Many modern studies of cultural innovation and demographic change rest on the proposition that social learning is a key process in the spread of novel variants. We agree with this proposition, but we also suggest that the selectivity of social learning, with respect to a skill or knowledge, has largely been overlooked in considering how the tempo of cultural evolution depends on population size. We evaluate contrasting predictions ranging from cases of extreme selectivity, where everyone learns from the best individual in the group, to entirely nonselective, unbiased social learning, where everyone learns from one another. At the highly selective end of the spectrum, population size should correlate strongly with the tempo of cultural evolution. At the nonselective end, where social learning is unbiased, there should be little correlation between population size and tempo of cultural evolution. For any given case study, characterizing the relative selectivity of social learning is crucial to successfully predicting the effect of population size on cultural evolution.