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This is a very useful and provocative question, and there's a lot to bring in to an answer.
First off - for those reading who might not know - the 'Domino theory' was the Cold War idea that once one country in Asia fell to communism (Vietnam, for example), then that would have a knock-on effect and increase the likelihood of neighbouring countries becoming communist. As the 'dominos' fell, there was the (perceived) chance the the chain would eventually reach critical places like India, Japan or Australia. The idea really came to public prominence during the first administration of US president Dwight D. Eisenhower (1953-57). In a press conference on April 7, 1954, Eisenhower (responding to a journalist's question about the importance of Indochina (Vietnam, Cambodia, etc) to the "free world", stated that:
"Finally, you have broader considerations that might follow what you would call the 'falling domino' principle [emphasis mine]. You have a row of dominoes set up, you knock over the first one, and what will happen to the last one is the certainty that it will go over very quickly. So you could have a beginning of a disintegration that would have the most profound influences.
Now, with respect to the first one, two of the items from this particular area that the world uses are tin and tungsten. They are very important. There are others, of course, the rubber plantations and so on. Then with respect to more people passing under this domination, Asia, after all, has already lost some 450 million of its peoples to the Communist dictatorship, and we simply can't afford greater losses.
But when we come to the possible sequence of events, the loss of Indochina, of Burma, of Thailand, of the Peninsula, and Indonesia following, now you begin to talk about areas that not only multiply the disadvantages that you would suffer through loss of materials, sources of materials, but now you are talking really about millions and millions and millions of people.
Finally, the geographical position achieved thereby does many things. It turns the so-called island defensive chain of Japan, Formosa, of the Philippines and to the southward; it moves in to threaten Australia and New Zealand. It takes away, in its economic aspects, that region that Japan must have as a trading area or Japan, in turn, will have only one place in the world to go- that is, toward the Communist areas in order to live. So, the possible consequences of the loss are just incalculable to the free world."
OK, that's the basics laid out for everyone and anyone who is interested! So back to the question: was it just propaganda or was there actually something behind the 'domino theory' It's crucial to consider some immediate, short and medium-term context for all of this.
In the immediate term, at the point Eisenhower makes his statement in April 1954, things are looking pretty bleak for the French in Indochina. The battle of Dien Bien Phu - where French forces were eventually crushed by the communist Viet Minh - was raging, and it looked like the communists were going to boot the French imperialists out. To all intents and purposes it seems as if another communist government is going to come to power in Asia. Now, at the conclusion of the Indochina War, Vietnam is split in two (communist controlled north, US-backed south) there's a promise that elections to be held in 1956 will unify the country under whomever is victorious. But Washington certainly doesn't want a communist victory (which is likely). So, important context: It looks possible that communists might take over another Asian nation!
In the short term, the Chinese Civil War ended in August 1949 with a victory for the communist side, led by Mao Zedong, Zhou Enlai, and others. The defeated, American-backed Nationalist side - led by Jiang Jeshi (sometimes referred to in older texts as Chiang Kai-Shek) retired to the island of Formosa (now Taiwan) and established the Republic of China. For many Americans the 'loss of China' was a huge shock, and led to president Harry Truman being attacked from all sides for being 'soft' on communism. So, more important context: one of the world's most populous countries has just become communist! If it can happen in China, why might it not happen elsewhere?
Stepping back into the medium term, we should consider the 1930s. Bear in mind that many of those in leadership positions during the 1940s, 50s, and 60s had direct experience of the rise and spread of fascism in the 1920s and 1930s. Italy, Germany, Austria, Romania, Spain, and other nations all turned towards fascism (or variants thereof) to a greater or lesser extent. Therefore the idea of the 'domino effect' of a a politically ideology spreading out and 'infecting' other nations is not so illogical. If you place yourself in the position of Dwight Eisenhower in 1954, having seen what happened over the last couple of decades, the 'domino theory' isn't quite a daft as it might seem to us. So, even more important context!: There is a historical logic to the idea of the domino theory.
The combination of historical memories of the 1930s, the 'loss' of China, and the impending French defeat in Vietnam all provide the perceptual background to the domino theory idea. As I said, there's an internal logic to all of this in terms of the zero-sum game of the Cold War, where there are only (perceptually) winners or losers. We frequently look back on the ideas and thinking of historical figures and go "How could they possibly think that?" But hindsight is best avoided and when you get down to it, maybe Eisenhower, Dulles, and the rest actually believed that the dominoes might fall.
Were they going to fall, though? Hindsight tells us that the US-backed Republic of Vietnam lacked legitimacy in the eyes of many of its citizens, and couldn't really compete with the communists in terms of authentic ideas about Vietnamese independence. Would the dominos have fallen elsewhere? In India, while post-independence leader Jawharlal Nehru adopted some Soviet ideas about centralised planning and industrialisation, he was by no means beholden to communist ideology. Indeed, when the Indian Communist Party won power in the souther state of Kerala, he dispatched his daughter Indira Gandhi to suppress them. In Indonesia the Sukharno government initially worked with the local communist party, but in the 1960s Indonesian communists are wiped out in vast massacres where approximately 500,000 people are murdered. The British had also successfully suppressed a communist insurgency in Malaya (now Malaysia) in the 1950s.
Counterfactuals are problematic, and we can only examine what did happen. There wasn't a cascade of falling dominos in the 1950s and 1960s. However, that doesn't mean to say that those in power in Washington didn't believe that it might be imminent. And a lot of the time, perception is more important than reality.
Hope this helps.
Malcolm
Useful reading
Gregg Brazinsky, Winning the Third World: Sino-American Relations During the Cold War (Chapel Hill: University of North Carolina Press, 2017)
Paul Thomas Chamberlin, The Cold War’s Killing Fields: Rethinking the long peace (New York: HarperCollins, 2018)
Odd Arne Westad, The Cold War: A world history (London: Allen Lane, 2017)