少数人在社交网络中成为多数人
Minority Becomes Majority in Social Networks
摘要：
人们经常观察到，智能体倾向于模仿社交网络中邻居的行为。这种模仿行为可能导致采取与代理人认为正确的行为不同的公共行为的战略决策，这可能会颠覆整个群体的行为。在本文中，我们考虑的情况下，代理人表示偏好超过两个选项和模型的社会压力与多数动态：在每一步代理被选中，其偏好是由她的邻居的大多数偏好所取代。在平局的情况下，代理不改变她当前的偏好。如果每个代理的偏好与至少一半的邻居的偏好一致，则代理偏好的概况是稳定的（因此，系统处于平衡状态）。我们问是否有网络拓扑结构，是强大的社会压力。也就是说，我们问是否有这样的图，其中初始配置文件中的大多数偏好总是与从该配置文件可到达的所有稳定配置文件中的大多数偏好一致。我们完全刻画了这个鲁棒性的图形显示，这是可能的，只有当图形没有边缘，或者是一个集团或非常接近一个集团。换句话说，除了这几个图之外，每个图都至少有一个初始偏好轮廓，其中多数动态可以颠覆初始多数。我们还表明，当少数群体的规模至多为社交网络规模的1/4时，决定一个图是否允许少数群体成为多数群体是NP难的。
英文摘要：
It is often observed that agents tend to imitate the behavior of their neighbors in a social network. This imitating behavior might lead to the strategic decision of adopting a public behavior that differs from what the agent believes is the right one and this can subvert the behavior of the population as a whole. In this paper, we consider the case in which agents express preferences over two alternatives and model social pressure with the majority dynamics: at each step an agent is selected and its preference is replaced by the majority of the preferences of her neighbors. In case of a tie, the agent does not change her current preference. A profile of the agents' preferences is stable if the preference of each agent coincides with the preference of at least half of the neighbors (thus, the system is in equilibrium). We ask whether there are network topologies that are robust to social pressure. That is, we ask if there are graphs in which the majority of preferences in an initial profile always coincides with the majority of the preference in all stable profiles reachable from that profile. We completely characterize the graphs with this robustness property by showing that this is possible only if the graph has no edge or is a clique or very close to a clique. In other words, except for this handful of graphs, every graph admits at least one initial profile of preferences in which the majority dynamics can subvert the initial majority. We also show that deciding whether a graph admits a minority that becomes majority is NP-hard when the minority size is at most 1/4-th of the social network size.
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