Adversity magnifies the importance of social information in decision-making.

Decision-making theories explain animal behaviour, including human behaviour, as a response to estimations about the environment. In the case of collective behaviour, they have given quantitative predictions of how animals follow the majority option. However, they have so far failed to explain that in some species and contexts social cohesion increases when conditions become more adverse (i.e. individuals choose the majority option with higher probability when the estimated quality of all available options decreases). We have found that this failure is due to modelling simplifications that aided analysis, like low levels of stochasticity or the assumption that only one choice is the correct one. We provide a more general but simple geometric framework to describe optimal or suboptimal decisions in collectives that gives insight into three different mechanisms behind this effect. The three mechanisms have in common that the private information acts as a gain factor to social information: a decrease in the privately estimated quality of all available options increases the impact of social information, even when social information itself remains unchanged. This increase in the importance of social information makes it more likely that agents will follow the majority option. We show that these results quantitatively explain collective behaviour in fish and experiments of social influence in humans.