The British Loony Party

I remember when a nonexistent person won student body president in college.

Who would get to decide if it's a joke candidacy?

Yes. A result of winner-take-all elections is that we have trench-style (as in World War 1 trench warfare) politics: two parties stand very close to each other on the political spectrum with ~45% support each, very little gets done, and the only thing that really happens is that the front where the trenches are moves a few meters to the left or the right. Right now, both trenches are deep into center-right territory as far as the left/right economic spectrum is concerned.

I think there is a difference between the parties, but not so much along left-right lines. These cultural issues (gay rights, abortion, evolution) might seem trivial to Europeans, but that's because there isn't a credible threat of abortion being recriminalized in Sweden, nor of evolution being stricken from the classrooms in France. The Religious Right isn't a majority in the US, but they are powerful. Bush would not have been able to get domestic support for the War on Iraq without the dominionists (those who believe bringing violence to the Middle East will hasten the End Times and Rapture) on board. They're about 10-15% of the voting populace.

The Democratic party is a center-right party that would be labeled conservative by European standards but generally considered reasonable; the Republican party is not much further to the economic right but is far more authoritarian and zealous.