The paper treats opinion dynamics under bounded confidence when agents employ, beside an arithmetic mean, means like a geometric mean, a power mean or a random mean in aggregating opinions. The different kinds of collective dynamics resulting from these various ways of averaging are studied and compared by simulations. Particular attention is given to the random mean which is a new concept introduced in this paper. All those concrete means are just particular cases of a partial abstract mean, which also is a new concept. This comprehensive concept of averaging opinions is investigated also analytically and it is shown in particular, that the dynamics driven by it always stabilizes in a certain pattern of opinions. Copyright Springer Science + Business Media, Inc. 2005opinion dynamics, bounded confidence, averaging, power mean, random mean, abstract means,
By a simple extension of the bounded confidence model, it is possible to model the influence of a radical group, or a charismatic leader on the opinion dynamics of 'normal' agents that update their opinions under both, the influence of their normal peers, and the additional influence of the radical group or a charismatic leader. From a more abstract point of view, we model the influence of a signal, that is constant, may have different intensities, and is 'heard' only by agents with opinions, that are not too far away. For such a dynamic a Constant Signal Theorem is proven. In the model we get a lot of surprising effects. For instance, the more intensive signal may have less effect; more radicals may lead to less radicalization of normal agents. The model is an extremely simple conceptual model. Under some assumptions the whole parameter space can be analyzed. The model inspires new possible explanations, new perspectives for empirical studies, and new ideas for prevention or intervention policies.
Abstract:The Journal of Mathematical Sociology (JMS) started in 1971. The second issue contained its most cited article: Thomas C. Schelling, "Dynamic Models of Segregation". In that article, Schelling presented a family of models, one of which became a canonical model. To date it is called the Schelling model -an eponym that affixes the inventor's name to the invention, one of the highest forms of scientific recognition. In the very first issue of JMS, James Minoru Sakoda published an article entitled "The Checkerboard Model of Social Interaction". Sakoda's article more or less went unrecognized. Yet, a careful comparison demonstrates that in a certain sense the Schelling model is just an instance of Sakoda's model. A precursor of that model was already part of Sakoda's 1949 dissertation submitted to the University of California at Berkeley. A substantial amount of evidence indicates that in the 1970s Sakoda was well known and recognized as a computational social scientist, whereas Schelling was an unknown in the field. A generation later, the pattern of recognition almost completely reversed: Sakoda had become the unknown, while Schelling was the well-known inventor of the pioneering Schelling model. This article explains this puzzling pattern of recognition. Technical and social factors play a decisive role. Some contrafactual historical reflection suggests that the final result was not inevitable.
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