The wisdom of crowds?

February 9, 2014

From the Seattle Times: 700,000 at Seahawks parade? Doesn’t add up, experts say.

It’s a lighthearted article, but it touches on the methodology of crowd estimation and uses some basic math to show that the number of parade attendees was less than the official estimate of 700,000.

How did readers respond to this dollop of evidence-based analysis? There were several themes, as exemplified by the following online quotes. (My interpretations are in brackets.)

(1) Semians: “Quit trying to overanalyze everything and simply live in the moment.” [We shouldn't care about this information.]

(2) picklesp: “It sure as heck felt like 700,000 from ground level.” [This information doesn't match my personal experience.]

(3) Peterkirk: “These guys are just trying to rain on our parade for whatever reason, and well tough, it didn’t rain on the parade on Wednesday and your diatribe (reporting?) isn’t going to make it rain today.” [This information doesn't make me feel good, so I'll ignore it.]

(4) Mr. Mytzlplk: “The ‘experts’ vary by 200,000 in their ‘real analysis.’ The fact that they’re so far off from each other tells me that they don’t know what they’re doing.” [Experts disagree about the details, so their analyses are worthless.]

(5) picklesp: “Experts get paid to pontificate.” [Experts have their own biases and agendas -- which is true.]

(6) gloryhound: “I’m also skeptical of these two ‘experts” qualifications.” [The "experts" aren't really experts.]

The above excerpts are from some of readers’ HIGHEST-rated comments. Here are two of the LOWEST-rated ones:

[from dawgsage:]

Actually 2.5 sq. ft /person is a square of almost 19 inches per side. Measuring the width of my body without a coat shows approximately 19 inches shoulder to shoulder, with a coat let’s add an inch making it 20 inches. A 2.5 square foot rectangle, with one side 20 inches would then require the other side to be 16.2 inches, from front to back. Conservatively, my measurement is 10 inches front to back. This means there would be 6.2 inches forward from my front to the back of the body of the person in front, and 6.2 inches in the back of me to the body of the next person, while laterally I am shoulder to shoulder to the adjacent people. So no I do not think it is not like standing in line, you really can’t get more crowded than that unless you were in an Iraqi prison under Saddam. So I believe the basis of the low estimates are credible.

[from CO Dawg:]

Rather than just say “well I don’t believe you!” to the experts, just do this simple experiment: put on a winter jacket (remember, it was cold that day) and stand against the wall with your arms against your side, then have someone mark the wall with chalk at your elbows. Measure that width. Then turn sideways and mark again the two widest points (belly and bottom for me, your points may vary). Measure that width.

Now, grab a calculator and multiply your personal width by personal depth. That is the square footage of space you occupy if you were standing in a crowd elbow to elbow belly to back and back to belly, like at a rock concert, and represents a good indication of the maximum crowd density at the parade.

When i did this with a sweatshirt on i came up with 2.1 feet wide and 1.25 feet deep, for 2.65 square feet, a little above the minimum cited. However, if i put on a winter jacket it adds an inch to all four sides so the measurements jump up to 2.25 by 1.42 feet, or 3.2 square feet. Adding just one more inch to each measurement increases my footprint to 3.8 square feet, and adding 3 inches increases it to 4.7 square feet. I wont presume anything about your personal space requirements, but when someone is 3 inches away from me, i still feel pretty crowded. I can thus conclude that the experts have presented a reasonable range for each person’s footprint

I have no means to measure the overall footprint of the crowd along the route, but had they asked me to do crowd estimates i would have employed the same methodology they use (measurements from an aerial photo), and probably would have come up with numbers similar to their’s. I would have multiplied the overall crowd foot print by an average space per person of 3.5 square feet (generally splitting the difference between my numbers), added 15% to account for people standing outside the footprint or watching from offices, and likely come up with a forecast of somewhere between 350-400k. Which is still a heck of a crowd.

And for those of you dismissing my opinion because of my location, we’re not immune to overly enthusiastic crowd estimates in Denver, too. I was at a presidential campaign speech in Civic Park that supposedly was attended by 100,000 people, and didnt even need to do the math to know that estimate was comically high.

So, to summarize: dismissal of the information for any old reason? Thumbs up! Attempts to check the math and verify its reasonableness? Thumbs down!

