The lack of wisdom of crowds?

Posted on by S. Abbas Raza

Erik B. Steiner in Wired:

Coinjar1A few weeks ago, I asked the internet to guess how many coins were in a huge jar. For more than 27 years, my parents had saved their spare change. My mother recently trucked the whole load to a bank to cash in, and in so doing finally learned the stockpile’s actual value, or at least the value as calculated by that particular coin-counting machine. The update from Mom got me wondering: Might someone be able to guess that amount? What about our collective estimate—is the crowd really as wise as some say it is?

The mathematical theory behind this kind of estimation game is apparently sound. That is, the mean of all the estimates will be uncannily close to the actual value, every time. James Surowiecki’s best-selling book, Wisdom of the Crowd, banks on this principle, and details several striking anecdotes of crowd accuracy. The most famous is a 1906 competition in Plymouth, England to guess the weight of an ox. As reported by Sir Francis Galton in a letter to Nature, no one guessed the actual weight of the ox, but the average of all 787 submitted guesses was exactly the beast’s actual weight.

Galton, who also happens to be the inventor of eugenics, was shocked to find such value in “democratic judgment.”

The notion that the hive is more intelligent than the individuals comprising it is a seductive one, and a keystone of today’s bottom-up Big Data revolution. It’s democratic ideology, open-source goodness, the “invisible hand,” and New Age humility all wrapped into a big networked hug.

But is it true?

More here. By the way, I was one of the people who took part in the experiment. Below are emails between Erik and me. I didn't do so good! 🙂

***

Dear Abbas,

By popular demand, here are your personalized coin jar contest results.

The actual value: $379.54
Your guess: $203.5
You were $176.04 off.

Your guess was closer than 68.3% of the participants.
Amongst people who 'actually did the math' your rank was 45/149.

I'd be interested in knowing how you actually did the math. There seems to be some discussion in the article comments about how difficult this task is – I'm honestly surprised people think it is so challenging.

Anyway, fun stuff, and thanks for participating.

regards,

erik

***

Hi Eric,

I assumed that the coins visibly identifiable in the photo (the ones with faces pressed against the glass) more or less represented the frequency of pennies, nickels ,dimes, and quarters in the whole jar, so I counted them, which gave me some percentages. (This may have been a flawed assumption for several reasons.)
Then I just tried to estimate visually how many coins seemed to be packed into a 1 cubic inch space. Then I estimated the total filled volume of the jar in cubic inches and multiplied it by the coins/cubic inch estimate to get a total number of coins.
Then I used the percentages of different coins to come up with a total dollar value. I was really hoping to be closer! 🙂
A very smart physicist I sent the problem to came up with $600+, so that makes me feel a little better.
Here's a little thing I wrote about estimating stuff some years ago, by the way:
All best,
Abbas