Consensus Analysis of A Long-Range Opinion Model with A Small Confidence Bound
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- 英文论文题名：Consensus Analysis of A Long-Range Opinion Model with A Small Confidence Bound
- 论文作者：Jiangbo Zhang ; Yiguang Hong
- 英文论文作者：Jiangbo Zhang ; Yiguang Hong ; Jiangbo Zhang is with the faculty of science ; Southwest Petroleum University ; Key Lab of Systems and Control ; Academy of Mathematics and Systems Science ; Chinese Academy of Sciences
- 年：2017
- 作者机构：Jiangbo Zhang is with the faculty of science,Southwest Petroleum University;Key Lab of Systems and Control,Academy of Mathematics and Systems Science,Chinese Academy of Sciences;
- 英文论文关键词：opinion dynamics ; consensus probability ; confidence bound ; long-range interaction
- 会议召开时间：2017-07-26
- 会议录名称：第36届中国控制会议论文集（A）
- 英文会议录名称：Proceedings of the 36th Chinese Control Conference（A）
- 语种：英文
- 分类号：O211
- 学会代码：KZLL
- 会议名称：第36届中国控制会议
- 会议地点：中国辽宁大连
- 主办单位：中国自动化学会控制理论专业委员会
- 学会名称：中国自动化学会控制理论专业委员会
- 页数：6
- 文件大小：417k
- 原文格式：D
- 会议级别：全国
摘要
In this paper, we propose a bounded-confidence opinion model and focus on the study of the opinion consensus probability based on long-range opinion interactions. In this model, each agent updates its opinion using some agents' opinion values according to its confidence bound. We provide a lower bound of the opinion consensus probability when the confidence bound is sufficiently small. Also, we give discussion and simulation examples for the opinion evolution along with some adjustable parameters.
In this paper, we propose a bounded-confidence opinion model and focus on the study of the opinion consensus probability based on long-range opinion interactions. In this model, each agent updates its opinion using some agents' opinion values according to its confidence bound. We provide a lower bound of the opinion consensus probability when the confidence bound is sufficiently small. Also, we give discussion and simulation examples for the opinion evolution along with some adjustable parameters.
In this paper, we propose a bounded-confidence opinion model and focus on the study of the opinion consensus probability based on long-range opinion interactions. In this model, each agent updates its opinion using some agents' opinion values according to its confidence bound. We provide a lower bound of the opinion consensus probability when the confidence bound is sufficiently small. Also, we give discussion and simulation examples for the opinion evolution along with some adjustable parameters.
引文
[1]S.Fortunato,V.Latora,A.Pluchino and A.Rapisarda,“Vector opinion dynamics in a bounded confidence consensus model”,International Journal of Modern Physics C,vol.16(2005),pp.1535-1551.
[2]G.Shi and K.Johansson.“The role of persistent graphs in the agreement seeking of social networks”,IEEE J.on Selected Areas in Communications(supplement),vol.31(2013)pp.1-13.
[3]B.Touri,Product of random stochastic matrices and distributed averaging,Ph.D.dissertation,Dept.of Industrial Engineering in the Graduate College of the University of Illinois at Urbana-Champaign(UIUC)(2011).
[4]J.Lorenz,Managing Complexity:Insights,Concepts,Applications,Springer:Berlin(2008).
[5]J.Lorenz,“A stabilization theorem for dynamics of continuous opinions”,Physica A,vol.335(2005),pp.217-223.
[6]V.Blondel,J.Hendrickx and J.Tsitsiklisˇc,“On Krause’s multi-agent consensus model with state-dependent connectivity”,IEEE Trans.Autom.Control.,vol.54,Nov(2009),pp.2586-2596.
[7]G.Como and F.Fagnani,“Scaling limits for continuous opinion dynamics systems”,Annals of Applied Probability,vol.21,no.4(2011),pp.1537-1567.
[8]N.Friedkin and E.Johnsen,“Social influence networks and opinion change”.In E.J.Lawler and M.W.Macy(eds.),Advances in Group Processes,JAI Press(1999),pp.1-29.
[9]A.Czirok,T.Vicsek,“Collective behavior of interacting selfpropelled particles”.Physica A,vol.281(2006),pp.17-29.
[10]J.Hu and Y.Hong,“Leader-following coordination of multiagent systems with coupling time delays”,Physica A,vol.374(2007),pp.853-863.
[11]G.Shi,M.Johansson,and K.Johansson,“How agreement and disagreement evolve over random dynamic networks”,IEEE J.on Selected Areas in Communications,vol.31(2013),pp.1061-1071.
