影响异质的二元决策
Binary decision making with very heterogeneous influence
摘要：
我们考虑一个扩展的二进制决策模型中，节点作出决定的基础上影响偏置的平均值，他们的邻居的状态，类似于伊辛自旋眼镜现场随机场。在这些影响变得非常重尾的极限中，模型的行为会发生显著变化。在完全图上，或者在具有大影响的节点具有大度的图上，该模型的特征在于具有不可预测数量的宏观冲击的新"相"，没有相关的临界现象。在随机图中，最有影响力的节点的程度是小的人口规模相比，一个可预测的玻璃相没有相变出现。这两个新相的分析结果是在极限情况下得到的。我们使用数值模拟来探索更一般的情况下的模型。在我们的简单模型的背景下，在许多情况下，与非常有影响力的决策者相关的阶段很容易通过实验从同质影响阶段中区分出来。
英文摘要：
We consider an extension of a binary decision model in which nodes make decisions based on influence-biased averages of their neighbors' states, similar to Ising spin glasses with on-site random fields. In the limit where these influences become very heavy-tailed, the behavior of the model dramatically changes. On complete graphs, or graphs where nodes with large influence have large degree, this model is characterized by a new "phase" with an unpredictable number of macroscopic shocks, with no associated critical phenomena. On random graphs where the degree of the most influential nodes is small compared to population size, a predictable glassy phase without phase transitions emerges. Analytic results about both of these new phases are obtainable in limiting cases. We use numerical simulations to explore the model for more general scenarios. The phases associated with very influential decision makers are easily distinguishable experimentally from a homogeneous influence phase in many circumstances, in the context of our simple model.
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