In the biased q-voter model with contrarians, an exactly balanced 50-50 opinion split occurs only on the lines p=1/2 or alpha=1/2; all other parameters lead to a stable majority.
Redner, Comptes Rendus
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Analysing contrarian behaviour using nonlinear biased $q$-voter model
In the biased q-voter model with contrarians, an exactly balanced 50-50 opinion split occurs only on the lines p=1/2 or alpha=1/2; all other parameters lead to a stable majority.