He was known for his quantitative analysis of national trends and patterns in voting behavior, the development of the "Party Systems" model, and the assembling of county election returns for the entire country.
[4] In 1964, Burnham published an article on the 1962 U.S. Senate election in Alabama, when Republicans made their first strong showing for federal office since Reconstruction in the state known as "The Heart of Dixie."
The Republican James D. Martin of Gadsden, an oil products distributor, challenged veteran Democrat J. Lister Hill of Montgomery and fell only a few thousand votes short of victory.
Burnham found it ironic that a Republican from the populist North Alabama ran strongly in the cities and Black Belt, while the Democratic senator from the capital city of Montgomery appealed to the northern hill country, where voters appreciated programs like the Tennessee Valley Authority and were less racially conscious because of the relatively small number of African Americans in their region.
Two years after the Hill-Martin race, Burnham correctly forecast that the inroads of presidential Republicanism would continue in the South, but competition at the state and local levels would take root slowly.