  A diversity of decision-making systems has been observed in animal
collectives. In some species, choices depend on the differences of the numbers
of animals that have chosen each of the available options, while in other
species on the relative differences (a behavior known as Weber's law) or follow
more complex rules. We here show that this diversity of decision systems
corresponds to a single rule of decision-making in collectives. We first
obtained a decision rule based on Bayesian estimation that uses the information
provided by the behaviors of the other individuals to improve the estimation of
the structure of the world. We then tested this rule in decision experiments
using zebrafish (Danio rerio), and in existing rich datasets of argentine ants
(Linepithema humile) and sticklebacks (Gasterosteus aculeatus), showing that a
unified model across species can quantitatively explain the diversity of
decision systems. Further, these results show that the different counting
systems used by animals, including humans, can emerge from the common principle
of using social information to make good decisions.
