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\section{Introduction}  The paper focuses on a specific class of opinion diffusion processes in which opinions are binary, and agents are influenced by exactly one influencer, possibly themselves, of which they copy the opinion. This is an extremely simple model of opinion diffusion on networks, and is of interest for two reasons. First, it corresponds to a class of processes which lies at the interface of two classes of diffusion processes which that  have remained so far unrelated: the stochastic opinion diffusion model known as DeGroot's \cite{Degroot_1974}, and the more recent propositional opinion diffusion model due to \cite{Grandi:2015:POD:2772879.2773278}. The processes we study---called here Boolean DeGroot processes---are the $\set{0,1}$ limit case of the DeGroot stochastic processes and, at the same time, the limit case of propositional opinion diffusion processes where each agent has access to the opinion of exactly one neighbor. Second, it provides an abstract model with which to analyze some aspects the popular, and currently much discussed, aggregation system called liquid democracy \cite{liquid_feedback}. We will see that Boolean DeGroot processes offer a novel and natural angle on the issue of delegation cycles in liquid democracy.  \paragraph{Contributions of the paper}