Politics – Means and Ends

June 5, 2011
Posted by Jay Livingston

Matt Yglesias posted at this chart of poll results in eight states that elected Republican governors. In seven of the eight, if the election were held today, Democrats would win.

(Click on the chart for a larger view.)

Matt calls this shift “buyer’s remorse” and takes it as a rejection of GOP policies (his post is here). Gabriel Rossman has a different take.
Repeat after me: REGRESSION TO THE MEAN.

I don’t doubt that some of this is substantive backlash to overreach on the part of politically ignorant swing voters who didn’t really understand the GOP platform, but really, you’ve still got to keep in mind REGRESSION TO THE MEAN.
Politicos like Yglesias might have overlooked this possibility because regression to the mean is mostly a matter of random “error variation,”* or unexplained variation. Intuitively, that doesn’t seem to fit with political opinions. If I get an unusually high score in a bowling game or a math test, I can try to explain it – something about my footwork or concentration. But I also realize that I may have been playing over my head. I have some sense of my true level of ability. I also know that my scores vary, and for reasons I can’t always explain. If you tell me that my lower score in the next game is regression to the mean, I’m not going argue.

It’s much harder to think this way about my opinion about the governor or anyone else’s opinion for that matter. Whether or not I’d vote for him is not a sample of my opinion. It is my opinion. It’s not random, it’s not an error, and it’s not unexplained. I know why I would or wouldn’t vote for him, and I figure that the same is true for other voters. So you can see why discussions of political shifts tend to leave out regression to the mean.

Even so, is the political shift here regression to the mean? It might help if we had some idea of what the mean is. Suppose that the mean is 50/50 Democratic/Republican. A shift from 8-0 in favor of the GOP to 1-7 in favor of the Democrats is regression way beyond the mean. So, like Lucy, we still have some splainin to do.

* I do not know, though I should, how this variation came to be called “error” or why we persist in using that term.


Anonymous said...

First, I agree with you that there is a substantive backlash phenomena that is bigger than just regression to the mean.

Nonetheless, I think regression to the mean is part of this, and more to the point I think that just because we can tell a substantive story about something doesn't mean that it's not also probabilistic. In some cases the substantive processes can add up to emergent probability. This is why sociologists have a hard time understanding simulations --- we tend to want to tell substantive stories rather than just seeing them as approximated by noise.

This XKCD comic pretty much sums up my view of the world

Jay Livingston said...

Agreed. I'm sure that part of the shift is regression to the mean. But my other point was that this regression is very anti-intuitive when applied to opinions and ideas. So imposing a narrative is all the more tempting. (An even clearer example is the "analysis" of the daily stock market report, which usually anthropomorphizes the market and then makes up an explanation for what the market was thinking about.)

If I were more energetic, I would have looked at past elections in those states to get some idea of that the means were. Don't political scientists do this sort of stuff?