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Asynchronous Majority Dynamics on Binomial Random Graphs

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The process stabilizes in a correct consensus in extbf{O}(n extlog ^2 n/ extlog extlog n) steps with high probability.
In sparse graphs, the termination time extbf{ ext{T} = (1+o(1))n extlog n} depends on node selections.
Dense graphs face an information cascade where incorrect consensus occurs with non-negligible probability.
Majority dynamics in networks significantly impacts how agents learn and reach consensus on information.

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The process stabilizes in correct consensus in sparse graphs, suggesting dynamics in information aggregation.

Mohan et al. (2025) studied this question.

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