[12]G.Shi and K.Johansson,“Randomized optimal consensus of multi-agent systems”,Automatica,vol.48,no.12(2012),pp.3018-3030.
[13]Y.Lou and Y.Hong,“Target aggregation of multiple mobile agents by multiple leaders with markovian switching topologies”,Automatica,vol.48(2012),pp.559-563.
[14]N.E.Friedkin,A.V.Proskurnikov,R.Tempo and S.E.Parsegov,“Network science on belief system dynamics under logic constraints”,Science,Vol.354(6310),2016,pp.321-326.
[15]H.Ishii and R.Tempo,“Distributed randomized algorithms for the Page Rank computation”,IEEE Transactions on Automatic Control,vol.55(9)(2010),pp.1987-2002.
[16]W.Mei,N.E.Friedkin,K.Lewis and F.Bullo,“Dynamic models of appraisal networks explaining collective learning”,IEEE Conf.on Decision and Control,Las Vegas,2016,pp.3554-3559.
[17]I.Yaniv and M.Milyavsky,“Using advice from multiple sources to revise and improve judgments”,Organizational Behavior and Human Decision Processes,vol.103(1)(2007),pp.104-120.
[18]T.Plümper and C.W.Martin,“Multi-Party Competition:A Stochastic Equilibrium Analysis,”Available at Social Science Research Network(SSRN):http://ssrn.com/abstract=692621or http://dx.doi.org/10.2139/ssrn.692621,March 2005.
[19]G.Weisbuch,G.Deffuant,F.Amblard,and J.Nadal,“Meet,Discuss and Segregate!”Complexity,7(2002),pp.55-63.
[20]E.J.Rosi,“Mass and Attentive Opinion on Nuclear Weapons Tests and Fallout,1954C1963,”Public Opinion Quarterly,vol.29(2),1965,pp.280-297.
[21]C Castellano,S Fortunato,V Loreto.“Statistical physics of social dynamics,”Reviews of modern physics,81(2009),pp.591-646.
[22]F.Fagnani and S.Zampieri,“Randomized consensus algorithms over large scale networks,”IEEE Journal on Selected Areas in Communications,vol.26,2008,pp.634-649.
[23]J.Zhang and Y.Hong,“Opinion Evolution Analysis for ShortRange and Long-Range Deffuant-Weisbuch Models,”Physica A:Statistical Mechanics and its Applications,vol.3922013,pp.5289-5297.
[24]J.Zhang and G.Chen,“Covergence rate of the asymmetric Deffuant-Weisbuch dynamics,”Journal of Systems Science and Complexity,vol.28(4),2015,pp.773-787.
[25]J.Zhang,“Convergence Analysis for Asymmetric DeffuantWeisbuch Model,”Kypernetica,vol.50,2014,pp.32-45.
[26]J.Zhang and Y.Hong,“Fluctuation analysis of a long-range opinion dynamics,”Proc.IEEE Conf.Decision and Control,Los Angeles,USA,Dec.2014.
[27]D.Helbing,Managing Complexity:Insights,Concepts,Applications,Springer Publishing Company,Incorporated:Berlin;2007.
[28]C.Meyer,Matrix analysis and applied linear algebra,First Edition,Society for Industrial and Applied Mathematics(SIAM),Philadelphia;2000.
[29]Y.Chow and H.Teicher,Probability Theory:Independence Interchangeability Martingales,Second Edition,SpringerVerlag Press,Heidelberg Berlin,1978.
[30]H.Chen,Stochastic Approximation and Its Applications,Kluwer Academic Publishers,Netherlands;2002.
[31]R.Durrett,Probability Theory and Examples,Fourth Edition,Cambridge University Press,New York;2010.
[2]G.Shi and K.Johansson.“The role of persistent graphs in the agreement seeking of social networks”,IEEE J.on Selected Areas in Communications(supplement),vol.31(2013)pp.1-13.
[3]B.Touri,Product of random stochastic matrices and distributed averaging,Ph.D.dissertation,Dept.of Industrial Engineering in the Graduate College of the University of Illinois at Urbana-Champaign(UIUC)(2011).
[4]J.Lorenz,Managing Complexity:Insights,Concepts,Applications,Springer:Berlin(2008).
[5]J.Lorenz,“A stabilization theorem for dynamics of continuous opinions”,Physica A,vol.335(2005),pp.217-223.
[6]V.Blondel,J.Hendrickx and J.Tsitsiklisˇc,“On Krause’s multi-agent consensus model with state-dependent connectivity”,IEEE Trans.Autom.Control.,vol.54,Nov(2009),pp.2586-2596.
