The two-party system is well-entrenched in the United States, and the blame usually falls on the First Past the Post (FPP) system.
It is true that FPP discourages third parties. Suppose that you have an election in one constituency, and three candidates A, B and C are competing to be first past the post. Now suppose that A and B are likely to finish at first and second place respectively. If you are a supporter of candidate C while B is your second choice, voting for C will in fact help A. Once you realize this, you, as a voter will shift your vote to B. When enough voters do the same, C will realize that he or she has no chance, and drop out of the race. Over a long enough period, the lesson will be learnt, and the constituency will be left with only two parties.
Does this explain why the US has only two parties? Not really. What is true for one constituency does not necessarily hold when scaled up. You could have only two viable parties in a constituency, but they don’t have to be the same two parties across the nation.
In a parliamentary democracy, for example, third parties have an incentive to exist, because they can punch above their weight in coalition governments. It is claimed that the presidential system in the US favours a two party system because it makes the whole country a single constituency. But that does not make sense. The US also had a fairly strong Congress that takes its law-making duties seriously. Why aren’t there multiple parties representing differing interests in the Congress?
Also, the US is geographically large, moderately diverse and a strongly federal country. Why aren’t there regional parties as we have in India? “Presidential Elections” is not a good answer. The parties could easily line up behind two major candidates at election time. The continued persistence of the two party system in the US requires an explanation.
I believe the explanation is that political parties in the US are unlike parties anywhere else in the world. They are big-tent parties. They are much more bottom-up than parties elsewhere. Their leaderships, such as they are, have very little leeway to steer their parties in their preferred direction.
Third parties form when a faction or an ideological grouping feels too constricted within the confines of an existing party. Because the two major parties are big tents, that is but a dim possibility in the USA. In other countries, if you disagree with the party leadership, you often have no option but to split and form another party. In the US, the party leadership has very little control over your career. Your career is decided by your performance at the primaries.
In India, regional parties are a way to handle the diversity of the country. They also provide popular local leaders the freedom of manoeuvre they wouldn’t have if they were part of a larger national party. But in the US, all politicians are free agents anyway. There is no need for a local politician to form a regional party to be independent of the national leadership.
Given this, how would a third party improve the politics of the USA? Aspiring third parties like the Libertarian Party and the Green Party complain that the two mainstream parties do not give space to minority viewpoints. Really? What stops someone from forming a libertarian wing of the Republican Party or a green wing of the Democratic Party? If those ideas have enough appeal to win elections, they should have enough supporters who would be willing to register as members of those parties and vote for libertarians or greens in primaries.
Actually I suspect that the third parties’ real complaint is that if they tried to work within the two major parties, they would have to compromise on their core principles. That is a valid complaint. The politicians and policies that emerge from within the two major parties are the result of compromises forged among the major wings of those parties.
But how would it be any different if, instead of a two party system, you had multiple parties, each with a core set of principles of its own? Those parties would still have to join together in a coalition to come to power, and in a coalition, they would have to compromise on some of their principles. We have seen the weird results that coalitions throw up in India.
I could be wrong here, but third parties in the US seem to show up exclusively for the presidential election. They put up candidates, they complain a lot about how there is no space for alternative voices and then they disappear for 4 years. This seems to me to be no way to build an alternative. If they really need to build a party, there’s a lot of organizational work that would be needed. I would expect them to focus on winning lower level elections first and then work their way upwards. They are either not doing this, which means that they are not serious; or they are trying to do this and failing, which supports my point that there is really no need for them.
And if for some reason, they think that a presidential candidate that doesn’t fit clearly into one of the two major groups coming out of the blue and getting elected just like that is the right way to change the political system, the recent election of Donald Trump has proven that that too is possible within the two party system. (I mean that the election is possible, not the change.)
Overall, I do not understand the case for a multi-party system in the US. There is nothing that such a system can bring to the table, either good or bad, that the two-party system with American characteristics does not already provide. It is precisely those specifically American characteristics that have stopped third parties from emerging, not the generic stuff like the FPP system or the presidential form of government.