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We explore the possibilities of enforcing and preventing consensus incontinuous opinion dynamics that result from modifications in the communicationrules. We refer to the model of Weisbuch and Deffuant, where $n$ agents adjusttheir continuous opinions as a result of random pairwise encounters whenevertheir opinions differ not more than a given bound of confidence $\eps$. A high$\eps$ leads to consensus, while a lower $\eps$ leads to a fragmentation intoseveral opinion clusters. We drop the random encounter assumption and ask: Howsmall may $\eps$ be such that consensus is still possible with a certaincommunication plan for the entire group? Mathematical analysis shows that$\eps$ may be significantly smaller than in the random pairwise case. On theother hand we ask: How large may $\eps$ be such that preventing consensus isstill possible? In answering this question we prove Fortunato's simulationresult that consensus cannot be prevented for $\eps>0.5$ for large groups. %Next we consider opinion dynamics under different individual strategies andexamine their power to increase the chances of consensus. One result is thatbalancing agents increase chances of consensus, especially if the agents arecautious in adapting their opinions. However, curious agents increase chancesof consensus only if those agents are not cautious in adapting their opinions.

About the Power to Enforce and Prevent Consensus by Manipulating Communication Rules