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.
The product of these two curves matches the prediction of the one-third hypothesis.
and given that p and q are each equal to 1/2, Engelmann's One-Third Hypothesis can be readily deduced.
A perfect example of the OTH was illustrated by Wayne Youngquist’s 1968 “Wooden Shoes and the One-Third Hypothesis,” which documented the German population in Milwaukee little more than a century ago.
[2] The first empirical test of Engelmann’s OTH came in the form of the 1967 Detroit riot.
[1] Sam Butler, in 2011, explicitly cited Engelmann and the One-Third Hypothesis in his analysis of London's riots and their aetiology.
Early on K. S. Srikantan correctly questioned the assumption that p and q are each equal to ½.
The terminology, though appropriate, has become ambiguous because “critical mass” is used in a variety of ways that do not suggest the OTH at all.