Reaching Consensus by Allowing Moments of Indecision

Group decision-making processes often turn into a drawn out and costly battle between two opposing subgroups. Using analytical arguments based on a master equation description of the opinion dynamics occurring in a three-state model of cooperatively interacting units, we show how the capability of a social group to reach consensus can be enhanced when there is an intermediate state for indecisive individuals to pass through. The time spent in the intermediate state must be relatively short compared to that of the two polar states in order to create the beneficial effect. Furthermore, the cooperation between individuals must not be too low, as the benefit to consensus is possible only when the cooperation level exceeds a specific threshold. We also discuss how zealots, agents that remain in one state forever, can affect the consensus among the rest of the population by counteracting the benefit of the intermediate state or making it virtually impossible for an opposition to form.