Ratio-Dependent Contrarian Activation in Opinion Dynamics

I study the impact of mixed contrarians on the opinion dynamics of a heterogenous population with conformists using the Galam Majority Model. Activation of contrarians is a function of the majority/minority ratio in the local groups of discussion. Restricting the group size to 3, two types of contrarians are included in respective proportions c3,0 for configurations with ratio 3 to 0 and c2,1 for ratio 2 to 1. I then derive the explicit update equation and analytically obtain the fixed points, their stability, and the resulting full two-dimensional landscape of the dynamics of opinion. Setting c3,0=c2,1=c recovers the original results obtained with uniform contrarians. The findings allow for considering a wide spectrum of new disruptive strategies to secure either a majority/minority ending ensuring the opinion having the larger initial support to win, or a single attractor dynamics at fifty/fifty, which implies a random winner regardless of initial supports.