Power of the Crowd

Athanasios Batakis (1) , Pierre Debs , Dorian Le Peutrec

1 IDP - Institut Denis Poisson

Consider an n-ary tree of height m: each leaf has one of k opinions or not. In other words, for i ∈ {1,. .. , k}, x at generation m thinks i with probability pi and nothing with probability p0. Moreover the opinions are independently distributed for each leaf. Opinions spread along the tree based on a specific rule: the majority wins! In this paper, we study the asymptotic behavior of the distribution of the opinion of the root when m → ∞.

Mots clés: Galton Watson; Dynamical System; Elections; Random Walk

Domaines: Analyse classique [math.CA]

Athanasios Batakis, Pierre Debs, Dorian Le Peutrec. Power of the Crowd. Discrete and Continuous Dynamical Systems - Series A, 2022, 42 (12), pp.6063-6096. ⟨10.3934/dcds.2022138⟩. ⟨hal-03481343v2⟩