Distribution of Consensus in a Broadcasting-based Consensus-forming Algorithm
- 5 March 2021
- journal article
- research article
- Published by Association for Computing Machinery (ACM) in ACM SIGMETRICS Performance Evaluation Review
- Vol. 48 (3), 91-96
- https://doi.org/10.1145/3453953.3453974
Abstract
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.Keywords
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