Deviations from the majority: A local flip model

We study the effect of probabilistic distortions to local majority rules used in Galam model opinion dynamics and bottom-up hierarchical voting. A different probability for a flip against within discussion group is associated with each ratio / minority. The cases groups sizes 3 5 are investigated detail. For voting, corresponds `faithless elector', representative who decides vote choice their electing group. Depending on probabilities, exhibits rich variety patterns dynamics, which include novel features topology landscape. In particular, size 5, we uncover first time an interplay between five fixed points, split into either three attractors two tipping points or depending probabilities. Larger also analysed. These were absent former versions model, has at maximum any size. results shed new light series social phenomena triggered by one single individual acts majority.