Confusion about the changing positions of political parties in the U.S., from Andrew at Statistical Modeling, Causal Inference, and Social Science.
There are fairly standard models that allow one to plot political opinions in a two-dimensional "issue space", with the two dimensions being roughly "social" and "economic"; the two-party system dictates that these essentially get projected down to a single dimension. The post alludes to them, and refers to an argument that the Democrats and Republicans may have switched positions in the last century or so via a rotation of 180 degrees in this space. (As counterintuitive as it seems given the current ideological stances of the major parties, the Republicans started out as the anti-slavery party.) Andrew is not convinced -- the argument seems to rely on an assumption that states remain constant in their political leanings, which isn't true -- but it at least seems like something that could happen.
So in another century, could the parties rotate all the way around and get back where they started? And if the alignment of the two major parties in issue space in 2100 ends up being the same as that in 1900, is it more likely to happen by the rotation continuing in the direction it's going, or by reversal? This is basically a question about winding numbers, in a sense I really don't want to make precise because it's kind of silly.