While no legislation hinges on this particular estimate, I’m troubled by the attitudes displayed here, i.e., limited interest in the nuances of data and relevant expertise. I submit that, in other arenas, this limited interest has led to the popularity of positions like “evolution is just a theory,” “vaccines cause autism,” “global warming is a hoax,” and “animal testing is unnecessary.”

In response, we scientists can grumpily bemoan an incurious public … or we can recognize that facts alone don’t always move the needle of public opinion, and we can get better at appealing to people’s emotions and imaginations.

comments from a data denialist

do the math!


  1. Greg,

    Interesting and not surprising, at least given my experience of a general lack of appreciation for nuance in argument and an inability for critical and non-linear thought even amongst a fair proportion of those who have been fortunate enough to receive a post-secondary “standard American education”.

    One origin of such attitudes is that we seem to be doing a poor job of teaching that science is really more about disagreement than agreement; that any field will have controversies and that “experts” will disagree, or have different interpretations of the same data. It is likely that if one were to look into the published literature on “crowd counting” that there is a rich theoretical basis for making estimates. This does not mean that the government entities are using any of this in their estimates. But I do know that there are approaches that should do a reasonable job of estimating “point counts” from digital HR satellite images, if available. This estimation protocol and associated analysis is well-developed and used by many industries and the government, including, likely, the NSA. A digital satellite image of a crowd and some closer view video of an actual crowd (to establish an estimated distribution of the ‘Brownian motion” of a typical crowd member allows for some quite accurate estimates of “points” (persons) within the image. Those reading the article may think, based upon what they have been taught, that there can be no disagreement unless someone is wrong. In this case I do think that the estimates are wrong but I am not sure what the origin of the error is since the methodology utilized was not fully disclosed.

    However, a basic issue with the treatment by the general public of “data” and “experts” in the example above is that in newspaper comment threads (and threads like this as well) anyone can comment, including those who have no basis for commenting. I have always been of the position that “not everyone is entitled to an opinion”, something that is generally considered anti-American and that has gotten me into trouble with more than one Senior VP of Research and/or CEO in large corporate America.

    A final point is that we, as scientists, seem to be too accommodating of “experts” who are not expert and often we do not take the time to discover this and uncover the hypocrisy. It is not easy and it is time consuming but it is our “garden” and we should be committed to “weeding” to ensure healthy growth……. in this case, I think that one might find that the quoted “experts” are not experts at all; they may be practitioners but not experts.

  2. Greg,

    I intended to leave a link to a TED Talk relevant here on numerous fronts:

    1. the “duty of care” on the part of the journalist who wrote the story
    2. the standards that we should all hold up and expect
    3. the importance of each “little” correction/clarification in the concatenated “whole” of any discourse

    Puttnam makes many points that surely ring true not just for the media, journalists, artists, and the viability of a secure democracy but for scientists as well in their day-to-day activities and in broader interaction with society.


    • Robert, thanks for the link. I hadn’t seen that before.

      I am very sympathetic to Puttman’s views, but I’m not sure that he is offering solutions per se. As newspapers struggle to survive financially, is it realistic or fair to declare that they should uphold lofty standards of conduct for everyone’s benefit — profits be damned?

      • Greg,

        I think one of Puttnam’s points is more of a warning about what can happen when profit is the primary purpose with reporting.

        Perhaps there is a business case for being a reliable source for information and analysis that is not subject to the vagaries of the wishes of the commercial entities that are advertising with your outlet? I think such a business case arises only if we, the consumers, expect such reporting. The extent to which we accept sub-standard articles and incomplete (or purposefully one-sided) reports will likely define the world we end up living in.

        Puttnam is rather polar, but I hope his appeal makes one think a bit more about how important it is, from international to national to regional to local issues. The basic journalistic standard of presenting analysis of an issue from as neutral a position as is attainable seems to be slipping away and being replaced by “position” pieces that do not do a good job of illuminating the nuance and complexity that is so important to good decision-making. Having such reporting further influenced by advertisers is not, in my mind, an acceptable situation, but one that is all too frequent today.

  3. […] friend and Seattle resident Greg Crowther notes that the crowd size at the Seattle Seahawks Superbowl victory parade was badly overestimated by the […]

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