The limit point in the Jante's law process has an absolutely continuous distribution
Crane, Edward and Volkov, Stanislav LU
(2024)
In Stochastic Processes and their Applications
168.
- 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... (More)
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.
(Less)
- author
- Crane, Edward
and Volkov, Stanislav
LU
- organization
- publishing date
- 2024-02
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- Consensus formation, Interacting particle system, Jante's law process, Keynesian beauty contest, Rank-driven process
- in
- Stochastic Processes and their Applications
- volume
- 168
- article number
- 104252
- publisher
- Elsevier
- external identifiers
-
- scopus:85178144311
- ISSN
- 0304-4149
- DOI
- 10.1016/j.spa.2023.104252
- language
- English
- LU publication?
- yes
- id
- 19a5089b-6a21-4cb6-b995-b1be608d0e9c
- date added to LUP
- 2023-12-18 14:08:13
- date last changed
- 2023-12-18 14:08:13
@article{19a5089b-6a21-4cb6-b995-b1be608d0e9c,
abstract = {{<p>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 R<sup>d</sup>. 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.</p>}},
author = {{Crane, Edward and Volkov, Stanislav}},
issn = {{0304-4149}},
keywords = {{Consensus formation; Interacting particle system; Jante's law process; Keynesian beauty contest; Rank-driven process}},
language = {{eng}},
publisher = {{Elsevier}},
series = {{Stochastic Processes and their Applications}},
title = {{The limit point in the Jante's law process has an absolutely continuous distribution}},
url = {{http://dx.doi.org/10.1016/j.spa.2023.104252}},
doi = {{10.1016/j.spa.2023.104252}},
volume = {{168}},
year = {{2024}},
}