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Power of the Crowd

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arxiv 2112.08042 v3 pith:ANSP7D4K submitted 2021-12-15 math.PR math.DS

Athanasios Batakis , Pierre Debs , Dorian Le Peutrec This is my paper · ORCID
classification math.PRmath.DS
keywords opinionsleafprobabilitytreealongasymptoticbehaviorconsider
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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 $m \to +\infty$.

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