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A student asked me today, "How do they know how many people attended a large group event, for example, the Stewart/Colbert 'Rally to Restore Sanity' in Washington D.C.?" News outlets report estimates in the tens of thousands, but what methods are used to get those estimates, and how reliable are they?

One article apparently based their estimate on parking permits... but what other techniques do we have? Please note I am not talking about capture/recapture experiments or anything of the like.

I don't have any idea. I would guess in advance that there aren't specific methods for something like this, and whatever's there is very ad hoc (such as how many parking permits were sold). Is this true? For purposes of national security - of course - it would be possible to have an analyst sit down with satellite photographs and physically bean-count the number of people there. I doubt this method is used very often.

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You could also use other anecdotal evidence (e.g. amount of garbage generated compared to normal). – Shane Nov 1 '10 at 20:56
But Stewart specifically asked to leave the place cleaner then they got it :) – Tal Galili Nov 1 '10 at 21:13
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DC metro ridership might factor in. Also overflow from the mall, when they stopped letting people in, might place a minimum -- assuming one has reasonable historical estimates of how many fit in the mall. – ars Nov 1 '10 at 21:23
@Shane @ars yes, you are right. Now that you mention it, there should be other correlates running around, too, which may do a pretty good job of predicting crowd size. – G. Jay Kerns Nov 1 '10 at 22:26
The National Park Service is no longer providing these estimates, as they are always controversial. They used to do this estimate by taking aerial photographs of a suitably chosen (non-random I guess) well-defined set of patches of real estate on the National Mall, counting the number of people in each square, and estimating total attendance from it. Clearly the time and order of pictures matters and contributes to the bias, especially with a moving crowd. – Hans Engler Apr 15 '11 at 0:32
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8 Answers

up vote 11 down vote accepted

You could estimate the people per square meter (use a few areas, of at least a few square meters each to get a good estimate) and multiply this by the size of the area.

Here is an article on this topic: http://www.lifeslittlemysteries.com/how-is-crowd-size-estimated--1074/

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Thanks. This was essentially just what I was looking for. (I should have googled crowd size instead of population size, yours is there with a bunch of others). – G. Jay Kerns Nov 1 '10 at 22:31
up vote 7 down vote

As a follow up to this question (thanks to all for the answers), Significance magazine just published an article about this very question (it's the cover story, to boot): "How many were there when it mattered? Estimating the sizes of crowds." September 2011, volume 8, issue 3, pages 104-107, by Ray Watson and Paul Yip.

It looks like they are trying to post an electronic version at the link above, but it didn't work for me just now when I tried.

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up vote 3 down vote

Tim's linked article is great, though I think the company that counts people in grids is making it out to be easier than it really is.

In the local (DC) papers, I've seen quotes about Metro rider usage (except there were two other major events downtown the same day), attempts to count people at security checkpoints, grid square counting from aerial photos, quoting the numbers put on Park Service event applications, etc, none of which impress me in a large town with many things going on concurrently.

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Yes, I agree that it is a harder problem than many would like to admit. In fact, it's not even trivial to define what it means to "attend"; do we mean just stopping by for a second, staying all day long?, etc. I think the actual problem is too hard to solve exactly, and I am happy to hear about first order approximations. :-) – G. Jay Kerns Nov 1 '10 at 22:37
up vote 3 down vote

Mobile phone providers can count the number of phones in the area. Having an estimate of the mean number of phones/person good approximation can be calculated. This looks simple, so I assume it is in practice.

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This would be slightly disturbing, but also probably quite inaccurate. You need a signal from the phone to at least three towers to get even an approximate estimate of location, and with the blocking and reflection of radio waves caused by big buildings in cities, I'd imagine that those estimates would be pretty loose. If it's in the center of a city, with lots of other people around, this would be pretty useless. That said, the number of phones with GPS in them that phone home without notification is probably getting quite large by now... – naught101 Nov 23 '12 at 5:00
up vote 3 down vote

There are companies that specialize in counting people. For instance,

www.lynce.es

(I am not affiliated nor have any interest whatsoever in such company). They hung cameras over the groups they want to count, shoot pictures and actually count heads. They only make small adjustaments when it comes to estimate people under trees or other objects which prevent direct vision.

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up vote 1 down vote

Here's an idea (but I am not sure this could work in practice): place a free wifi access point, and count the number of connections ( of iPhones, blackbery...).

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@Uri, thanks, hadn't thought about that. – G. Jay Kerns Nov 1 '10 at 22:37
Cool idea, but how would you get an estimate of how many people have appropriate phones? – naught101 Nov 23 '12 at 5:01
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As an alternative to WiFi mentioned by Uri, you could place Bluetooth scanner(s) in 'strategic' locations of your venue. I've attended a presentation during MPA workshop about such development in Netherlands.

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up vote 0 down vote

A police officer told me once that they had rules of thumb to guesstimate attendance at demonstrations (don't ask me for specifics), probably based on what Tim said.

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Thanks, I had wondered how police make their guesstimates and if you ever run across that information I would appreciate your posting it back here, for the record. – G. Jay Kerns Nov 1 '10 at 22:32
Well, I asked, but he didn't remember. On a lighter note, Rob Hyndman has a story about the way headline numbers are arived at. Scroll down a bit on robjhyndman.com/researchtips/statistical-jokes – Owe Jessen Nov 3 '10 at 15:09

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