Power of the Crowd

Abstract

Consider an Galton Watson tree of height $m$: each leaf has one of $k$ opinions or not. In other words, for $i\in \{1,...,k\}$, $x$ at generation $m$ thinks $i$ with probability $p_i$ and nothing with probability $p_0$. 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 $m\to +\infty$.

30 pages, 13 figures, 1 table