论文标题
在有限连接的图上的多元偏爱模型中共识的概率
Probability of consensus in the multivariate Deffuant model on finite connected graphs
论文作者
论文摘要
Deffuant模型是一种空间随机模型，用于观点动态，其中个人位于代表社交网络的连接图上，并以单位间隔中的数字为特征，代表他们的意见。该系统根据以下平均步骤演变：当邻居对以1的比率互动时，并且仅当他们的意见之间的距离不超过一定的信心阈值时，每种互动都会导致邻居的意见彼此接近。到目前为止，有关该模型的所有数学结果都假设个体位于整数上。相比之下，我们研究了社交网络可以是任何有限连接图的更现实的情况。此外，我们将意见空间扩展到标准向量空间的任何有限凸子集，在该范围内，该规范用于衡量观点之间的分歧或距离水平。我们的主要结果给出了共识概率的下限。有趣的是，我们的证明导致了一个普遍的下限，取决于置信度阈值，意见空间〜（凸子集和规范）以及初始分布，但不取决于社交网络的规模或拓扑。
The Deffuant model is a spatial stochastic model for the dynamics of opinions in which individuals are located on a connected graph representing a social network and characterized by a number in the unit interval representing their opinion. The system evolves according to the following averaging procedure: pairs of neighbors interact independently at rate one if and only if the distance between their opinions does not exceed a certain confidence threshold, with each interaction resulting in the neighbors' opinions getting closer to each other. All the mathematical results collected so far about this model assume that the individuals are located on the integers. In contrast, we study the more realistic case where the social network can be any finite connected graph. In addition, we extend the opinion space to any bounded convex subset of a normed vector space where the norm is used to measure the level of disagreement or distance between the opinions. Our main result gives a lower bound for the probability of consensus. Interestingly, our proof leads to a universal lower bound that depends on the confidence threshold, the opinion space~(convex subset and norm) and the initial distribution, but not on the size or the topology of the social network.
