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Majority dynamics and the median process: Connections, convergence and some new conjectures

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  • Amir, Gideon
  • Baldasso, Rangel
  • Beilin, Nissan

Abstract

We consider the median dynamics process in general graphs. In this model, each vertex has an independent initial opinion uniformly distributed in the interval [0,1] and, with rate one, updates its opinion to coincide with the median of its neighbors. This process provides a continuous analog of binary majority dynamics. We deduce properties of median dynamics through this connection and raise new conjectures regarding the behavior of majority dynamics on general graphs. We also prove these conjectures on some graphs where majority dynamics has a simple description.

Suggested Citation

  • Amir, Gideon & Baldasso, Rangel & Beilin, Nissan, 2023. "Majority dynamics and the median process: Connections, convergence and some new conjectures," Stochastic Processes and their Applications, Elsevier, vol. 155(C), pages 437-458.
    • Handle: RePEc:eee:spapps:v:155:y:2023:i:c:p:437-458
    DOI: 10.1016/j.spa.2022.10.015
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    References listed on IDEAS

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    1. Benjamini, Itai & Chan, Siu-On & O’Donnell, Ryan & Tamuz, Omer & Tan, Li-Yang, 2016. "Convergence, unanimity and disagreement in majority dynamics on unimodular graphs and random graphs," Stochastic Processes and their Applications, Elsevier, vol. 126(9), pages 2719-2733.
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    More about this item

    Keywords

    Majority dynamics; Median process;

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