Non-convergence in heterogeneous Hegselmann-Krause dynamics: The bounded influence model
Peter Hegarty, Damiano Ognissanti, Edvin Wedin
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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