Stochastic bounded confidence opinion dynamics

In a vast body of opinion dynamics literature, an agent updates its opinion based on the opinions of its neighbors in a static social graph, regardless of their differences in opinions. In contrast, the bounded confidence opinion dynamics does not presume a static interaction graph, and instead limits interactions to those agents that share related opinions (i.e., whose opinions are close to one another). We generalize the bounded confidence opinion dynamics model by incorporating stochastic interactions based on opinion differences and the endogenous evolution of the agent opinions, which itself is a random process. We analytically characterize the conditions under which this stochastic dynamics is stable in an appropriate sense.

[1]  F. Fagnani,et al.  Scaling limits for continuous opinion dynamics systems , 2009 .

[2]  Rainer Hegselmann,et al.  Opinion dynamics and bounded confidence: models, analysis and simulation , 2002, J. Artif. Soc. Soc. Simul..

[3]  Guy Fayolle,et al.  Transient phenomena for Markov chains and applications , 1992, Advances in Applied Probability.

[4]  S. Foss,et al.  AN OVERVIEW OF SOME STOCHASTIC STABILITY METHODS( Network Design, Control and Optimization) , 2004 .

[5]  Alireza Tahbaz-Salehi,et al.  Consensus Over Ergodic Stationary Graph Processes , 2010, IEEE Transactions on Automatic Control.

[6]  Reza Olfati-Saber,et al.  Consensus and Cooperation in Networked Multi-Agent Systems , 2007, Proceedings of the IEEE.

[7]  Robert Y. Shapiro,et al.  Hearing the Opposition: It Starts at the Top , 2013 .

[8]  Jan Lorenz,et al.  Continuous Opinion Dynamics under Bounded Confidence: A Survey , 2007, 0707.1762.

[9]  S. Fortunato,et al.  Statistical physics of social dynamics , 2007, 0710.3256.

[10]  Jonathan H. Manton,et al.  Opinion dynamics with noisy information , 2013, 52nd IEEE Conference on Decision and Control.

[11]  Emilio Hernández-García,et al.  The noisy Hegselmann-Krause model for opinion dynamics , 2013, 1309.2858.

[12]  Luc Moreau,et al.  Stability of multiagent systems with time-dependent communication links , 2005, IEEE Transactions on Automatic Control.

[13]  Tao Li,et al.  Consensus Conditions of Multi-Agent Systems With Time-Varying Topologies and Stochastic Communication Noises , 2010, IEEE Transactions on Automatic Control.

[14]  Peter E. Caines,et al.  Social dynamics in mean field LQG control: Egoistic and altruistic agents , 2010, 49th IEEE Conference on Decision and Control (CDC).

[15]  Asuman E. Ozdaglar,et al.  Constrained Consensus and Optimization in Multi-Agent Networks , 2008, IEEE Transactions on Automatic Control.

[16]  Éva Tardos,et al.  Maximizing the Spread of Influence through a Social Network , 2015, Theory Comput..

[17]  Adrian Carro,et al.  The Role of Noise and Initial Conditions in the Asymptotic Solution of a Bounded Confidence, Continuous-Opinion Model , 2012, Journal of Statistical Physics.

[18]  John N. Tsitsiklis,et al.  On Krause's Multi-Agent Consensus Model With State-Dependent Connectivity , 2008, IEEE Transactions on Automatic Control.

[19]  James N. Druckman,et al.  How Elite Partisan Polarization Affects Public Opinion Formation , 2013, American Political Science Review.

[20]  Behrouz Touri,et al.  Multi-dimensional Hegselmann-Krause dynamics , 2012, 2012 IEEE 51st IEEE Conference on Decision and Control (CDC).

[21]  Donald F. Towsley,et al.  The effect of network topology on the spread of epidemics , 2005, Proceedings IEEE 24th Annual Joint Conference of the IEEE Computer and Communications Societies..

[22]  A. Ozdaglar,et al.  Discrete Opinion Dynamics with Stubborn Agents , 2011 .

[23]  Matthew O. Jackson,et al.  Naïve Learning in Social Networks and the Wisdom of Crowds , 2010 .

[24]  Asuman E. Ozdaglar,et al.  Opinion Fluctuations and Disagreement in Social Networks , 2010, Math. Oper. Res..