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Is Los Angeles really the densest city in the US?

It’s common to compare cities by their average density, but it leaves out a lot of useful information. The US Census Bureau’s new data on population-weighted density suggests a better way.

It seems counter-intuitive to most people who’ve been there, but it’s now almost a truism that Los Angeles is the densest city in the US.

According to a paper by Stone and Mees (gated, but I’ve summarised the salient bit here), urbanised Los Angeles is considerably denser than urbanised New York. Indeed, even Sydney is as dense as New York and Melbourne is denser than Chicago.

That might sound strange, but Stone and Mees aren’t wrong. It depends on how density is measured.

The US Census Bureau released a new report this week that helps make sense of the confusion. It distinguishes between the average density and population-weighted density (PWD) of cities.

Average density is straightforward and familiar. It’s the total area of a city divided by its total population (although there are different definitions of some parameters, such as where a city begins and ends). It’s what Stone and Mees use.

PWD, on the other hand, breaks the city up into convenient geographical units like suburbs. It ‘weights’ (multiplies) the density of each suburb by its share of the city’s total population. It gives equal weight to each person rather than each sq km.

Thus the density of a one sq km suburb with 10,000 residents (say) contributes a lot more to the final score than the density of another one sq km suburb with only 1,000 residents. The average density of these two suburbs combined is 5,500, but the PWD is 9,181.

Using 2010 data, the Census Bureau says New York has a slightly higher average density than Los Angeles (it uses different boundaries to the Stone and Mees paper). But when measured by PWD, New York turns the tables decisively – it is two and a half times denser than Los Angeles.

PWD gives due recognition to the large proportion of New York residents who live in the dense core e.g. Manhattan, Brooklyn. Although the outer suburbs are also quite populous, their low density means they contribute considerably less to the final PWD score than they do when average density is measured.

Using PWD, the four densest major cities in the US according to the Bureau are, in order, New York, San Francisco, Los Angeles and Chicago. Los Angeles is still near the top and is much the same density as San Francisco, but both are way behind New York and well ahead of Chicago.

The Census Bureau’s report only shows the four densest major cities. When I discussed PWD about a year and half ago (Does density matter for mode share?), the data I cited used a larger number of cities (see second exhibit).

This data isn’t comparable with the Census Bureau’s data set (different boundaries again and it’s for 2000) but it helps to illustrate the difference between the two ways of calculating density. Moreover it uses superior units (urbanised areas) to the Census Bureau’s metropolitan areas. The rank order of the top four cities when measured by PWD is the same in both sets, though.

Weighted vs average density, selected US cities, 2000 (source: Chris Bradford)

As I noted in my earlier post, relatively sprawling cities like Denver, Phoenix, Houston, Riverside and Portland all rank higher on average density than on PWD. Conversely, cities with relatively dense cores like Chicago, Philadelphia and Boston rank higher on PWD.

The ‘distance’ between cities is also very different on the two measures. The top ranked city is only 1% denser than the second ranked city when average density is used and four times as dense as the bottom ranked city.

However there are much bigger differences when density is measured by PWD. Top ranked New York is two thirds denser than second ranked San Francisco and eight times as dense as sprawling Atlanta.

Stone and Mees argue there’s only a small positive correlation between city density and public transport mode share. They use average density, however, so I’m not persuaded they’re right. I’d like to see the same analysis done using PWD.

I’ve previously discussed a paper that does just that for 30 US cities. It establishes there’s a stronger relationship than Stone and Mees find, but even so it’s not especially strong. It’s an important paper in the context of this discussion so I’ll revisit it shortly as a follow-up to this post.

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  • 1
    IkaInk
    Posted October 17, 2012 at 12:21 pm | Permalink

    Alan, it’s probably a simple mistake, but the link you’ve provided that implies you will lead to the Stone and Mees paper actually just links to another post you’ve written where the paper is mentioned (which is linked to again lower down). That post also doesn’t link to the Stone and Mees paper, but once again links to another post you’ve written that mentions it. Finally this third post links to the paper, but doesn’t mention its behind a pay-wall. A link directly to it, and a mention of the paywall would be nice.

  • 2
    Alan Davies
    Posted October 17, 2012 at 1:33 pm | Permalink

    IkaInk #1:

    Thanks, fixed. It shits me that Australian academics don’t make copies of their papers easily available as “working papers” as many US academics do.

  • 3
    Russ
    Posted October 17, 2012 at 5:36 pm | Permalink

    IkaInk, by the by, but since you are in Victoria, it is worth mentioning that the State Library carries most major journals and can be accessed electronically, once you have joined. A quick look shows that is true of most other states too, although your mileage might vary. Given the outrageous cost of journal subscriptions, the general public ought to make better use of them.

