Optimal use of simplified social information in sequential decision-making

Social animals can improve their decisions by attending to those made by others. The benefit of this social information must be balanced against the costs of obtaining and processing it. Previous work has focused on rational agents that respond optimally to a sequence of prior decisions. However, full decision sequences are potentially costly to perceive and process. As such, animals may rely on simpler social information, which will affect the social behaviour they exhibit. Here, I derive the optimal policy for agents responding to simplified forms of social information. I show how the behaviour of agents attending to the aggregate number of previous choices differs from those attending to just the most recent prior decision, and I propose a hybrid strategy that provides a highly accurate approximation to the optimal policy with the full sequence. Finally, I analyse the evolutionary stability of each strategy, showing that the hybrid strategy dominates when cognitive costs are low but non-zero, while attending to the most recent decision is dominant when costs are high. These results show that agents can employ highly effective social decision-making rules without requiring unrealistic cognitive capacities, and indicate likely ecological variation in the social information different animals attend to.