I’ve heard it said 1000 times that the US is 2 party political system, but I just don’t understand what mechanisms push it to be that way? Why are 3rd parties so weak or unlikely?
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Because of the first-past-the-post election mechanism. All votes that don’t win a district are lost. In each district the Party with the most votes gets 1 person in the electoral college or parliament, no matter how close it was, and no matter who made second place.
If you vote a third party then you harm yourself and the party you like the least is benefiting from it.
Imagine you prefer Democrats over Relublicans. Even more you’d like the Green party to win, so you decide to elect green. But it doesn’t matter who gets hiow many votes, only the most votes ot your district matter, so your decision made the Democrats lose one vote and the Relublicans win. Even if Green plus Democrats together are 66% of the votes, split evenly, the Repuplicans can win with 34%
In a proportional system your vote would still get counted. Other Green party voters in other districts get pooled together. If neither Democrats nor Republicans get 50% of votes, then they are forced to form a coalition government, and your green party is much more likely to ally with the Democrats, so you gain something by voting them in any case.
Another option is ranked choice, where you can say “I vote green, but if green isn’t in the top 2 I vote Democrats” wich is basically a preemptive tiebreaker election if noone gets the absolute majority.
This is by the way known as [Duverger’s Law](https://en.m.wikipedia.org/wiki/Duverger%27s_law)
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