Final answer:
The Harding, Coolidge, and Hoover administrations shared a common element of emphasizing big business and corporate power, aligned with pro-business policies.
Step-by-step explanation:
The common element of the Harden, Coolidge, and Hoover administrations was an emphasis on big business and corporate power. These administrations focused on pro-business policies, reflecting a laissez-faire approach reminiscent of the Gilded Age's politics. Coolidge famously declared that "the business of America is business," signifying this pro-corporate attitude. Furthermore, both Hoover and Mellon shared a belief in running the government with business efficacy. Despite starting a few progressive policies, Hoover's administration remained rooted in a firm belief that economic fluctuations were part of the normal business cycle and favored balanced budgets and the gold standard over interventionist economic measures.