The noisy voter model is a stylized representation of opinion dynamics. Individuals copy opinions from other individuals, and are subject to spontaneous state changes. In the case of two opinion states this model is known to have a noise-driven transition between a unimodal phase, in which both opinions are present, and a bimodal phase, in which one of the opinions dominates. The presence of zealots can remove the unimodal and bimodal phases in the model with two opinion states. Here we study the effects of zealots in noisy voter models with $M>2$ opinion states on complete interaction graphs. We find that the phase behavior diversifies, with up to six possible qualitatively different types of stationary states. The presence of zealots removes some of these phases, but not all. We analyze situations in which zealots affect the entire population, or only a fraction of agents, and show that this situation corresponds to a single-community model with a fractional number of zealots, further enriching the phase diagram. Our study is conducted analytically based on effective birth-death dynamics for the number of individuals holding a given opinion. Results are confirmed in numerical simulations.

中文翻译：

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多州嘈杂选民模型中的狂热分子

嘈杂的选民模型是舆论动态的典型代表。个人会复制其他人的意见，并且会自发发生状态变化。在有两种意见状态的情况下，已知该模型在单峰阶段（其中存在两种意见）和双峰阶段（其中一种意见占主导）之间具有噪声驱动的过渡。狂热者的存在可以消除具有两种观点状态的模型中的单峰和双峰相。在这里，我们研究了狂热者在嘈杂的选民模型中的影响，$\mathrm{中号}>2$完整互动图上的意见状态。我们发现，相位行为多样化，最多有六种可能在质量上不同类型的稳态。狂热者的存在消除了其中某些阶段，但并非全部。我们分析了狂热分子影响整个人口或只有一小部分特工的情况，并表明这种情况对应于具有少量狂热分子的单社区模型，从而进一步丰富了相图。我们的研究是基于有效的生死动力学对持有给定意见的个人数量进行分析性地进行的。结果在数值模拟中得到证实。