The critical value of the deffuant model equals one half

Nicolas Lanchier

The critical value of the deffuant model equals one half

Research output: Contribution to journal › Article › peer-review

Abstract

Similarly to the popular voter model, the Deffuant model describes opinion dynamics taking place in spatially structured environments represented by a connected graph. Pairs of adjacent vertices interact at a constant rate. If the opinion distance between the interacting vertices is larger than some confidence threshold ε > 0, then nothing happens, otherwise, the vertices' opinions get closer to each other. It has been conjectured based on numerical simulations that this process exhibits a phase transition at the critical value ε_c = 1/2. For confidence thresholds larger than one half, the process converges to a global consensus, whereas coexistence occurs for confidence thresholds smaller than one half. In this article, we develop new geometrical techniques to prove this conjecture.

Original language	English (US)
Pages (from-to)	383-402
Number of pages	20
Journal	Alea
Volume	9
Issue number	2
State	Published - 2012

Keywords

Interacting particle system
Random walks
Social dynamics.

ASJC Scopus subject areas

Statistics and Probability

Cite this

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title = "The critical value of the deffuant model equals one half",

abstract = "Similarly to the popular voter model, the Deffuant model describes opinion dynamics taking place in spatially structured environments represented by a connected graph. Pairs of adjacent vertices interact at a constant rate. If the opinion distance between the interacting vertices is larger than some confidence threshold ε > 0, then nothing happens, otherwise, the vertices' opinions get closer to each other. It has been conjectured based on numerical simulations that this process exhibits a phase transition at the critical value εc = 1/2. For confidence thresholds larger than one half, the process converges to a global consensus, whereas coexistence occurs for confidence thresholds smaller than one half. In this article, we develop new geometrical techniques to prove this conjecture.",

keywords = "Interacting particle system, Random walks, Social dynamics.",

author = "Nicolas Lanchier",

note = "Funding Information: We thank Dr Herbert A. Simon of Carnegie Mellon for his input to this research and Dr Chris F. Kemerer of MIT for providing us with the project data. W e are grateful to the organization that supplied us with additional project data. W e also thank the anonymous reviewers for their valuable comments. This research was supported in part by a grant from the NSF Computer and Computation Research, Software Engineering Program, CCR-8921287.",

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language = "English (US)",

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AU - Lanchier, Nicolas

N1 - Funding Information: We thank Dr Herbert A. Simon of Carnegie Mellon for his input to this research and Dr Chris F. Kemerer of MIT for providing us with the project data. W e are grateful to the organization that supplied us with additional project data. W e also thank the anonymous reviewers for their valuable comments. This research was supported in part by a grant from the NSF Computer and Computation Research, Software Engineering Program, CCR-8921287.

PY - 2012

Y1 - 2012

N2 - Similarly to the popular voter model, the Deffuant model describes opinion dynamics taking place in spatially structured environments represented by a connected graph. Pairs of adjacent vertices interact at a constant rate. If the opinion distance between the interacting vertices is larger than some confidence threshold ε > 0, then nothing happens, otherwise, the vertices' opinions get closer to each other. It has been conjectured based on numerical simulations that this process exhibits a phase transition at the critical value εc = 1/2. For confidence thresholds larger than one half, the process converges to a global consensus, whereas coexistence occurs for confidence thresholds smaller than one half. In this article, we develop new geometrical techniques to prove this conjecture.

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The critical value of the deffuant model equals one half

Abstract

Keywords

ASJC Scopus subject areas

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