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\subsection{Backgdrop: Convergence in deGroot Processes and Propositional Opinion Diffusion}  Convergence results have been given both for DeGroot processes \cite{Golub_2010} and for propositional opinion diffusion for specific a class of  aggregation procedures \cite{Grandi:2015:POD:2772879.2773278}. Let us briefly recall those results. In the case of DeGroot processes, a graph guarantees that any distribution of opinion will converge if and only if ''every set of nodes that is strongly connected and closed is aperiodic" (Jackson, p.233).  %\footnote{A set of nodes is said to be ``strongly connected" if there is a directed path from any node to any other node in the set, ``closed" if there is no link from nodes in the set to nodes outside the set, and aperiodic if the greatest common divisor of all directed cycles is $1$}