The one-third hypothesis (OTH) is a sociodynamic theory asserting that a subgroup's prominence increases as it approaches one-third of the total population and diminishes after it exceeds that number. It was first stated by sociologist Hugo O. Engelmann in a letter to the American Sociologist in 1967:
"...we would expect that the most persistent subgroups in any group would be those which approximate one-third or, by similar reasoning, a multiple of [i.e., a power of] one-third of the total group. Being the most persistent, these groups also should be the ones most significantly implicated in ongoing sociocultural transformation. This does not mean that these groups need to be dominant, but they play prominent roles."
The OTH involves two mathematical curves. One represents the likelihood that a subgroup of a specific size will emerge. The other represents the probability that it will persist. The product of these two curves matches the prediction of the one-third hypothesis.