On election night and in the days since then, we have seen many maps that look like this:

We can correct for this by making use of a cartogram, a map in which the sizes of states have been rescaled according to their population. That is, states are drawn with a size proportional not to their sheer topographic acreage -- which has little to do with politics -- but to the number of their inhabitants, states with more people appearing larger than states with fewer, regardless of their actual area on the ground. Thus, on such a map, the state of Rhode Island, with its 1.1 million inhabitants, would appear about twice the size of Wyoming, which has half a million, even though Wyoming has 60 times the acreage of Rhode Island.

Here are the 2004 presidential election results on a population cartogram of this type:

The cartogram reveals what we know already from the news: that the country was actually very evenly divided by the vote, rather than being dominated by one side or the other.

But we can go further. We can do the same thing also with the county-level election results and the images are even more striking. Here is a map of US counties, again colored red and blue to indicate Republican and Democratic majorities respectively:

Similar maps have appeared in the press, for example in USA Today, and have been used as evidence that the Republican party has wide support. Again, however, a cartogram gives a more accurate picture. Here is what the cartogram looks like for the county-level election returns:

Again, the blue areas are much magnified, and areas of blue and red are now nearly equal. However, there is in fact still more red than blue on this map, even after allowing for population sizes. Of course, we know that nationwide the percentages of voters voting for either candidate were almost identical, so what is going on here?

The answer seems to be that the amount of red on the map is skewed because there are a lot of counties in which only a slim majority voted Republican. One possible way to allow for this on a map, suggested by Robert Vanderbei at Princeton University, is to use not just two colors, red and blue, but instead to use red, blue, and shades of purple to indicate percentages of voters. Here is what the normal map looks like if you do this:

And here's what the cartogram looks like:

In this map, the red counties occupy only a rather small portion of the total area, most of the country appearing either in blue or in shades of purple.

© 2004 M. T. Gastner, C. R. Shalizi, and M. E. J. Newman