Discrete Opinion Dynamics with Stubborn Agents

39 Pages Posted: 21 Jan 2011

See all articles by Ercan Yildiz

Ercan Yildiz

Massachusetts Institute of Technology (MIT) - Laboratory for Information and Decision Systems

Daron Acemoglu

Massachusetts Institute of Technology (MIT) - Department of Economics; Centre for Economic Policy Research (CEPR); National Bureau of Economic Research (NBER)

Asuman E. Ozdaglar

Massachusetts Institute of Technology (MIT) - Department of Electrical Engineering and Computer Science

Amin Saberi

Stanford University - Department of Management Science & Engineering

Anna Scaglione

University of California, Davis - Electrical and Computer Engineering Department

Date Written: January 20, 2011

Abstract

We study discrete opinion dynamics in a social network with "stubborn agents" who influence others but do not change their opinions. We generalize the classical voter model by introducing nodes (stubborn agents) that have a fixed state. We show that the presence of stubborn agents with opposing opinions precludes convergence to consensus; instead, opinions converge in distribution with disagreement and fluctuations. In addition to the first moment of this distribution typically studied in the literature, we study the behavior of the second moment in terms of network properties and the opinions and locations of stubborn agents. We also study the problem of "optimal placement of stubborn agents" where the location of a fixed number of stubborn agents is chosen to have the maximum impact on the long-run expected opinions of agents.

Keywords: Opinion Dynamics, Social Networks, Stubborn Agents, Voter Model

Suggested Citation

Yildiz, Ercan and Acemoglu, Daron and Ozdaglar, Asuman E. and Saberi, Amin and Scaglione, Anna, Discrete Opinion Dynamics with Stubborn Agents (January 20, 2011). Available at SSRN: https://ssrn.com/abstract=1744113 or http://dx.doi.org/10.2139/ssrn.1744113

Ercan Yildiz (Contact Author)

Massachusetts Institute of Technology (MIT) - Laboratory for Information and Decision Systems ( email )

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Daron Acemoglu

Massachusetts Institute of Technology (MIT) - Department of Economics ( email )

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Centre for Economic Policy Research (CEPR)

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National Bureau of Economic Research (NBER)

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Asuman E. Ozdaglar

Massachusetts Institute of Technology (MIT) - Department of Electrical Engineering and Computer Science ( email )

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Amin Saberi

Stanford University - Department of Management Science & Engineering ( email )

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Stanford, CA 94305-9025
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Anna Scaglione

University of California, Davis - Electrical and Computer Engineering Department ( email )

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Davis, CA 95616
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