From the Comments: Relative Weighted Average Densities

Not too long ago, I disputed some density calculations used by Wendell Cox and cited in the NY Sun’s Culture of Congestion blog. Cox and CoC were using Census density figures, which showed that Los Angeles, counterintuitively, is more dense than New York. In response, I wrote:

But as I wrote before, and as Sandy Ikeda completely ignored, this doesn’t particularly matter. Average density is a foolish measure to use here. The New York core is far, far denser than Los Angeles’, and the only reason LA comes out ahead is because its suburbs are geographically constrained by topography and are therefore denser than New York’s distant exurbs. No one in their right mind would visit New York City and come away thinking it was less dense than LA. That’s because it isn’t, not in any meaningful sense.

Los Angeles is hemmed in by its geography, so it can’t just keep spreading at ever lower densities out into the wilderness. As such, its density profile is like a plateau–not all that tall at anyone point, but with a respectable average height, because the long tails are excised. New York, by contrast, is like a mountain. It has an enormous peak containing most of the mass, but the flattening sides of the mountain continue on for miles.

In other words, the fact that the last million or so people in the New York metro area occupy an incredibly large area while the last million or so Angelenos are in moderate density suburbs packed against the very edge of the basin, skews the relative density figures, making them pretty uninformative.

The solution is to calculate a weighted average density. In other words, you break up the Metro area into smaller pieces (like Census tracts) and average the densities of each tract, weighted by the population of each tract. This adjusts the total average density to reflect how tightly packed most of the people are; that is, it is a truer statement about the average density at which any given resident of the Metro area lives.

This seems like the kind of thing that could be very onerous to calculate. Happily, reader Austin Contrarian, who first suggested using weighted averages in comments here, has done the hard work:

I’ve calculated “weighted averages” for NY and LA using census data. The census department breaks down a metropolitan area into various “central places,” and gives the population and density for each. It lumps everyone else into the “not in central place category,” and gives the density for this population.

Using this data, I calculated weighted average density using the formula described in my second comment. I got:

LA: 7,960
NY: 14,786

I.e., NY is almost twice as dense under this method, something we all intuitively know.

By comparison, the Census Department lists these as the average densities for the metropolitan area:

LA: 7,068
NY: 5,309

Note that LA’s weighted density is not much greater than it’s MSA-wide average density.
I’m preparing a post on my blog with data for different cities, along with a more detailed description and justification of this methodology.

Many thanks, AC.