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A simple consensus model for an increasing population of agents with i.i.d incoming opinions

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  • Markou, Ioannis

Abstract

In this short note we study what happens in a symmetric opinion model when we send the total interacting population N(t) to infinity as t→∞. We assume that new population enters the system with opinions that are i.i.d random vectors with finite mean and variance. We give sharp conditions on the rate of population growth that is required for convergence to a global consensus in opinions. More particularly, we show that if the total population increases at a rate N(t)∼etα, then α<1 is necessary and sufficient condition for convergence to the mean of incoming opinions, and the convergence is achieved at an algebraic rate.

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  • Markou, Ioannis, 2025. "A simple consensus model for an increasing population of agents with i.i.d incoming opinions," Statistics & Probability Letters, Elsevier, vol. 220(C).
    • Handle: RePEc:eee:stapro:v:220:y:2025:i:c:s0167715224003146
    DOI: 10.1016/j.spl.2024.110345
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    1. Rainer Hegselmann & Ulrich Krause, 2002. "Opinion Dynamics and Bounded Confidence Models, Analysis and Simulation," Journal of Artificial Societies and Social Simulation, Journal of Artificial Societies and Social Simulation, vol. 5(3), pages 1-2.
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