社会中的信任：一个随机房室模型
Trust in society: A stochastic compartmental model
AI总结：
本文提出一个随机房室模型研究社会信任动态，将人群分为信任者、怀疑者和质疑者，分析长期行为，发现寿命和人口增长增加完全失信任比例，且说服率与质疑者数量非单调，并揭示确定性模型局限。
摘要：
本文研究了一个新颖的随机房室模型，该模型描述了社会中信任的动态变化。人口被划分为三个房室，分别代表社会中的信任水平：信任者、怀疑者和质疑者。研究的重点在于评估长期动态，在“有限置信”的假设下（即信任者和质疑者之间不进行交流）。我们陈述并分类了系统平均行为的平稳点。我们发现，预期寿命的增加以及更大的人口规模可能会增加完全失去信任的个体比例。此外，质疑者说服怀疑者加入其阵营的速率与质疑者的预期数量之间的关系并非单调——并非总是更具说服力就能确保群体的生存。我们通过数值方法展示了分析的有效性。由于针对社会动态的随机房室模型研究并不常见，我们特别揭示了确定性房室模型的局限性。在我们的实验中，我们使用了流体和扩散近似技术以及Gillespie模拟。
英文摘要：
This paper studies a novel stochastic compartmental model that describes the dynamics of trust in society. The population is split into three compartments representing levels of trust in society: trusters, skeptics and doubters. The focus lies on assessing the long-term dynamics, under `bounded confidence' i.e., trusters and doubters do not communicate). We state and classify the stationary points of the system's mean behavior. We find that an increase in life-expectancy, and a greater population may increase the proportion of individuals who lose their trust completely. In addition, the relationship between the rate at which doubters convince skeptics to join their cause and the expected number of doubters is not monotonic -- it does not always help to be more convincing to ensure the survival of your group. We numerically illustrate the workings of our analysis. Because the study of stochastic compartmental models for social dynamics is not common, we in particular shed light on the limitations of deterministic compartmental models. In our experiments we make use of fluid and diffusion approximation techniques as well as Gillespie simulation.
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