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

We explore the possibilities of enforcing and preventing consensus in continuous opinion dynamics that result from modifications in the communication rules. We refer to the model of Weisbuch and Deffuant, where $n$ agents adjust their continuous opinions as a result of random pairwise encounters whenever their opinions differ not more than a given bound of confidence $\text{eps}$. A high $\text{eps}$ leads to consensus, while a lower $\text{eps}$ leads to a fragmentation into several opinion clusters. We drop the random encounter assumption and ask: How small may $\text{eps}$ be such that consensus is still possible with a certain communication plan for the entire group? Mathematical analysis shows that $\text{eps}$ may be significantly smaller than in the random pairwise case. On the other hand we ask: How large may $\text{eps}$ be such that preventing consensus is still possible? In answering this question we prove Fortunato’s simulation result that consensus cannot be prevented for $\text{eps}>0.5$ for large groups. % Next we consider opinion dynamics under different individual strategies and examine their power to increase the chances of consensus. One result is that balancing agents increase chances of consensus, especially if the agents are cautious in adapting their opinions. However, curious agents increase chances of consensus only if those agents are not cautious in adapting their opinions.