  • 4
    Dylan Nicholson
    Posted October 17, 2012 at 7:10 pm | Permalink

    For most purposes, what matters is that you have a critical mass of people living within a given contiguous area at a certain density – not what the arbitrary ‘city limits’ are. Manhattan and Brooklyn combined have over 4 million people living at roughly 20,000/km2, whereas the city of LA has a bit less than that living at 3,000/km2. If you compare all 5 boroughs (>8 million at well over 10,000/km2) with LA+Orange County (just under 8 million at about 3,000/km2), the comparison is a little less stark, but either way I don’t think it makes any sense to consider LA even in the same league.

  • 5
    Dylan Nicholson
    Posted October 17, 2012 at 7:17 pm | Permalink

    And for reference, Melbourne’s ~4 million live at about 1500/km2. In reality there IS no critical mass of Melbournians living at a high enough density to make it an interesting comparison to the genuinely major cities of the world – even the ~40000 living in the City of Melbourne are only at about 2400/km2.

  • 6
    Dylan Nicholson
    Posted October 17, 2012 at 7:20 pm | Permalink

    …whereas the 2.2 million residents of the City of Chicago are at 4400/km2, so I’d say it’s meaningless to claim Greater Melbourne is denser than Greater Chicago.

  • 7
    Alan Davies
    Posted October 17, 2012 at 8:15 pm | Permalink

    Dylan Nicholson #4,5,6:

    LA might not be in the same league as NY, but even on the more expansive boundaries used by the Census Bureau (compared to what you’re using), it’s still the third densest major city in the US, measured by PWD.

    City limits do matter though (and so the sub units), even with PWD. For example, the US Census bureau finds the degree of Concentration (PWD/AD) for NY is 6.3, but Chris Bradford’s data set shows it as 2.8. Gary Barnes’ figure is 4.7. The assumptions matter.

    Stone and Mees show the average density of urbanised Melbourne is denser than urbanised Chicago. So what you’re really saying with your Melbourne/Chicago comparison is that average density is a meaningless measure.

  • 8
    Dylan Nicholson
    Posted October 18, 2012 at 9:44 am | Permalink

    I’m saying as far as any meaningful discussion about the pros/cons of having a large number of people living at a certain density, the city limits are largely irrelevant (though they may have a political impact).
    Comparing average density over too large an area is the problem, especially if those areas contain significant sub-sections of extreme low density (e.g. I’m reasonably familiar with greater Boston, which is practically semi-rural for much of it, but the core is clearly a much denser and more significant concentration of people than any Australian city has. I suspect Greater Chicago may be much the same. Greater LA is more consistently populated through-out, though of course much of the Hollywood hills area is pretty sparse.)

  • 9
    Dylan Nicholson
    Posted October 18, 2012 at 9:55 am | Permalink

    Actually this map of LA country broken up into cities shows the difficulty of trying to measure what and what isn’t “Los Angeles”!

    http://www.laalmanac.com/geography/ge30ba.htm

    It’d be interesting to see the city boundaries for Orange County on that map too, as its clearly part of the greater LA metropolitan area, whereas the other counties to the north and east are not really urban, except the western part of San Bernadino.

    You do have to wonder the history behind such bizarre boundaries…

  • 10
    Dylan Nicholson
    Posted October 18, 2012 at 11:07 am | Permalink

    Just wasted far too much time trying to back up my claims about Boston – I wanted to see how it compared to Chicago, but the “Greater Boston” area of ~4 million residents really includes far too much semi-rural sections, and it’s almost impossible to find out what density the central ~2 million live at. However the central 1 million (from all of Suffolk County, plus a number of bordering cities, including Cambridge and Quincy from surrounding counties) seem to be at about 3700/km2.
    In contrast the 1 million of us living in the 9 densest LGAs in Melbourne are at about 2700/km2, so not as dramatically different as a I first thought.

  • 11
    Dylan Nicholson
    Posted October 18, 2012 at 11:30 am | Permalink

    BTW I’d have to say, if I knew that we had a real vision and commitment to ensuring that much of Melbourne’s population growth in the next 10-20 years was to be concentrated in the inner area, to the point we build up that critical mass of ~2 million people at around 4000/km2, I’d actually be quite excited about the sort of changes that would bring. Sadly I suspect it will be mostly the same sort of poorly thought-out sprawl that we’ve seen for the previous 20 years.

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