Time to consensus

The dynamics of a two-state decision-making model (DMM) with a tunable control parameter K is described. On all-to-all (ATA) networks, the system undergoes a phase transition at a critical value of Kc=1. Scale-free networks were also found to undergo phase transitions, but the value of Kc increases as the scale-free exponent increases. Time to consensus is defined as a first passage time to a specified threshold of the global mean field, which represents a level of majority for the network. At criticality, the time to consensus for sparse networks with broad degree distributions (e.g., scale-free networks) approaches that of the ATA networks, although somewhat more cooperation (higher Kc) is required.