Final answer:
The doctrine referred to as Mutual Assured Destruction (MAD) prevented the US and the Soviet Union from attacking each other during the Cold War due to the fear of total annihilation.
Step-by-step explanation:
The doctrine by which both the US and the Soviet Union built up their military power to ensure peace was called Mutual Assured Destruction (MAD). This policy implied that both superpowers possessed the capacity to destroy one another completely in the event of a nuclear attack, thereby preventing any first strike due to the fear of total annihilation. The fear of these devastating results made the United States and Soviet Union more likely to step back from direct warfare, relying on nuclear arsenals for defense through deterrence.