Would it be bad for America if the GOP became irrelevant?

[Selatius]

31. You could only break the two-party monopoly by imposing a majority rule for elections.

(i.e. you require that a candidate for a seat in the House or Senate must win more than 50% of the vote or face a run-off)

If you did this in Congress, in a decade or two, the two-party monopoly would be finished.

As it stands, only requiring that the winner get the plurality and not a majority for the seat invokes Duverger's Law.

http://en.wikipedia.org/wiki/Duverger%27s_law

If it were a race between a right-wing Democrat, a far-right Tea Partier, and a left-wing Green Party candidate, you would vote for the candidate closest to your ideal, and if he does not win the first round of elections, then you vote for the alternate. In this example, you would likely vote for the Green Party in the first round, and if that candidate loses, you throw your vote behind the right-wing Democrat to prevent the Tea Partier from winning. In this manner, you don't have to worry about splitting the vote and handing victory to the total opposite of what people wanted, like George W. Bush in 2000.

A faster version of this is called IRV or instant run-off voting. That's like the above example, but it's done in one election, not two.