Deviations from the Majority: A Local Flip Model

Abstract

We study the effect of local distortions to the majority rule on the dynamics of opinions using an extension of the Galam model. At each iteration of the local updates of opinion, the new model accounts for different probabilities of a local flip against the local majority as a function of the ratio of majority / minority within the discussing group. Depending of those probabilities, the model exhibits a wide variety of patterns which include new features in the topology of the landscape driving the dynamics. In particular, we uncover a rich interplay between attractors and tipping points coupled with both monotonic and alternating dynamics. The cases of group sizes 3 and 5 are investigated in detail, and we find regimes that feature competition between three attractors for size 5. Larger groups are also analysed. The local flip model also applies to the study of bottom-top hierarchical voting, where each group elects a representative at the next higher level according to the local majority in the group. The local flip corresponds to a representative who decides to vote against the choice of their electing group, i.e. a 'faithless elector'. The results shed a new light on a series of social phenomena triggered by one single individual who acts against the local majority.

Radicalism: The asymmetric stance of Radicals versus Conventionals

“…To study the effect of above asymmetric propensity to engage in a debate with people in a group, we expand the Galam Model of opinion dynamics into the Weighted Galam Model (WGM) to include weighted local majority rules [5][6][7][8][9]. The WGM is part of sociophysics [10][11][12][13][14], which includes numerous works devoted to the dynamics of opinion [15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33].…”