent disagreement or consensus depending on how biased individuals are. In other words, homophily alone, without biased assimilation, is not sufficient to polarize society. Quite interestingly, biased assimilation also provides insight into the following related question: do internet based recommender algorithms that show us personalized content contribute to polarization? We make a connection between biased assimilation and the polarizing effects of some random-walk based recommender algorithms that are similar in spirit to some commonly used recommender algorithms.
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            Author and article information

            Journal
            2017-02-25
            1702.07912

            http://arxiv.org/licenses/nonexclusive-distrib/1.0/

            Custom metadata
            Extended abstract form appearing in AAMAS 2017 (Sao Paulo, Brazil)
            cs.SI cs.DM physics.soc-ph

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