Speaker
Description
We study the properties of the compass model, an opinion dynamics model, both through simulations and theoretical proofs.
The compass model can be described as an asynchronous continuous-state cellular automata. Imagine a group of people whose connections are given by an underlying graph structure. At every time-step one pair of neighboring people update their opinion. Opinions are represented as points on a circle. Once two people update their opinion their updated opinion is given as the midpoint of the shortest geodesic connecting their original opinions. This gives a mid-point averaging rule for opinions represented by angles.
We studied two scenarios: people standing in a finite row, and people standing in a circle. From a theoretical result by \cite{gantert} we know that in both cases opinions converge towards consensus, i.e. eventually everyone will come to agree on approximately the same opinion. However, in simulations we observed that for people standing in a circle topological trapping occurs, meaning that opinions get trapped for a long period of time in a state in which they wrap around the circle, thus causing opinions to be similar locally but differ greatly globally. We were able to show this behavior analytically and prove that it does not contradict the previous analytical results. For people standing in a line consensus is observed in simulations \cite{spitoni}.
Bibliography
@article{spitoni,
title = {Topological trapping in circular midpoint opinion dynamics},
journal = {Physica A: Statistical Mechanics and its Applications},
volume = {698},
pages = {131794},
year = {2026},
issn = {0378-4371},
doi = {https://doi.org/10.1016/j.physa.2026.131794},
url = {https://www.sciencedirect.com/science/article/pii/S0378437126005303},
author = {Annika Brockhaus and Wioletta M. Ruszel and Cristian Spitoni},
keywords = {Circular opinion dynamics, Midpoint dynamics, Metastability, Winding number, Topological trapping, Consensus},
}
@article{gantert,
title = {Strictly Weak Consensus in the Uniform Compass Model on $\mathbb{Z}$},
author = {Gantert, Nina and Heydenreich, Markus and Hirscher, Timo},
journal = {Bernoulli},
volume = {26},
number = {2},
pages = {1269--1293},
year = {2020},
doi = {10.3150/19-BEJ1155}
}
@article{Deffuant2000,
title = {Mixing Beliefs Among Interacting Agents},
author = {Deffuant, Guillaume and Neau, Dominique and Amblard, Fr{\'e}d{\'e}ric and Weisbuch, G{\'e}rard},
journal = {Advances in Complex Systems},
volume = {3},
number = {01n04},
pages = {87--98},
year = {2000},
doi = {10.1142/S0219525900000078}
}
@techreport{a8cfcdb2c962480bb007c32c19dd7f6e,
title = "Topology, noise, and parallel updates in circular opinion dynamics",
author = "Ruszel, Wioletta M. and Spitoni, Cristian",
year = "2026",
month = mar,
day = "23",
doi = "10.48550/ARXIV.2603.21838",
language = "English",
publisher = "arXiv",
type = "WorkingPaper",
institution = "arXiv",
}
@mastersthesis{thesis,
author = {Annika Brockhaus},
title = {Ergodicity properties of opinion models},
school = {Utrecht University},
year = {2024},
type = {Master's thesis}, % Optional
note = {Available at: https://studenttheses.uu.nl/handle/20.500.12932/48012}, % Optional
}
