Wednesday, November 12, 2008

How Purple Is It, Rowan?

As I get older (a topic that's been much on my mind of late), I seem to be more and more acutely aware of other peoples' tendency to present as clever an idea that turns out later to be either a parlor trick, a tautology, a conclusion based on false assumptions, or some combination of all three. I believe the clinical term for this heightened sensitivity to pretentiousness is, "turning into a cranky old man," but I'll have to check my clinical literature and get back to you.

I mention all of this because of a new web site, uploaded by a certain Robert Vanderbei of Princeton University, intended to prove to us that we in this country are all really just one big amalgam of cheerfully cohabiting Republicans and Democrats, all of whom are capable of changing our vote on a four-year dime. It's an intrinsically appealing supposition, made even more appealing by the fact that Dr. Vanderbei chooses to make it visually--using an animated GIF of the past twelve Presidential elections, with the national map shaded county-by-county in various gradients of purple to reflect the proportion of votes received by the Republican and the Democrat each time. "Hey," we're supposed to think, "look at how purple the map is!" Then, after a few more of the slides have loaded, we're supposed to think, "Hey, look at how purple it always is!" And indeed to that extent Dr. Vanderbei is inarguably correct: Just how different is the map of 1976 from that of 1980, by this metric? The short answer is, not much.

Unfortunately, the maps in question (while fascinating to look at for any number of reasons) fail rather spectacularly to support Dr. Vanderbei's implicit assertion that the whole country is a mixed aggregate of more-or-less uniformly distributed partisans and independents. I hate to be the person to rain on such a sexy parade, but the maps simply don't suggest what they are implied to suggest, to even the tiniest degree.

To begin with there is the small problem of how our brains process color. I don't know about you, but the mid-point shade of purple (the one that would represent 50% Republican and 50% Democratic support in a particular county) looks an awful lot bluer to me than it looks red. Purple is, in my subjective assessment at least--and probably a lot of other peoples' as well--much more accurately described as a shade of blue than as a shade of red, not least because its position in the color prism is adjacent to blue and at the opposite end from red. For this reason, each four-year cycle's map will appear uniformly bluer than it really is. (And if you hesitate to agree, watch the movie again and make special note of 1980 and 1984, when the Democratic candidates for President were getting clobbered coast-to-coast, but whose maps appear not particularly redder than any of the others in the loop.)

The problem that this color-processing misdirect presents for vetting the underlying argument would be acute enough, but in fact there is a significantly bigger problem with the maps being advocated by Dr. Vanderbei: the counties don't decide the President, the states do. And the reason this is such a fatal flaw in the visual argument is that the dispersion of voters isn't uniform across the various counties in a state. Have a look at the border areas of Texas and ask yourself if you'd have expected to see anything like their shade, anywhere near Texas. It's tempting to presume that we all share in the power of our government, but the bitter reality that Dr. Vanderbei is apparently unwilling to face is that the blue-hued voters along the Rio Grande are routinely disenfranchised by the will of the more densely concentrated Republicans in the redder counties of their state.

The upshot of all of this is, in a plurality-take-all model of electoral votes, the notion that individual counties can tell us anything by their shading is no less misguided than the idea that the popular vote can tell us anything, either. It's just plainly and simply not the way we pick our Presidents--and, accordingly, not a particularly compelling visual. As long as more people vote for George Bush than John Kerry in the state of Florida, the map of Florida can look as purple as it wants to, and the outcome will be the same.

Dave O'Gorman
("The Key Grip")
Gainesville, Florida

4 comments:

shabec said...

There you go again--Kerry got more votes in FL (and Ohio) but in both states the election was stolen. When you add in that larceny, the man's map is even more garbage!
How about that huge county in MN, that is very blue. I can't think of an explanation for that. How is it looking for Franken, by the way?

Calvin and Hobbes said...

As of now, Franken trails by 206 votes. You can refresh this link to get updates.

I have no idea where they are in counting mail-in and absentee ballots, but I think they might be done. The recount has not yet started.

According to Political Wire, Begich in AK has a 3 vote lead with many thousands of votes left to count, however he's already made up a 3000 vote deficit in one day of counting, so *fingers crossed*...

Robert Vanderbei said...

David:

It seems to me that we are half in agreement. I agree with your statements about county level data being rather irrelevant (at least if they are painted pure red or pure blue). In fact, that is exactly why I made the first Purple America map after the 2000 election. But, I disagree with your claim that purple looks more like blue than red. In a rainbow, the color to the "left" of blue is indigo, not purple. Purple does not appear in such a spectrum because purple is a 50-50 mix of red and blue. If that looks more bluish than reddish on your computer screen, then I think your screen is not calibrated properly. Of course, there's not much I can do about that. Anyway, I explain these things in greater detail in
http://orfe.princeton.edu/~rvdb/tex/elections/elections.pdf


Also, not sure if you've seen this year's maps...

http://www.princeton.edu/~rvdb/JAVA/election2008/

The Key Grip said...

The hypothesis that purple looks subjectively more blue than red is easily tested: all one would have to do is explain the metric to a man on the street and then show that person an un-labeled copy of the 1988 election. I've got a steak dinner that says they'd predict Democratic victory, which would be the end of this business about my computer monitor being out of adjustment or some-such.

The color prism, last time I checked, runs "red, orange, yellow, green, blue, indigo, and violet." Depending on whether we consider purple to be indigo or violet, my assertion is that the purple of these maps is being processed as either on the wrong side of blue or *way* on the wrong side of blue, and is thus skewing the implicit interpretation of the maps.

Second, the "pure red or pure blue / purple" distinction in county coloring is not germane to my challenge on the question of whether shading by counties is itself an informative exercise: Yes, a county shaded pure blue because it received one more vote for the Democrat is a misrepresentation of the influence that county had in the election, of course -- because it conceals that county's contribution to the other candidate's statewide total. We are in agreement about that much; it just happens not to be relevant to the objection I've raised.

My argument is that a mostly blue shading of a sparsely populated county in a ruby-red state (for example) is *equally* misleading, since the population of the counties isn't visible on the map. Since we don't elect Presidents by "one county one vote," any map that shows returns by county is only as informative as that lack of context, which I would argue should be explicitly disclaimed at the bottom of the map, will allow.