Zipf's law before the monetary economy and written administration: volume distribution of kofun, ancient Japanese burial mounds

Abstract

We analyze the volume distribution of kofun, large mounded tombs constructed in the Japanese archipelago mainly from the mid-third through the seventh century CE. We ask whether the distribution of collectively mobilized resources in an ancient society without a monetary economy or written administration could follow Zipf's law, as observed in modern firm sales. Here, Zipf's law refers to a power-law distribution with an exponent close to one. Using a nationwide database, we estimate kofun volumes as a proxy for labor and resources mobilized by the constructing groups, and the volume distributions archipelago-wide and by region, period, and mound type. We find that the volume distribution of keyhole-shaped kofun exhibits a Zipf-like upper tail with a cumulative power-law exponent close to unity, while its central part is close to log-normal---a shape that resembles the distribution of modern firm sales. Moreover, many regional and temporal differences appear primarily as scale differences: after median normalization, most distributions collapse onto a common curve and remain approximately Zipf-like. However, some exceptional groups exist---such as the politically central Kinki region---that show heavier-than-Zipf tails (cumulative exponents below unity), indicating stronger concentration among the largest kofun. To interpret these regularities, we introduce a Kesten-type stochastic growth model with stopping and reorganization. The model provides a unified account in which the log-normal-like body, Zipf-like tail, and regional/temporal variations arise from a common growth process. Together, these findings raise the possibility that collectively mobilized resources exhibited a Zipf-like structure already in the Kofun period.