Vote and population density

Aleks sends along this graph:

The axis labels are at horrible positions—-the y-labels are at 0, 22.5, 45, 67.5, and 90??? instead of the obvious 0, 25, 50, 75, 100, and the x-axis is on some bizarre hybrid of linear and log scales—-also it’s not clear what the data are. Counties, I’d guess, but in that case you might as well plot the data along with everything else. Also I’d prefer one line rather than two: no big deal here but if you do want to augment the graph with raw data it would be best to have only one line.

The second line conveys no useful additional information but gives the graph an appealing Rorschach-like pattern that might be just what it takes to go viral. . . .

Anyway, I was reminded of this old graph of Democratic vote share vs. population density from Jonathan Rodden, who wrote, “I would like to see when this relationship developed, in which states, etc. My hunch is that suburbanization, especially after the race riots, significantly reduced the heterogeneity of cities. The era of Democrats winning 80 percent of the presidential vote in big cities seems fairly recent”:


As Jonathan noted, the pattern of high-density areas voting strongly Democratic is relatively new. (But I don’t buy the way his lines curve up on the left; I suspect that’s an unfortunate artifact of using quadratic fits rather than something like lowess or spline.) Also there seems to be some weird discretization going on in the population densities for the early years in his data. But the main trends in the graphs are clear.

Jonathan added the following comment: “The relatively high values on the left side of graphs in early years is due to Southern Democrats and some mining districts. Graphs of the UK, Australia, and Canada look very similar during the same period, with left voting concentrated in urban and mining districts.”

More details (and further graphs) here, also here.

5 Responses to Vote and population density

  1. MikeM December 6, 2012 at 7:47 pm #

    Some years ago Goodall, Kafadar & Tukey published an article (in American Statistician, I think) suggesting the use of what they called “urbanicity” instead of pop. density as a measure of county-level population concentration. The telling example is Clark County NV, which because of its large area was considered low-density, but the population was concentrated in the Las Vegas metro area.

  2. Jim December 7, 2012 at 11:27 am #

    I’ve always hated graphs that have two lines which are simply mirror images of one another. perhaps they seem more common in political science because of the strong two-party system, but they seem the visual equivalent of making a positive statement, then repeating it by stating it in negative terms:

    1. “Obama won because he captured an larger than normal percentage of the Hispanic vote.”
    2. “Romney lost because he failed to capture as much of the Hispanic vote as normal.”

    (I realize those are simplifications, just go with it.)

    The first statement is preferable, to me at least, but either would be okay. Both are unnecessary.

    • Andrew Gelman December 7, 2012 at 8:47 pm #


      I agree completely. But I think the symmetry is visually pleasing to many people.

  3. Janne December 11, 2012 at 7:30 am #

    But the lines aren’t really mirror images are they? You did have more than two candidates after all.

    • Andrew Gelman December 11, 2012 at 11:18 am #


      The lines do look like mirror images to me; it’s possible they were created using two-party vote shares. Even if not, the votes for minor parties are so small as to be essentially invisible. That’s why, above, I wrote, “The second line conveys no useful additional information.”