数学物理学报(英文版) ›› 2014, Vol. 34 ›› Issue (4): 1029-1040.doi: 10.1016/S0252-9602(14)60067-9

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CONSENSUS FORMATION OF TWO-LEVEL OPINION DYNAMICS

Yilun SHANG   

  1. SUTD-MIT International Design Center, Singapore University of Technology and Design, 20 Dover Drive, 138682, Singapore
  • 收稿日期:2013-06-24 修回日期:2013-10-01 出版日期:2014-07-20 发布日期:2014-07-20
  • 基金资助:

    This research was partially supported by a SUTD-MIT IDC Grant.

CONSENSUS FORMATION OF TWO-LEVEL OPINION DYNAMICS

Yilun SHANG   

  1. SUTD-MIT International Design Center, Singapore University of Technology and Design, 20 Dover Drive, 138682, Singapore
  • Received:2013-06-24 Revised:2013-10-01 Online:2014-07-20 Published:2014-07-20
  • Supported by:

    This research was partially supported by a SUTD-MIT IDC Grant.

摘要:

Opinion dynamics have received significant attention in recent years. This pa-per proposes a bounded confidence opinion model for a group of agents with two different confidence levels. Each agent in the population is endowed with a confidence interval around her opinion with radius αd or (1 − α)d, where α∈ (0, 1/2] represents the differentiation of
confidence levels. We analytically derived the critical confidence bound dc = 1/(4α) for the two-level opinion dynamics on Z. A single opinion cluster is formed with probability 1 above this critical value regardless of the ratio p of agents with high/low confidence. Extensive numerical simulations are performed to illustrate our theoretical results. Noticed is a clear impact of p on the collective behavior: more agents with high confidence lead to harder agreement. It is also experimentally revealed that the sharpness of the threshold dc increases with α but does not depend on p.

关键词: social dynamics, bounded confidence, phase transition, Monte Carlo simulation

Abstract:

Opinion dynamics have received significant attention in recent years. This pa-per proposes a bounded confidence opinion model for a group of agents with two different confidence levels. Each agent in the population is endowed with a confidence interval around her opinion with radius αd or (1 − α)d, where α∈ (0, 1/2] represents the differentiation of
confidence levels. We analytically derived the critical confidence bound dc = 1/(4α) for the two-level opinion dynamics on Z. A single opinion cluster is formed with probability 1 above this critical value regardless of the ratio p of agents with high/low confidence. Extensive numerical simulations are performed to illustrate our theoretical results. Noticed is a clear impact of p on the collective behavior: more agents with high confidence lead to harder agreement. It is also experimentally revealed that the sharpness of the threshold dc increases with α but does not depend on p.

Key words: social dynamics, bounded confidence, phase transition, Monte Carlo simulation

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