In one of my previous incarnations I was a statistician of sorts. More precisely, I was one of two Statistical Process Control Coordinators for a major Compact Disc manufacturer. What Statistical Process Control
is, and why it is at once beautiful, powerful, effective, and woefully ignored, is a story for another time.
It was during this time that I became acquainted with Edward R. Tufte's book The Visual Display of Quantitative Information
. This book is also beautiful, powerful, and effective. Humans are animals who depend primarily on our sense of sight, and we would do well to understand how information can best be presented by visual means. More people should be familiar with this book.
By now most people in the U.S. have seen maps of the Red State/Blue State division that developed during the 2004 U.S. Presidential election. Most people can tell you whether they live in a Red or Blue State, and many arguments have sprung up over why Blue States are intellectually superior to Red States, or why Red States are morally superior to Blue States.
The U.S. Electoral system is based on (in almost all states) a winner-take-all approach: whichever candidate gets the most votes in a given state gets all of that state's Electoral votes. The Electoral votes for each state
are equal to the number of Senators and Representatives that state has in the U.S. Congress. The number of Representatives will vary based on a state population census taken every 10 years, but the number of Senators is fixed at two for each state. The Electoral system therefore gives a statistical advantage to less-populous states, in that their Electoral strength will be out of proportion to their actual share of the total population - which is one of the reasons why a candidate can win the Electoral vote even when the other candidate wins the popular vote. (See here
for a good example of the disproportionality: California has a voting-age population 66 times greater than Wyoming, but has an Electoral strength only 18 times greater. Each Electoral vote in Wyoming represents 123,333 voters, while each Electoral vote in California represents 443,636 voters.)
But more importantly from a visual representation of data point of view, there is a lack of geographical proportion on the map of the United States. Larger states are not necessarily more heavily populated. Utah is more than twice the size of Pennsylvania, but does not have twice the population. But on Election night, Utah was colored solid red, and Pennsylvania was solid blue. The visual message was: big state red, small state blue. Red bigger than blue.
For someone looking at the Red State/Blue State map of the U.S., the visual message is: What a blowout. There are a lot more Red States than Blue States. How can anyone think this election was close?
But the reality is, it was
close. And the divisions between Red and Blue are a lot blurrier than most people realize.Robert J. Vanderbei
of Princeton University has created the "Purple Map
" of the U.S. popular vote, a map that gives a county-by-county breakdown of the U.S. color-coded along a continuous scale from all-red (100% Bush) to all-blue (100% Kerry). Unsurprisingly, most counties come out as some shade of purple, and much of the Red/Blue distinction starts to fade.
While the Purple map of the popular vote helps to dispel the Red/Blue illusion of the winner-take-all approach (which is, however, reality when it comes to how the Electoral votes are counted), it does not address the geographical illusion. A large, sparsely-populated county will have a disproportionately greater visual impact than a more densely-populated county that is somewhat smaller.Michael Gastner, Cosma Shalizi, and Mark Newman of the University of Michigan
built on Robert Vanderbei's work and presented the popular vote data on a map called a "population cartogram", which allocates area based on population. Their analysis is worth taking a look. Go on. Look here
. I promise we'll wait for you.
On a county-by-county level, a county with a large population will appear larger on a population cartogram than a county with a smaller population, regardless of the actual geographical size of each county. When the county-level "Purple Map" is combined with the county-level population cartogram, a much more visually meaningful representation of the popular vote results. Now the map resembles the side of a volcano, with islands of cool blue rock surrounded by flows of hot lava. An analysis of the blue rocks and red flows will yield far more insight into voting patterns than do the Red State/Blue State maps.
Thanks to Vanderbei, Gastner, Shalizi, Newman, and others, we can see beyond the Red and the Blue and watch as much of the perceived disunity throughout the country fades to purple.Also thanks to President Bongo and Jerry, two commentors over at Adam Felber's Fanatical Apathy, for showing the way to these maps.