In the past two decades several methods for objectively measuring cultural evolution have been developed. It is now possible to measure the degree of cultural evolution, but we know very little about its processes. Theorists have long proposed that among human societies warfare is the primary mechanism of natural selection. In other words, they say it is through success in warfare that societies evolve. We tested this theory cross-culturally on a world-wide sample of forty-nine societies. We used rigorous controls for diffusion and data error. We found no real evidence at all in our sample that a society's success in warfare (as measured by territorial change) was substantially related to its level of cultural evolution. From this we presume that ordinarily the chief selective mechanism in cultural evolution is more likely to be not warfare but peaceful diffusion through voluntary borrowing of specific traits by one society from its neighbor.