The key players in the decision to drop the atomic bomb were U.S. President Harry S. Truman, his Secretary of State James F. Byrnes, and Secretary of War Henry L. Stimson. All three men had their own agendas when it came to using the bomb.
Estimates of a U.S. invasion of Japan ranged from 30,000 to 2 million casualties. The higher numbers might have been wartime propaganda to get the American public onside for use of the atomic bomb. Preventing loss of life in an invasion was the official reason given for dropping the bomb in August 1945.
Truman's decision was made quickly on the heels of the successful test of the atomic bomb in July 1945. After the test, Truman was no longer interested in diplomatic solutions with Japan, or urging the Soviets to enter the Pacific war.
There is speculation the bomb was really used as a dramatic demonstration to the Soviets, who were after "war trophies" in the Pacific.
Irving Janis, author of "Groupthink", proposed a decision theory model to explain the Hiroshima decision. He called it the "Wow, Grab it!" Model or "Elated Choice Decision Rule". The model states that when there is a strong feeling of elation, or a "raring to go" feeling, leaders tend to quickly grab at a solution that seems to satisfy all their problems at once, and move quickly to implementing that decision without looking any further into alternatives. There are many signs that Truman acted according to this decision theory model, when he quickly moved to drop the bomb after its successful test.
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