Commenting on our comparison of 1896 and 2000, Jonathan Rodden sent in this graph of Democratic vote share vs. population density in congressional districts from 1952-1996:

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.

P.S. I don’t like that the graphs go below 0 and above 1, but that’s probably a Stata default. I don’t hold it against Jonathan–after all, he made a graph for me for free–but I do think that better defaults are possible.

I'm not sure why you dislike the Y axis on these graphs. If you put 0 and 1 at the very extremes of the plot area, you can't really see points that actually lie at 0 or 1. Giving a little "data margin" by making 0-1 take up about 95 percent of the vertical space allows you to see all the points on equal footing. A point at 1 or at 0 is potentially an important point, putting it right at the boundary of the graph is a mistake in my opinion.

Now why some of the DATA is above 1 is a different question… see graph 1972 and 1984

Hmm, so this "hypothetical scenario" allows Democrats to get more than 100% of the vote (1984, possibly 1972).

Are those particular districts in Chicago by any chance?

This looks rather like a quadratic fit (see esp 1984) – how about something a little more flexible?

Right, this was a quick and dirty graph made at 2 AM. The quadratic fit was not a good choice; lowess would be better. The reason for values above 1 is that I applied a "uniform swing" to the districts in each year to evaluate hypothetical 50/50 elections. So in a couple of landslide victories for Republicans, the adjustment pushed an urban Democrat bailiwick above 1. Clearly not the best way to do this, but seemed ok at 2 AM. Also, 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.

Also data below 0 in 1964.

But yes, you can tune the y axis extent easily in Stata. And use other smooths than a quadratic fit, which does look too crude.

Congressional districts are gerrymandered and sometimes snake all over the map. Thus, it would be interesting to see this same population density vs. Republic vote graphs for something less artificial like counties, which generally originated to center around a population cluster.

Of course, counties differ wildly in population, so LA County with 10 million people and a county in Texas with 300 people really aren't the same, so the graph would be dominated by tiny Republican counties. Maybe you could make the population of the county proportional to the size of the dot?