One of the ingredients that characterize the social structure of animal societies is dominance relationship, where a dominant individual takes priority in the access to food, mates, and etc., over a subordinate one. When dominance relation is transitive in a group, i.e. when A>B and B>C suggest A>C, its social structure is called linear dominance hierarchy. Linear dominance is widely observed in various animal societies, yet the mechanism of its emergence is still largely unknown.

Here we theoretically attempt to unveil conditions that facilitate linear dominance hierarchy formation. Specifically, we pay attention to the role of learning behavior.

In our model, we consider a group of individuals who perform a Bayesian learning to infer physical strength of others. An observer of a conflict updates the estimated probability of its winning against either of the contestants via a Bayesian rule. Therefore, the outcome of a dyadic conflict affects future decision making of not only contestants themselves but also third-party observers.

Our analysis reveals that the presence of opportunities to observe conflicts between others dramatically promotes linear hierarchy formation. It is so even when all individuals in the group are equal in physical strength. Our results strongly support the social dynamics hypothesis in linear hierarchy formation.