Laws of Divine Power in the Greek Pantheon

In ancient Greek polytheism, worshippers could choose which gods they would address, and in doing so they expected some form of benefit in a quid pro quo relationship. We look into the optimal choice of which god to worship as a function of the presumed strategy of the gods for returning favors to the worshippers, and relate it to a form of divine efficiency measure. At the equilibrium the model also shows that the least-worshipped god receives at least a certain volume of devotion. We propose two different approaches that may account for the assumed divine efficiency measure, one based on projecting characteristics of human performance onto the gods, and the other based on a random growth model for the benefits of addressing each god. Both approaches imply that observed acts of worship would follow a type of power law. We gathered data from a large volume of epigraphic and literary sources on actual acts of worships from the ancient Greeks, and it allows us to show that the distributions of these acts at the polis level effectively follow power laws with a particularly high degree of regularity. The number of votive acts towards the least-worshipped gods also match the model's prediction. We test the extent to which the known characteristics of the poleis affect the shape of these distributions, and find little explanatory power. The shape of the distribution of votive acts across gods hence appears to have followed a general law for the Ancient Greeks.