I have already quoted President Eisenhower and the Geneva Agreement of 1954. Read it this time.He was not elected
Would have is irrelevant.
It was justified because he was the aggressor.
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This page from President Eisenhower's Memoires, Mandate for Change, page 372, shows that he believed Ho Chi Minh would have won any free election in Vietnam in 1954. This is certainly why the U.S. did not permit such an election, though the Geneva Convention of 1954 required it.
I am convinced that the French could not win the war because the internal political situation in Vietnam, weak and confused, badly weakened their military position. I have never talked or corresponded with a person knowledgeable in Indochinese affairs who did not agree that had elections been held as of the time of the fighting, possibly 80 per cent of the populations would have voted for the Communist Ho Chi Minh as their leader rather than Chief of State Bao Dai.
Selection from Eisenhower's Memoires
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The Final Declaration of The Geneva Conference: On Restoring Peace in Indochina, July 21, 1954
4. The Conference takes note of the clauses in the agreement on the cessation of hostilities in Viet-Nam prohibiting the introduction into Viet Nam of foreign troops and military personnel as well as of all kinds of arms and munitions.
6. The Conference recognizes that the essential purpose of the agreement relating to Viet-Nam is to settle military questions with a view to ending hostilities and that the military demarcation line should not in any way be interpreted as constituting a political or territorial boundary...
7. In order to insure that sufficient progress in the restoration of peace has been made, and that all the necessary conditions obtain for free expression of the national will, general elections shall be held in July 1956, under the supervision of an international commission composed of representatives of the member states of the International Supervisory Commission referred to in the agreement on the cessation of hostilities. Consultations will be held on this subject between the competent representative authorities of the two zones from April 20, 1955, onwards.
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The War in Vietnam happened because the United States prevented a fair election in which a stark, raving Communist would have won by a massive margin.