A Simple Threshold Captures the Social Learning of Conventions

A persistent puzzle across the cognitive and social sciences is how people manage to learn social conventions from the sparse and noisy behavioral data of diverse actors, without explicit instruction. Here, we show that the dominant theories of social learning perform poorly at capturing how individuals learn conventions in canonical coordination experiments that task them with matching their behaviors while interacting in social networks. Across experiments, participants' learning behavior systematically deviates from both imitation and statistical optimization. Instead, we find that participants follow a categorical, two-stage learning process: they behave probabilistically until they acquire enough information about each other to trigger a mental threshold and then their behaviors stabilize. We precisely identify this threshold using the Tolerance Principle, a parameter-free equation first developed to model how children learn rules in language. Our simulations show that threshold-based agents often produce social learning that is more accurate than imitating and optimizing agents. We further show that the Tolerance Principle offers an improved model of how a critical mass of dissenting actors can overturn established conventions. The superior performance of our model holds when comparing against a variety of optimization approaches, including Bayesian inference. These findings offer compelling evidence that a simple, mathematical threshold underlies individual and social learning, from grammatical rules to behavioral conventions.