30 June 2010

How not to visualize the electoral college

I went to the National Constitution Center in Philadelphia today.

As you may know, the Constitution provides that, in elections for the President, each state receives a number of electors equal to its total number of senators and representatives. Each state has two senators, and the number of representatives is proportional to the population. The number of representatives is adjusted after the census, which happens in years divisible by ten.

Why am I telling you this? Because at one point on the wall there was an animated map, which displayed how apportionment had changed between censuses. Each state was represented as a "cylinder", with base the state itself and height proportional to its number of electors. (Or representatives; it honestly would be impossible to tell the difference by eye, as in this scheme that would just push everything up by two units.) There was one such display in the animation for each census, with smooth transitions between them.

Since the eye wants to interpret the "volume" of a state as its number of electors, this has the effect of making geographically-large states look like they have better representation than they do. I noticed this by looking at New Jersey and Pennsylvania, which have areas of 7417 and 44817 square miles, and 15 and 21 electors respectively. The solid corresponding to Pennsylvania has about eight times the volume as that corresponding to New Jersey. New Jersey's an easy one to look at because it happens to be the most densely populated state at the present time, and in this visualization it is not the tallest.

The volume of the solid corresponding to each state is proportional to the product of its number of its electors and its area. The states for which this product is largest are, in order, Texas, California, Alaska, New York, Florida, Illinois, Arizona, Michigan, Pennsylvania, and Colorado. The first two of these, between them, have 41% of the total volume in this visualization.

I'd suggest replacing this with a model where volume is proportional to the number of electoral votes. Or, since that might have its own problems, a cartogram which evolves in time. The West would just grow out of nowhere.

3 comments:

unapologetic said...

Oh yeah, yearly steps between cartogram frames (data samples only every 10 frames recently), with actual geographic points matched up to guide the evolution and I'll bet you could get a really smooth animation. I'd love to see that.

CarlBrannen said...

Sort of related, you should write a post on the R2K polling lawsuit:

Charles Siegel said...

Not time evolving, but here's a cartogram for the 2008 election: http://www-personal.umich.edu/~mejn/election/2008/stateelecredblue1024.png

I'd definitely like to see a time-evolving one, too, though.