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

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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

## Keywords

Opinion dynamics Means of averaging Consensus Opinion stabilization## References

- Hegselmann, R., & Krause, U. (2002). Opinion dynamics and bounded confidence: Models, analysis, and simulation.
*Journal of Artificial Societies and Social Simulation*,*5*(3), 2.Google Scholar - Hegselmann, R., & Krause, U. (2005). Opinion dynamics driven by various ways of averaging.
*Computational Economics*,*25*, 381–405.CrossRefGoogle Scholar - Hegselmann, R., & Krause, U. (2015). Opinion dynamics under the influence of radical groups, charismatic leaders, and other constant signals: A simple unifying model.
*Networks and Heterogeneous Media*,*10*(3), 477–509.CrossRefGoogle Scholar - Krause, U. (2000). A discrete nonlinear and non-autonomous model of consensus formation. In S. Elaydi, G. Ladas, J. Popenda, & J. Rakowski (Eds.),
*Communication in difference equations*(pp. 227–236). Amsterdam: Gordon and Breach Publ.CrossRefGoogle Scholar - Krause, U. (2015).
*Positive dynamical systems in discrete time. Theory, models, and applications*. Berlin: De Gruyter.CrossRefGoogle Scholar - Xu, Y., & Cao, Y. (2018). Comments on “Opinion dynamics driven by various ways of averaging”.
*Computational Economics*. https://doi.org/10.1007/s10614-018-9871-0.