Consensus decision making on a complete graph: complex behaviour from simple assumptions

Abstract

In this paper we investigate a model of consensus decision making [Hartnett A. T., et al., Phys. Rev. Lett., 2016, 116, 038701] following a statistical physics approach presented in [Sarkanych P., et al., Phys. Biol., 2023, 20, 045005]. Within this approach, the temperature serves as a measure of fluctuations, not considered before in the original model. Here, we discuss the model on a complete graph. The main goal of this paper is to show that an analytical description may lead to a very rich phase behaviour, which is usually not expected for a complete graph. However, the variety of individual agent (spin) features - their inhomogeneity and bias strength - taken into account by the model leads to rather non-trivial collective effects. We show that the latter may emerge in a form of continuous or abrupt phase transitions sometimes accompanied by re-entrant and order-parameter flipping behaviour. In turn, this may lead to appealing interpretations in terms of social decision making. We support analytical predictions by numerical simulation. Moreover, while analytical calculations are performed within an equilibrium statistical physics formalism, the numerical simulations add yet another dynamical feature - local non-linearity or conformity of the individual to the opinion of its surroundings. This feature appears to have a strong impact both on the way in which an equilibrium state is approached as well as on its characteristics.