Minority Takeover in Majority Dynamics: Searching for Rare Initializations via the History Passing Algorithm
Marek Jankola, Freya Behrens, C\'edric Koller, Lenka Zdeborov\'a

TL;DR
This paper explores how a small initial bias in node states can lead to global consensus in majority dynamics on large random regular graphs, introducing a new algorithm to find such minority configurations.
Contribution
It introduces the history-passing reinforcement (HPR) algorithm to explicitly find initial minority configurations that lead to takeover in majority dynamics.
Findings
HPR successfully finds initial configurations with minority takeover.
The minimal density of initial +1 nodes is near the d1RSB phase onset.
HPR outperforms standard simulated annealing methods.
Abstract
We investigate how much bias in the initial configuration is required to drive global agreement in synchronous, deterministic majority dynamics on large random -regular graphs. Nodes take values and update their states at each discrete time step to align with the majority of their neighbors. Using the backtracking dynamical cavity method (BDCM), we estimate the minimal fraction of initial nodes required to achieve a consensus in time steps. Our analysis predicts that for an initial global minority of nodes is sufficient to quickly steer the entire system toward consensus on . We then investigate whether such initial conditions can be determined explicitly for a given large random regular graph. To this end, we introduce a new algorithm, which we name history-passing reinforcement (HPR), designed to find such initial configurations with a…
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Taxonomy
TopicsOpinion Dynamics and Social Influence · Complex Network Analysis Techniques · Distributed systems and fault tolerance
