Analysis of the high-dimensional naming game with committed minorities.
The naming game has become an archetype for linguistic evolution and mathematical social behavioral analysis. In the model presented here, there are N individuals and K words. Our contribution is developing a robust method that handles the case when K=O(N). The initial condition plays a crucial role in the ordering of the system. We find that the system with high Shannon entropy has a higher consensus time and a lower critical fraction of zealots compared to low-entropy states. We also show that the critical number of committed agents decreases with the number of opinions and grows with the community size for each word. These results complement earlier conclusions that diversity of opinion is essential for evolution; without it, the system stagnates in the status quo [S. A. Marvel et al., Phys. Rev. Lett. 109, 118702 (2012)PRLTAO0031-900710.1103/PhysRevLett.109.118702]. In contrast, our results suggest that committed minorities can more easily conquer highly diverse systems, showing them to be inherently unstable.
Department of Mathematical Sciences, Rensselaer Polytechnic Institute, 110 8th Street, Troy, New York 12180, USA.|Network Science and Technology Center, Rensselaer Polytechnic Institute, 110 8th Street, Troy, New York 12180, USA.
William
W
Pickering
Network Science and Technology Center, Rensselaer Polytechnic Institute, 110 8th Street, Troy, New York 12180, USA.|Department of Computational Intelligence, Wroclaw University of Technology, 50-370 Wroclaw, Poland.
Boleslaw K
BK
Szymanski
Department of Mathematical Sciences, Rensselaer Polytechnic Institute, 110 8th Street, Troy, New York 12180, USA.|Network Science and Technology Center, Rensselaer Polytechnic Institute, 110 8th Street, Troy, New York 12180, USA.
Chjan
C
Lim
D000465:Algorithms; D000072357:Applied Behavior Analysis; D003198:Computer Simulation; D019277:Entropy; D005716:Game Theory; D006801:Humans; D008962:Models, Theoretical