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A well-known use of this metaphor was a justification for the Vietnam War, coined by Eisenhower: if Vietnam fell to communism, then Cambodia would be next, then Laos, and eventually all of Southeast Asia. It was also used by the USA during the Johnson administration to justify support for the overthrow of Indonesian president Sukarno in 1965.
See also: Butterfly effect, Snowball effect, Mathematical induction, Domino theory, Slippery slope