Lack of consensus in social systems

Abstract

We propose an exactly solvable model for the dynamics of voters in a two-party system. The opinion formation process is modeled on a random network of agents. The dynamical nature of interpersonal relations is also reflected in the model, as the connections in the network evolve with the dynamics of the voters. In the infinite time limit, an exact solution predicts the emergence of consensus, for arbitrary initial conditions. However, before consensus is reached, two different metastable states can persist for exponentially long times. One state reflects a perfect balancing of opinions, the other reflects a completely static situation. An estimate of the associated lifetimes suggests that lack of consensus is typical for large systems.

Statistical physics of social dynamics

“…Finally, a Glauber zero-temperature spin dynamics has been recently considered in (Benczik et al, 2007), together with a particular link update rule, different from all previous cases: at each time step two nodes carrying equal spins are connected with probability p, while nodes with opposite values of the spin variable are connected with probability 1 − p. No topological fragmentation occurs in this case. Consensus is always reached on finite systems but exceedingly long disordered metastable states exist.…”

Dynamics of Social Group Competition: Modeling the Decline of Religious Affiliation

“…What we have shown by the generalization of the model to include network structure is surprising: even if conformity to a local majority influences group membership, the existence of some out-group connections is enough to drive one group to dominance and the other to extinction. In the language of references [7][8][9], the population will reach the same consensus, despite the existence of individual cliques, as it would without cliques, with only the addition of a time delay.…”

“…In this work, we focus on social systems comprised of two mutually exclusive groups in competition for members [5][6][7][8][9][10]. We compile and analyze a new data set quantifying the declining rates of religious affiliation in a variety of regions worldwide and present a theory to explain this trend.…”

Adaptive-network models of swarm dynamics

“…Furthermore, in collective motion it cannot be neglected that an agent's decision to move in a certain direction will determine the agents with whom it will interact next. However, a similar feedback of individual decisions on future interaction partners was also studied in recent works on opinion formation [16][17][18][19][20][21][22][23]. The resulting models incorporate both an opinion formation process on the network and a dynamic update of the network topology and thus fall into the class of adaptive networks (ANs) [24,25].…”