When does a crowd actually know the answer?

Picture Plymouth, 1906, the West of England Fat Stock and Poultry Exhibition. A showground fills with pens and sawdust, and at the center of it stands one ox, already slaughtered and dressed for market. A scientist named Francis Galton, already well known for a life spent measuring things most people never thought to measure, watches the crowd file past a table near the entrance. Anyone can write a guess of the ox’s dressed weight on a ticket and drop it in a box. Farmers guess. Butchers guess. So do the clerks and the passersby who have never priced a carcass in their life. Each person writes alone, seals a private answer, and moves on.

Galton collected the tickets once the fair closed, weeded out thirteen that were illegible, and sat down with 787 usable guesses. He sorted them low to high and took the middle one: 1,207 pounds. Then he checked it against the butcher’s scale. The ox’s real dressed weight: 1,198 pounds. Nine pounds off. In Galton’s own words, published in Nature that week, the vox populi was in this case 9 lb., or 0.8 per cent. of the whole weight too high. Seven hundred and eighty-seven strangers, none of them consulting any of the others, landed within one percent of a number none of them could have looked up.

(A footnote, since this story gets retold wrong almost as often as it gets retold at all. That first note in Nature reported the median, 1,207, because Galton’s real subject that week was democratic judgment: one voice, one vote, no voice weighted twice. The mean of the same 787 guesses waited three weeks to appear, surfacing only in a follow-up letter answering a reader’s question, and it landed even closer: 1,197 pounds, a single pound off the true weight. A 2014 statistical reanalysis, published in the journal Statistical Science, found small errors in Galton’s own published arithmetic. Corrected, the mean lines up with the true weight exactly.)

Sit with why this worked, because the reason is the whole argument. Ask 787 people to guess a weight, and every single one of them is wrong. One farmer eyes the shoulders and guesses heavy. A butcher prices it like a leaner breed and guesses light. A clerk with no feel for cattle at all guesses by a hunch and a glance. Each error comes from a different cause: a different eye, a different memory, a different private guess at how this ox compares to the last one they saw. Laid side by side, those errors point in every direction at once. Average all 787 of them and the parts that are only noise start to cancel, guess against guess, while the part everyone was actually looking at, one real ox, standing right there, is the part that survives the arithmetic.

James Surowiecki named the requirement in 2004, in a book that opens with this very story: The Wisdom of Crowds. He listed four conditions a crowd needs before its combined answer earns any trust. Diversity of opinion, first: each person should have private information even if it is just an eccentric interpretation of the known facts. Independence, second, the condition that carries the other three: people’s opinions are not determined by the opinions of those around them. Decentralization, third, so a farmer’s feel for livestock and a butcher’s feel for a carcass can each contribute what the other one lacks. Aggregation, fourth: some plain mechanism for turning 787 private judgments into one collective number, which in Galton’s case was a box of tickets and an afternoon spent sorting them by hand.

Independence is doing more work than the other three combined. Diversity supplies different errors to cancel. Decentralization supplies local knowledge nobody else in the room has. Strip out independence, though, and the whole cancellation trick collapses: the crowd stops contributing 787 separate observations and starts repeating one observation 787 times, with small cosmetic variations. Watch what that looks like.

Below sit two dozen of those guesses, drawn as ticks on a weight axis. Left alone to reason independently, the way the real fair worked, they land where you would expect. Flip the toggle, and the same crowd starts copying whoever guessed first instead.

Notice the trade the crowd just made. Independent, the ticks scatter wide and messy, no two guesses alike, and their center still lands almost exactly on the true weight. Copying, the scatter tightens into something that looks like consensus, confident and unanimous. That tighter cluster is also the one sitting further from the true weight. The agreement tightened even as the accuracy slipped the other way.

The toy crowd on that axis is a fair picture of a real experiment. In 2011, a team led by Jan Lorenz ran 144 people through five rounds of estimating real-world quantities, and in some rounds let each person see what everyone else had just guessed before answering again, published in the Proceedings of the National Academy of Sciences. Seeing the other numbers changed the group in three separate, measured ways. The team called the first the social influence effect: it pulled every private guess a little closer to the group’s number, shrinking the spread of opinion while the group’s actual error sat exactly where it started. They called the second the range reduction effect: it pushed the true answer toward the outer edge of the shrunken range, making the crowd less reliable exactly when it looked most unified. They called the third the confidence effect: people felt surer of their own guess the moment it started resembling everyone else’s, even though the guess itself had grown no more accurate. The feeling of agreement read as knowledge landing. What had actually landed was contagion, and it moved no one any closer to the answer.

Surowiecki’s own book ties this pattern straight to bubbles. The more influence a group’s members exert on each other, and the more personal contact they have with each other, the less likely it is that the group’s decisions will be wise ones, he wrote. In a bubble, all of the conditions that make groups intelligent - independence, diversity, private judgement - disappear, replaced by what he called a sort of single-mindedness.

The clearest modern case runs on real numbers instead of folklore. Between January 1995 and its peak, the NASDAQ Composite rose roughly 600 percent, closing at an all-time high of 5,048.62 on March 10, 2000, a climb carried by millions of investors reading the same headlines, watching the same rising line, and buying because the price was already rising: exactly the copy-the-leader cascade the ticks on that axis just showed you. By October 2002 the index had fallen roughly 78 percent from its peak, giving back the entire run. It took until April 2015, thirteen years later, to close above that old high again. Every one of those investors could give you their own private reason for buying. Together, they were 787 tickets that had all read each other’s number before writing down their own.