Jelly Beans

in Lifestyle Columns/The Science Column by

At a country fair in Plymouth in 1906, an unfortunate cow laid down his life for a place in mathematics history. The cow was a subject of a “guess-the-weight” competition, and the lucky person who came closest would win the slaughtered animal’s meat. The amazing thing was that nobody guessed it right, yet everybody got it right.

Statistician Francis Galton discovered this fact when the crowd’s individual guesses were totaled. The median guess of 1,207 pounds was accurate within 1 percent of the true weight of 1,198 pounds. Among 800 people who participated in the event from butlers to cattle experts, separate estimates made by these professionals were far off compared to the collective crowd’s wisdom.

The collective wisdom of the crowd simulates the estimation task of a sample from a probability distribution, inviting comparisons with individual cognition.The effect of statistical noise will ensure that two or more estimates of the same quantity will average to a value closer to the ground truth—and biased extreme values will average themselves out. Put simply, some people will overestimate while others will underestimate, and collectively, each member cancels out the error of the other. As a result, the group average estimation winds up being smarter than the sum of its parts.

We conducted a simulation here at SIS to see if this was true. During lunchtime, the crowd estimated the number of jellybeans in a jar in order to illustrate the power of collective wisdom. The guesses of 99 different students and faculty ranged from 200 to 16,000, but the average of all 99 guesses was 1,610 – only ten percent away from the actual value of 1,814.

Although the experimental data we collected were not as miraculous as those from previously known experiments, they still serve a point. Among 99 people who participated, there were only three people who were within range of 10 percent of actual number of jellybeans, and only one who got to the actual hundredth digits.

More than 75 percent of the people underestimated the number of jellybeans—as they seemed fearful to call out the number into thousands—but the extreme values on the right side of the axis successfully cancelled out the underestimations that the majority of people made.

It’s amazing to think that in a large enough group, the errors of everyone else, no matter how insignificant an individual may seem, can actually balance and correct our own shortcomings. It feels good, though a little bit strange to think that in a group, it’s possible for nobody to be correct, but for everybody to be right.

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