Why do you think the two party system has been so prevalent in places like the United States?

It's human nature to perceive all battles as between only two opponents: It naturally encourages only the strongest to be compared with any seriousness.
Aside from that, in the US especially, politics is expensive, and a free market naturally gravitates towards monopolies. The same is true in politics, though it wouldn't ever reach an actual monopoly.
Finally, I think it's a reflection of the primary ideological dichotomy: Compassion vs. Criticism. Often posed as "left vs. right", it encompasses social and economic policies. With two-party systems, you'll find that one takes one of these roles, the other takes the other. In the US, neither of the main parties are doing a very good job at representing their side, hence there are new populists on either side (Bernie and Trump), and one of them might just become president.
There's probably other things I haven't realised or remembered, but I think those are the most important factors.

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