Reply on Comments on “Opinion Dynamics Driven by Various Ways of Averaging” by Youzong Xu and Yunfei Cao

  • Ulrich KrauseEmail author

The comment by Xu and Cao (2018) considers “the two main findings in Hegselmann and Krause (2005) the Theorem on Opinion Stabilization and the Corollary on Consensus Formation” (Xu and Cao 2018, pp. 1–2). The statement is not quite correct, since the so-called “two main findings” refer only to the last section of Hegselmann and Krause (2005), a mathematical appendix. The main body of Hegselmann and Krause (2005), Sects. 1, 2 and 3, is not touched upon. Actually, the analysis given therein, the many observations made by computer simulations and the conclusions drawn are not affected by the comment. In what follows I will address the comments in Xu and Cao (2018) whereby I refer to the two parts of the Appendix for detailed arguments. As it turns out the claim made in Xu and Cao (2018, p. 9) on “the validity of the two main findings” is not correct.

The Theorem on Opinion Stabilization

This result in Hegselmann and Krause (2005, p. 401/402) relies on Lemma 2 Hegselmann and Krause (2005, ...


Opinion dynamics Means of averaging Consensus Opinion stabilization 


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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of BremenBremenGermany

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