[7]G.Como and F.Fagnani,“Scaling limits for continuous opinion dynamics systems”,Annals of Applied Probability,vol.21,no.4(2011),pp.1537-1567.
[8]N.Friedkin and E.Johnsen,“Social influence networks and opinion change”.In E.J.Lawler and M.W.Macy(eds.),Advances in Group Processes,JAI Press(1999),pp.1-29.
[9]A.Czirok,T.Vicsek,“Collective behavior of interacting selfpropelled particles”.Physica A,vol.281(2006),pp.17-29.
[10]J.Hu and Y.Hong,“Leader-following coordination of multiagent systems with coupling time delays”,Physica A,vol.374(2007),pp.853-863.
[11]G.Shi,M.Johansson,and K.Johansson,“How agreement and disagreement evolve over random dynamic networks”,IEEE J.on Selected Areas in Communications,vol.31(2013),pp.1061-1071.
[12]G.Shi and K.Johansson,“Randomized optimal consensus of multi-agent systems”,Automatica,vol.48,no.12(2012),pp.3018-3030.
[13]Y.Lou and Y.Hong,“Target aggregation of multiple mobile agents by multiple leaders with markovian switching topologies”,Automatica,vol.48(2012),pp.559-563.
[14]N.E.Friedkin,A.V.Proskurnikov,R.Tempo and S.E.Parsegov,“Network science on belief system dynamics under logic constraints”,Science,Vol.354(6310),2016,pp.321-326.
[15]H.Ishii and R.Tempo,“Distributed randomized algorithms for the Page Rank computation”,IEEE Transactions on Automatic Control,vol.55(9)(2010),pp.1987-2002.
[16]W.Mei,N.E.Friedkin,K.Lewis and F.Bullo,“Dynamic models of appraisal networks explaining collective learning”,IEEE Conf.on Decision and Control,Las Vegas,2016,pp.3554-3559.
[17]I.Yaniv and M.Milyavsky,“Using advice from multiple sources to revise and improve judgments”,Organizational Behavior and Human Decision Processes,vol.103(1)(2007),pp.104-120.
[18]T.Plümper and C.W.Martin,“Multi-Party Competition:A Stochastic Equilibrium Analysis,”Available at Social Science Research Network(SSRN):http://ssrn.com/abstract=692621or http://dx.doi.org/10.2139/ssrn.692621,March 2005.
[19]G.Weisbuch,G.Deffuant,F.Amblard,and J.Nadal,“Meet,Discuss and Segregate!”Complexity,7(2002),pp.55-63.
[20]E.J.Rosi,“Mass and Attentive Opinion on Nuclear Weapons Tests and Fallout,1954C1963,”Public Opinion Quarterly,vol.29(2),1965,pp.280-297.
[21]C Castellano,S Fortunato,V Loreto.“Statistical physics of social dynamics,”Reviews of modern physics,81(2009),pp.591-646.
[22]F.Fagnani and S.Zampieri,“Randomized consensus algorithms over large scale networks,”IEEE Journal on Selected Areas in Communications,vol.26,2008,pp.634-649.
[23]J.Zhang and Y.Hong,“Opinion Evolution Analysis for ShortRange and Long-Range Deffuant-Weisbuch Models,”Physica A:Statistical Mechanics and its Applications,vol.3922013,pp.5289-5297.
[24]J.Zhang and G.Chen,“Covergence rate of the asymmetric Deffuant-Weisbuch dynamics,”Journal of Systems Science and Complexity,vol.28(4),2015,pp.773-787.
[25]J.Zhang,“Convergence Analysis for Asymmetric DeffuantWeisbuch Model,”Kypernetica,vol.50,2014,pp.32-45.
[26]J.Zhang and Y.Hong,“Fluctuation analysis of a long-range opinion dynamics,”Proc.IEEE Conf.Decision and Control,Los Angeles,USA,Dec.2014.
[27]D.Helbing,Managing Complexity:Insights,Concepts,Applications,Springer Publishing Company,Incorporated:Berlin;2007.
[28]C.Meyer,Matrix analysis and applied linear algebra,First Edition,Society for Industrial and Applied Mathematics(SIAM),Philadelphia;2000.
[29]Y.Chow and H.Teicher,Probability Theory:Independence Interchangeability Martingales,Second Edition,SpringerVerlag Press,Heidelberg Berlin,1978.
[30]H.Chen,Stochastic Approximation and Its Applications,Kluwer Academic Publishers,Netherlands;2002.
[31]R.Durrett,Probability Theory and Examples,Fourth Edition,Cambridge University Press,New York;2010.