What happened at the Plymouth livestock fair
Francis Galton, an English scientist, had little respect for the judgment of the majority. At the fair, there was a prize contest: guess the bull's weight after butchering, and whoever came closest won. Each person wrote their guess on a numbered ticket. A few weeks later, Galton asked the organizers for the tickets: a handy chance to test what the voice of the people was worth.
There were about 800 tickets. He discarded 13 as spoiled, leaving 787. Galton arranged the guesses in ascending order and took the middle one: 1207 pounds. The actual carcass weight was 1198, about 543 kilograms. Less than 1% off.
- BeforeGalton is convinced that the majority's judgment is worth little
- 1906Plymouth livestock fair: hundreds of people write down an estimate on a ticket
- 1907A note in Nature: the middle of 787 answers is 1207 versus the actual 1198
- LaterThe average from the same table is 1197, 1 pound below the truth
The accurate answer came not from anyone's guess, but from their middle. Individual estimates varied widely: some were hundreds of pounds too low, others just as high. The right number wasn't in anyone's head - it appeared when the tickets were put together.
The mechanism is simple. When estimating weight by eye, each person makes errors in her own way: one compares the bull to a familiar cow, another is thrown off by the angle, a third rounds up. These errors are personal, not shared, so in a group they pull in different directions and cancel each other out. What remains is what everyone had in common - the live bull in front of them.
The result, I think, is more creditable to the trustworthiness of a democratic judgment than might have been expected.
When crowd averaging stops working
A crowd doesn't guess anything by itself: it's not people that get averaged, but their errors. For those errors to cancel out, people need to be wrong in different ways and separately. In Plymouth, the conditions happened to line up well, and it wasn't about the number of heads.
- On your ownPeople write down guesses silently, without seeing anyone else's. As soon as answers become audible, people start adjusting to each other.
- Different experienceA butcher, a farmer, and a random onlooker make different mistakes; similar people bring the same bias.
- Something to go onThe bull stood right in front of everyone. Without an anchor, you're averaging fantasies, not estimates.
- Actually count answersAn argument in a room isn't averaging: the most confident person wins.
Usually, the first point is what breaks down. In experiments where participants saw their neighbors' estimates, the range of answers quickly narrowed: the group converged on one number and believed in it more strongly than before, but did not get closer to the truth. Another way to ruin it is with a shared error: if everyone is convinced in advance that the bull is heavier than it looks, the middle will shift along with everyone else.
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Sources
- F. Galton. Vox Populi. Nature, 1907
- the average from the same table was calculated by a journal reader in a reply letter, and the data were recalculated by K. Wallis in 2014. On the narrowing of variation under mutual influence - Lorenz et al., PNAS, 2011