Distribution of Consensus in a Broadcasting-based Consensus-forming Algorithm
Distribution of Consensus in a Broadcasting-based Consensus-forming Algorithm
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基于广播的共识形成算法中的共识分布
DOI：
10.1145/3453953.3453974
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发表时间：
2021
期刊：
影响因子：
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通讯作者：
Shioda Shigeo
中科院分区：
文献类型：
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作者：
Akio Ikeda;Shioda Shigeo
即使最初的意见相同，共识形成算法中达成的共识通常不是一个常数，而是一个随机变量。在本文中，我们研究了基于广播的共识形成算法中共识的统计特性。我们关注两种极端情况：两个代理形成共识和无限多个代理形成共识。在两个代理的情况下，我们推导出共识分布函数的几个属性。在无限数量代理的情况下，我们表明，如果初始意见遵循稳定分布，那么共识也遵循稳定分布。此外，当初始意见遵循高斯分布、柯西分布或 L´evy 分布时，我们得出了共识概率密度函数的封闭式表达式。
The consensus achieved 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 statistical properties of the consensus in a broadcasting-based consensus-forming algorithm. We 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. In the infinite-numberof- 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 L´evy distribution.