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Non-freezing of the proximity digraph and non-pseudostable convergence in heterogeneous Hegselmann--Krause models: Counterexamples to conjectures and results of Mirtabatabaei and Bullo
Abstract
In 2012, Mirtabatabaei and Bullo studied heterogeneous Hegselmann--Krause models of opinion dynamics, where different agents may have different confidence or influence bounds. They conjectured that opinion vectors always converge, a fundamental problem that remains open. In support of this main conjecture they gave some partial results and made some auxiliary conjectures. Here we give counterexamples to two of these auxiliary conjectures, and even to one theorem in their paper. We explain why these disproved conjectures and false theorem nevertheless likely remain valid for almost all initial opinion vectors. In the last section (Section 7), we describe the role of AI in the production of the results in this paper.
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BibTeX
@misc{hegarty2026nonfreezing,
title = {{Non-freezing of the proximity digraph and non-pseudostable convergence in heterogeneous Hegselmann--Krause models: Counterexamples to conjectures and results of Mirtabatabaei and Bullo}},
author = {Peter Hegarty and Damiano Ognissanti and Edvin Wedin},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.03229},
eprint = {2610.03229},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.03229},
}
RIS
TY - UNPB
TI - Non-freezing of the proximity digraph and non-pseudostable convergence in heterogeneous Hegselmann--Krause models: Counterexamples to conjectures and results of Mirtabatabaei and Bullo
AU - Peter Hegarty
AU - Damiano Ognissanti
AU - Edvin Wedin
PY - 2026
DA - 2026/10/21
PB - arXiv
DO - 10.48550/arxiv.2610.03229
UR - https://arxiv.org/abs/2610.03229
AB - In 2012, Mirtabatabaei and Bullo studied heterogeneous Hegselmann--Krause models of opinion dynamics, where different agents may have different confidence or influence bounds. They conjectured that opinion vectors always converge, a fundamental problem that remains open. In support of this main conjecture they gave some partial results and made some auxiliary conjectures. Here we give counterexamples to two of these auxiliary conjectures, and even to one theorem in their paper. We explain why these disproved conjectures and false theorem nevertheless likely remain valid for almost all initial opinion vectors. In the last section (Section 7), we describe the role of AI in the production of the results in this paper.
ER -