Why do historical figures sometimes become the object of religious worship? Here, we propose that, above a certain group-size threshold, maintaining a belief in the continued existence of authority figures after their death preserves group coordination efficiency. That is, we argue that coordination activities in larger groups become more effective when they center on symbolic (although formerly real) bearers of authority; for smaller groups, we claim the opposite occurs. Our argument is pursued by way of a collective action model that makes anthropologically plausible assumptions about human sociality. One key finding is the existence of a group-size threshold that marks the difference between the two different collective action regimes, one with and one without the presence of a deified historical figure. Another is that, in larger groups, priest-like castes naturally emerge as a consequence of the benefits of personally identifying with the deified agent.