Universality and Invariance in Hegselmann-Krause Opinion Dynamics: Proof of Three Conjectures
Fuente:
arXiv
Guardado en:
| Autor principal: | |
|---|---|
| Formato: | Preprint |
| Publicado: |
2025
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866912548496867328 |
|---|---|
| author | Molignini, Paolo |
| author_facet | Molignini, Paolo |
| contents | Three conjectures from [R. Hegselmann, The Journal of Artificial Societies and Social Simulations 26(4), 11 (2023)] about the Hegselmann-Krause opinion dynamics and the structure of $ε$-switches are proved. The first conjecture states that the number of $ε$-switches for any given initial opinion distribution is always finite, guaranteeing that the algorithm for enumerating them terminates. The second conjecture concerns the relationship between the dynamics of two consecutive $ε$-switches, showing that the opinion evolution is identical up to the switch time. The third conjecture establishes the invariance of the dynamics under positive-affine transformations of the initial distribution, with a corresponding rescaling of all $ε$-switch values. Together, these results provide a formal foundation for the empirical observations reported in the literature and offer a step towards a systematic classification of BC-processes based on their initial conditions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_15982 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Universality and Invariance in Hegselmann-Krause Opinion Dynamics: Proof of Three Conjectures Molignini, Paolo Physics and Society Mathematical Physics Chaotic Dynamics Three conjectures from [R. Hegselmann, The Journal of Artificial Societies and Social Simulations 26(4), 11 (2023)] about the Hegselmann-Krause opinion dynamics and the structure of $ε$-switches are proved. The first conjecture states that the number of $ε$-switches for any given initial opinion distribution is always finite, guaranteeing that the algorithm for enumerating them terminates. The second conjecture concerns the relationship between the dynamics of two consecutive $ε$-switches, showing that the opinion evolution is identical up to the switch time. The third conjecture establishes the invariance of the dynamics under positive-affine transformations of the initial distribution, with a corresponding rescaling of all $ε$-switch values. Together, these results provide a formal foundation for the empirical observations reported in the literature and offer a step towards a systematic classification of BC-processes based on their initial conditions. |
| title | Universality and Invariance in Hegselmann-Krause Opinion Dynamics: Proof of Three Conjectures |
| topic | Physics and Society Mathematical Physics Chaotic Dynamics |
| url | https://arxiv.org/abs/2508.15982 |