Monotonicity in the averaging process

Ben-Naim, E.; Krapivsky, P. L.

doi:10.1088/1751-8121/ac354f

Title: Monotonicity in the averaging process

Journal Article · 19 November 2021 · Journal of Physics. A, Mathematical and Theoretical

DOI: https://doi.org/10.1088/1751-8121/ac354f · OSTI ID:1863743

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Los Alamos National Lab. (LANL), Los Alamos, NM (United States). Center for Nonlinear Studies (CNLS)
Boston Univ., MA (United States); Santa Fe Inst. (SFI), Santa Fe, NM (United States); Skolkovo Inst. of Science and Technology, Moscow (Russia)

In this work, we investigate an averaging process that describes how interacting agents approach consensus through binary interactions. In each elementary step, two agents are selected at random and they reach compromise by adopting their opinion average. We show that the fraction of agents with a monotonically decreasing opinion decays as e^-αt, and that the exponent is selected as the extremum from a continuous spectrum of possible values. The opinion distribution of monotonic agents is asymmetric, and it becomes self-similar at large times. Furthermore, the tails of the opinion distribution are algebraic, and they are characterized by two distinct and nontrivial exponents. We also explore statistical properties of agents with an opinion strictly above average.

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Research Organization:: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

Sponsoring Organization:: USDOE Laboratory Directed Research and Development (LDRD) Program

Grant/Contract Number:: 89233218CNA000001

OSTI ID:: 1863743

Report Number(s):: LA-UR-21-28699

Journal Information:: Journal of Physics. A, Mathematical and Theoretical, Vol. 54, Issue 49; ISSN 1751-8113

Publisher:: IOP PublishingCopyright Statement

Country of Publication:: United States

Language:: English

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