Probability laws of consensus in a broadcast-based consensus-forming algorithm
Probability laws of consensus in a broadcast-based consensus-forming algorithm
复制标题
基于广播的共识形成算法中的共识概率定律
DOI：
10.1080/15326349.2021.1982394
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发表时间：
2021
影响因子：
0.7
通讯作者：
Shioda Shigeo
中科院分区：
文献类型：
--
作者：
Katoh Dai;Shioda Shigeo
在共识形成算法中获得的共识通常不是一个常数，而是一个随机变量，即使初始意见是相同的。在本文中，我们研究了基于广播的共识形成算法中共识的概率规律。首先，我们推导了agent意见时间演化的基本方程。从导出的方程中，我们证明了该算法所得到的一致性是线性方程的不动点解。然后我们关注两种极端情况：由两个主体形成共识和由无限多个主体形成共识。在双智能体情况下，我们给出了共识分布函数的几个性质，并给出了一种计算共识分布函数的数值算法。在无限代理情况下，如果初始意见遵循稳定分布，则共识也遵循稳定分布。此外，我们导出了初始意见服从高斯分布、柯西分布或lsamvy分布时共识的概率密度函数的封闭表达式。
The consensus attained in the consensus-forming algorithm is not generally a constant but rather a random variable, even if the initial opinions are the same. In the present paper, we investigate the probability laws of the consensus in a broadcast-based consensus-forming algorithm. First, we derive a fundamental equation on the time evolution of the opinions of agents. From the derived equation, we show that the consensus attained by the algorithm is given as a fixed-point solution of a linear equation. We then focus on two extreme cases: consensus forming by two agents and consensus forming by an infinite number of agents. In the two-agent case, we derive several properties of the distribution function of the consensus with an algorithm for computing the distribution function of the consensus numerically. In the infinite-number-of-agents case, we show that if the initial opinions follow a stable distribution, then the consensus also follows a stable distribution. In addition, we derive a closed-form expression of the probability density function of the consensus when the initial opinions follow a Gaussian distribution, a Cauchy distribution, or a Lévy distribution.