A generic feature of bounded confidence type models is the formation of clusters of agents. We propose and study a variant of bounded confidence dynamics with the goal of inducing unconditional convergence to a consensus. The defining feature of these dynamics which we name the No one left behind dynamics is the introduction of a local control on the agents which preserves the connectivity of the interaction network. We rigorously demonstrate that these dynamics result in unconditional convergence to a consensus. The qualitative nature of our argument prevents us quantifying how fast a consensus emerges, however we present numerical evidence that sharp convergence rates would be challenging to obtain for such dynamics. Finally, we propose a relaxed version of the control. The dynamics that result maintain many of the qualitative features of the bounded confidence dynamics yet ultimately still converge to a consensus as the control still maintains connectivity of the interaction network.

中文翻译：

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有限的置信度动力学和图形控制：加强共识

有界置信度类型模型的一般特征是主体群集的形成。我们提出并研究了有界置信动力学的一种变体，其目的是引起无条件收敛到共识。这些动力学的定义特征，我们将其命名为“ No动态”在代理程序上引入了本地控制，以保留交互网络的连接性。我们严格地证明了这些动力导致无条件地收敛到共识。我们论证的定性性质使我们无法量化共识的出现速度，但是我们提供了数字证据，表明要获得如此快的动态收敛速度会很困难。最后，我们提出控件的宽松版本。所产生的动力学保持了有限置信度动力学的许多定性特征，但最终仍然收敛为共识，因为控件仍保持了交互网络的连通性。