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Finite-time consensus in a compromise process
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AI
DOI：10.1088/1751-8121/ae31c1.png)
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Abstract
En 中文
A compromise process describes the evolution of opinions through binary interactions. Opinions are real numbers, and at each step, two randomly selected agents reach a compromise by averaging their pre-interaction opinions. We prove that if the number N of agents is a power of two, then consensus emerges after a finite number of compromise events with probability one; otherwise, consensus cannot be reached in a finite number of steps, provided the initial opinions are in a general position. The number of steps required to reach consensus is random for N=2k with k >= 2. We prove that the smallest number of steps is k & sdot;2k-1 when the initial opinions are in a general position. For N = 4, we determine the distribution of the number of steps. In particular, we show that it has a purely exponential tail and compute all cumulants.
Keywords:
opinion dynamics
consensus
averaging process
Journal
J
IF:
2.1
Papers:
264
Citations:
0
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