Dynamics of Majority Rule
P. L. Krapivsky, S. Redner

TL;DR
This paper introduces a majority rule opinion dynamics model, analyzing how consensus is reached in different network structures, revealing that consensus time scales logarithmically in mean-field and varies with dimension in lattices.
Contribution
The study presents a new 2-state opinion model with detailed analysis of consensus times across different network topologies and dimensions.
Findings
Consensus time scales as ln N in mean-field.
On lattices, consensus time varies with dimension and shows strong fluctuations.
Final opinion usually matches initial majority, except in one dimension.
Abstract
We introduce a 2-state opinion dynamics model where agents evolve by majority rule. In each update, a group of agents is specified whose members then all adopt the local majority state. In the mean-field limit, where a group consists of randomly-selected agents, consensus is reached in a time that scales ln N, where N is the number of agents. On finite-dimensional lattices, where a group is a contiguous cluster, the consensus time fluctuates strongly between realizations and grows as a dimension-dependent power of N. The upper critical dimension appears to be larger than 4. The final opinion always equals that of the initial majority except in one dimension.
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