In the post about never calculating density for MSAs, I ended mentioning that the census report, after calculating densities for MSAs, switched to reporting population-weighted densities, which were more reasonable. This raises the issue of the choice of using population-weighted density versus plain old regular density, which for purposes of distinguishing in this post I will refer to as simple density.
Simple density is just the population (or count of something else) within some area, divided by the area. Population-weighted density takes the simple densities calculated for smaller subdivisions of the area (often census tracts) and calculates a weighted average of those densities, with the weighting by the populations of the tracts. While obviously related, simply density and population-weighted density are two different concepts. One cannot be considered better or an improvement on the other; they are different things.
It is easy to see how and why the two density values will differ. If the densities of all census tracts were identical, then population-weighted density would be the same as simple density. To the extent that people are more heavily concentrated in some tracts with higher densities than in others, those higher densities will be given more weight in calculating the population-weighted average and the population-weighted density will be greater than the simple density.
The advantage generally cited for using population-weighted density is that it is the average of the densities experienced by persons in the area within their neighborhoods (census tracts). And indeed, for some considerations of density, this makes sense. So what about simple density? It is very easy to show that simple density is equivalent to area-weighted density, the average densities of the tracts weighted by the areas of the tracts. (Areas cancel out to produce simple density). To the extent density is important in relation to the areas affected, simple density may be the logical choice.
Simple density is exactly that. It is well-understood. It raises few methodological issues. The one major problem when calculating densities of entire urban areas is that it is extremely sensitive to the extent of the area included. This is what makes it unreasonable to calculate simple densities for MSAs with varying and in some instances very large amounts of lightly-populated rural land included. (And this is why population-weighted density is more useful for such areas, because the densities of the less-populated areas are given little weight in the calculation of the total.)
Population-weighted density is a bit more complex than simple density, but it seems to be a reasonable, straightforward concept. But there are issues and choices that actually make things more involved than it may initially appear. First is the choice of the subareas for which the initial densities are calculated. I glossed over this when describing population-weighted density earlier, saying that census tracts were often used. If population-weighted density is the average density people in an area experience, then what is the smaller area within which that have this experience of density? The census reports data for census tracts, block groups, and blocks, from larger to smaller. Each could be used to calculate population-weighted density. The smaller the areas used, the larger will be the population-weighted density. And blocks can be aggregated into units of any size, offering a nearly infinite range of alternatives.
Next, census tracts (and the other areas) vary greatly in size across an urban area. Tracts are delineated to have populations that generally range from 1,200 to 8,000, with an optimal value of 4,000, according to the Census. This means that tracts can be very small in high-density areas and very large in low-density areas. Can we say that people experience density over a larger distance in low-density areas as opposed to high-density areas?
Since the tracts cover the entire area, nonresidential areas must be included within the boundaries of one or more tracts. This will affect tract densities, of course. Consider two identical neighborhoods, with exactly the same population and land area and, of course, density. It might be reasonable to conclude that the residents of the neighborhoods have the same experience of density. One neighborhood is designated as a census tract. The other neighborhood is adjacent to a nonresidential area which is included in its census tract, doubling its area and cutting its density in half.
Densities can and do vary within and between tracts. Some people within a tract, especially a spatially expansive tract, may have a very different experience of density than others. The experience of density of someone living near the boundary of a tract may depend nearly as much on the density of the adjacent tract.
All this is not to suggest that population-weighted density is not a useful concept. But it sure is a lot more complicated and raises many more issues than one might have thought initially.