杰出群体联盟：论舆论的形成
Eminence Grise Coalitions: On the Shaping of Public Opinion
摘要：
我们认为这是一个不断演变的观点网络。它包括多个人的一阶意见动态定义在连续的时间和发展的基础上一般外生定义的随时间变化的底层图。在这样的网络中，对于任意固定的初始时间，一个子集的个人形成一个突出的灰色联盟，简称为EGC，如果该子集中的个人能够通过合作选择自己的初始意见来领导整个网络达成任何期望的意见。在这一努力中，联盟成员被假设可以访问网络底层图的完整轮廓以及所有其他个人的初始意见。虽然完整的联盟的个人总是有资格作为一个EGC，我们建立了一个任意的时变网络的最小尺寸EGC的存在，还，我们开发了一个非平凡的上界和下界的大小。因此，我们表明，即使当底层图不保证收敛到一个全球或多个共识，一般限制联盟的代理可以引导公众舆论对所需的全球共识，而不影响任何预定义的图形交互，只要他们可以合作调整自己的初始意见。EGC的结构的几何见解。结果也扩展到离散时间的情况下，分解分离定理的关系也是明确的。
英文摘要：
We consider a network of evolving opinions. It includes multiple individuals with first-order opinion dynamics defined in continuous time and evolving based on a general exogenously defined time-varying underlying graph. In such a network, for an arbitrary fixed initial time, a subset of individuals forms an eminence grise coalition, abbreviated as EGC, if the individuals in that subset are capable of leading the entire network to agreeing on any desired opinion, through a cooperative choice of their own initial opinions. In this endeavor, the coalition members are assumed to have access to full profile of the underlying graph of the network as well as the initial opinions of all other individuals. While the complete coalition of individuals always qualifies as an EGC, we establish the existence of a minimum size EGC for an arbitrary time-varying network; also, we develop a non-trivial set of upper and lower bounds on that size. As a result, we show that, even when the underlying graph does not guarantee convergence to a global or multiple consensus, a generally restricted coalition of agents can steer public opinion towards a desired global consensus without affecting any of the predefined graph interactions, provided they can cooperatively adjust their own initial opinions. Geometric insights into the structure of EGC's are given. The results are also extended to the discrete time case where the relation with Decomposition-Separation Theorem is also made explicit.
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