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The limit point in the Jante’s law process has an absolutely continuous distribution

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  • Crane, Edward
  • Volkov, Stanislav

Abstract

We study a stochastic model of consensus formation, introduced in 2015 by Grinfeld, Volkov and Wade, who called it a multidimensional randomized Keynesian beauty contest. The model was generalized by Kennerberg and Volkov, who called their generalization the Jante’s law process. We consider a version of the model where the space of possible opinions is a convex body B in Rd. N individuals in a population each hold a (multidimensional) opinion in B. Repeatedly, the individual whose opinion is furthest from the centre of mass of the N current opinions chooses a new opinion, sampled uniformly at random from B. Kennerberg and Volkov showed that the set of opinions that are not furthest from the centre of mass converges to a random limit point. We show that the distribution of the limit opinion is absolutely continuous, thus proving the conjecture made after Proposition 3.2 in Grinfeld et al.

Suggested Citation

  • Crane, Edward & Volkov, Stanislav, 2024. "The limit point in the Jante’s law process has an absolutely continuous distribution," Stochastic Processes and their Applications, Elsevier, vol. 168(C).
    • Handle: RePEc:eee:spapps:v:168:y:2024:i:c:s0304414923002247
    DOI: 10.1016/j.spa.2023.104252
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