Opinion dynamics driven by various ways of averaging

被引:126
作者
Hegselmann R. [1 ]
Krause U. [2 ]
机构
[1] Department of Philosophy, University Bayreuth, Bayreuth
[2] Department of Mathematics, University Bremen, Bremen
关键词
Abstract means; Averaging; Bounded confidence; Opinion dynamics; Power mean; Random mean;
D O I
10.1007/s10614-005-6296-3
中图分类号
学科分类号
摘要
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. © Springer Science + Business Media, Inc. 2005.
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收藏
页码:381 / 405
页数:24
相关论文
共 20 条
[1]  
Arazy J., Claesson T., Janson S., Peetre J., Mean and their iterations, Proceedings of the Nineteenth Nordic Congress of Mathematics, pp. 191-212, (1985)
[2]  
Axelrod R., The dissemination of culture: A model with local convergence and global polarization, Journal of Conflict Resolution, 41, pp. 203-226, (1997)
[3]  
Benabou R., Heterogeneity, stratifcation and growth: Macroeconomic implications of community structure and school finance, American Economic Review, 86, pp. 584-609, (1996)
[4]  
Borwein J.M., Borwein P.B., Pi and the AGM. A Study in Analytic Number Theory and Computational Complexity, (1987)
[5]  
Ben-Naim E., Krapivsky P.L., Redner S., Bifurcations and patterns in compromise processes, Physica D, 183, pp. 190-204, (2003)
[6]  
Bullen P.S., Mitrinovic D.S., Vasic P.M., Means and Their Inequalities, (1988)
[7]  
Carlson B.C., Algorithms involving arithmetic and geometric means, American Mathematical Monthly, 78, pp. 496-505, (1971)
[8]  
Deffuant G., Amblard F., Weisbuch G., Faure Th., How can extremism prevail? A study based on the relative agreement interaction model, Journal of Artificial Societies and Social Simulation, 5, 4, (2002)
[9]  
Dittmer J.C., Consensus formation under bounded confidence, Nonlinear Analysis, 47, pp. 4615-4621, (2001)
[10]  
Hardy G.H., Littlewood J.E., Polya G., Inequalities, (1973)