Crowds hold a predictive power that can have startling accuracy.
The Wisdom of the Crowds
Published April 24, 2018
Narrator: In theory, these crowds hold a predictive power that can have startling accuracy, but it doesn't belong to any individual, only the group. And even then, it has to be viewed through the lens of mathematics. The theory is known as the "wisdom of crowds," a phenomenon first documented about a hundred years ago.
Statistician Talithia Williams is here to see if the theory checks out and to spend some time with the Fair's most beloved animal, Patches, a 14-year-old ox.
Talithia Williams: It was a fair, kind of like this one, where, in 1906, Sir Francis Galton came across a contest where you had to guess the weight of an ox, like Patches, you see here behind me.
Narrator: After the ox weight-guessing contest was over, Galton took all the entries home and analyzed them statistically. To his surprise, while none of the individual guesses were correct, the average of all the guesses was off by less than one percent. That's the wisdom of crowds.
But is it still true?
Talithia Williams: So, here's how I think we can test that today. What if we ask a random sample of people, here at the fair, if they can guess how many jellybeans they think are in the jar, and then we take those numbers and average them and see if that's actually close to the true number of jellybeans?
Guess how many jellybeans are in here.
Come on, guys. Everybody's got to have their guess.
I see your mind churning.
Fair Goer 1: Twelve-twenty-seven.
Fair Goer 2: Eight-forty-six.
Fair Goer 3: Probably, like 925?
Fair Goer 4: I think 1,000.
Talithia Williams: So, just write your number down. Uh huh, there you go.
Child at the Fair: Can I have a jellybean?
Narrator: The 135 guesses gathered from the crowd vary wildly.
Talithia Williams: The range of our guesses was from…the smallest was 183, the largest was 12,000. So, you can tell, folks were really guessing.
But when we take the average of our guesses, we get 1,522. So, the question is, how close is our average to the actual number of jellybeans? Well, now's the moment of truth.
All right, so the real number of jellybeans was 1,676. The average of our guesses was off by less than 10 percent, so there actually was some wisdom in our crowd.
Narrator: Though off by about 10 percent, the average of the crowd's estimates was still more accurate than the vast majority of the individual guesses. Even so, the wisdom of crowds does have limits. It can be easily undermined by outside influences and tends to work best on questions with clear answers, like a number.
The steps Talithia took reflect a process going on all around us these days in the work of statisticians.
Talithia Williams: Thanks everybody.
So, we collected this data, right? We analyzed it mathematically, and we got an estimate that was pretty close to the actual true value. That's math and statistics at work.
- PREDICTION BY THE NUMBERS
- Written, Produced, and Directed by
- Daniel McCabe
- Executive Producer
- Chris Schmidt
- Cara Feinberg
- © WGBH Educational Foundation 2018