POWER OF THE CROWD

Abstract

Consider a Galton Watson 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 → ∞.