Phase transitions, collective emotions and decision-making problem in heterogeneous social systems.

The paper considers the problem of collective decision-making as a second order phase-transition, which occurs in heterogeneous information-oriented communities possessing frequent information exchange between individuals. We examine the quantum-like model of simplified two-level cognitive systems (TLCS) interacting with a socially important (contextual) information field. The model exploits approaches to the modern social cohesion framework. We refer to some target network community, which is in close interaction (e.g. message exchange) with "reservour" (large network community) possessing infinite degree of freedom. We introduce a new approach for valence and arousal variables, used in cognitive sciences for the description of collective emotion states. We express them via collective polarization and population imbalance respectively. The model predicts a super-radiant phase transition for target network community leading to coherent polarization establishment in the socium. The valence and arousal parameters can be evaluated from actrors behaviour in social network communities as a result of immediate response (decision-making) to some notable news. We introduce Gaussian and Levy distribution functions to reveal the influence of social community inhomogeneity on decision-making features. We show that a critical (social) temperature is determined by the population imbalance (valence), detuning, field coupling strength parameter and relay to conditions of social polarization establishment. We predict coherent social energy release in a community without inversion due to its specific properties close to the superfluid paradigm in quantum physics, or social cohesion in sociology. We establish a connection of our model to the recently presented quantum-like model of the social laser to describe the waves of social protests as the result of collective decision-making process in the system with inversion of population in mental states. Finally, we compare our model with existing social impact models, a.k.a. cellular automata models, in the limit when social community perceives information field in the state induced by large information reservoir (mass-media). Notably, eliminating quantized field we lose important information how collective emotions (arousal) form in social community.