Consensus formation and change are enhanced by neutrality

Effective collective decision-making in human and animal groups requires robust mechanisms for consensus formation and change, typically via feedback loops in which individuals adapt their behavior and opinions based on their perception of others. Such processes have been observed in the onset of motion in insect swarms and are believed to manifest across scales from nucleosomes to entire societies. However, levels of participation can be highly variable over time, with individuals sometimes adopting neutral positions such as moving to the back of a group or abstaining from a vote. Here, we present a new theoretical and experimental analysis showing that neutrality has two important and hitherto unreported benefits to collective decision-making. First, it enables the robust formation of consensus in groups of individuals applying simple linear reasoning, updating their stance after consideration of at most one other individual at a time. Second, we find that neutral actors can facilitate efficient consensus change by reducing the effective population size during transitions. These findings are derived from a new general mathematical model of collective binary decision problems and validated against experiments with insect and human populations. Our results provide a parsimonious explanation of how groups of animals and humans quickly reach and overturn consensus, suggesting efficient solutions to collective decision-making problems.