Davidson was active in encouraging and promoting philately in the St. Louis, Missouri, area and throughout the state.
Because of his organizational and managerial talent, he served in various capacities in a number of national philatelic societies, such as the American Philatelic Society (APS), where he was director from 1971 to 1976, and also chaired the Literature Committee.
At the American Philatelic Research Library, Davidson was an original trustee, and later, he served as its president.
At the Smithsonian Institution in Washington, D.C., Davidson was named a Distinguished Philatelic Lecturer.
He was named to the American Philatelic Society Hall of Fame in 1999.