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Non-convergence in heterogeneous Hegselmann-Krause dynamics: The bounded influence model

  • Peter Hegarty
  • Damiano Ognissanti
  • Edvin Wedin
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Abstract

In a recent preprint, we found counterexamples to a number of auxiliary conjectures in a 2012 paper of Mirtabatabaei and Bullo, concerning convergence in two fundamental models of heterogeneous Hegselmann-Krause dynamics, the synchronized bounded confidence (SBC) and synchronized bounded influence (SBI) models. Building on our work, Etesami and Touri presented an example of an opinion vector which doesn't converge under SBC dynamics, resolving the main conjecture from the 2012 paper in that case. Here we complete this project by presenting an example of an opinion vector which doesn't converge under SBI dynamics. The example was found with the help of AI.

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Cite

BibTeXRIS
BibTeX
@misc{hegarty2026nonconvergence,
  title = {{Non-convergence in heterogeneous Hegselmann-Krause dynamics: The bounded influence model}},
  author = {Peter Hegarty and Damiano Ognissanti and Edvin Wedin},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.37246},
  eprint = {2610.37246},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.37246},
}
RIS
TY  - UNPB
TI  - Non-convergence in heterogeneous Hegselmann-Krause dynamics: The bounded influence model
AU  - Peter Hegarty
AU  - Damiano Ognissanti
AU  - Edvin Wedin
PY  - 2026
DA  - 2026/10/27
PB  - arXiv
DO  - 10.48550/arxiv.2610.37246
UR  - https://arxiv.org/abs/2610.37246
AB  - In a recent preprint, we found counterexamples to a number of auxiliary conjectures in a 2012 paper of Mirtabatabaei and Bullo, concerning convergence in two fundamental models of heterogeneous Hegselmann-Krause dynamics, the synchronized bounded confidence (SBC) and synchronized bounded influence (SBI) models. Building on our work, Etesami and Touri presented an example of an opinion vector which doesn't converge under SBC dynamics, resolving the main conjecture from the 2012 paper in that case. Here we complete this project by presenting an example of an opinion vector which doesn't converge under SBI dynamics. The example was found with the help of AI.
ER  -