Ask one person to guess the weight of an ox, the number of murders recorded in a country last year, or the outcome of an election, and you will usually get a rough answer. Ask hundreds of people, combine their answers sensibly, and something odd often happens: the combined answer is better than most of the individual guesses, and sometimes better than the experts. This idea is called the "wisdom of crowds." It is one of the most useful and most misunderstood ideas in the social sciences.
It is useful because it explains why prediction markets, forecasting tournaments, citizen science projects and even honeybee swarms can produce good judgments without a single expert in charge. It is misunderstood because people often treat it as a law that says "the majority is always right." It is nothing of the kind. Crowds can be very wise, but only when certain conditions hold. When those conditions break, crowds can be confidently, collectively wrong.
This article explains where the idea came from, the simple statistics behind it, the conditions that make it work, the experiments that show how it fails, and the clever methods researchers have built to get better answers out of groups. Along the way it visits a country fair in England, a laboratory in Zurich, a government-funded forecasting contest, a galaxy-sorting website, and a small island off the coast of Maine where scientists watched bees choose a new home.
An old idea: from Aristotle to the country fair
The thought that a group can be wiser than its members is ancient. Aristotle is usually credited as the first writer to put it down, in his Politics. He argued that many ordinary people, taken together, may be collectively better than a few people who are each individually excellent.
The modern story usually starts with Sir Francis Galton, the Victorian scientist and statistician. In 1906 Galton visited a livestock fair in Plymouth, England, where visitors could pay to guess the weight of a slaughtered and dressed ox. About 800 people entered. Galton, who was interested in measuring human ability, collected the tickets afterward and analyzed them. He reported his findings in 1907 in the journal Nature under the title "Vox Populi" (Latin for "the voice of the people").
The result surprised him. The middle value of all the guesses, the median, was 1,207 pounds. The actual weight was 1,198 pounds. The crowd's median was within 1 percent of the truth. Individual guesses ranged high and low, but in combination their errors largely cancelled out.
Galton reported the median rather than the average, and that choice matters: the median is less affected by a few wild guesses. His title, "the voice of the people," also hints at the link between crowd statistics and democratic decision-making that has followed the idea ever since.
Condorcet's jury theorem: the math of majority votes
More than a century before Galton, the French mathematician and philosopher the Marquis de Condorcet worked out a related result for yes-or-no decisions. In 1785 he published an Essay on the Application of Analysis to the Probability of Majority Decisions. In it he described what is now called Condorcet's jury theorem.
The setup is simple. A group must choose between two options, and exactly one of them is correct. Each member votes independently, and each has the same probability, call it p, of picking the right answer. The group decides by majority vote.
Condorcet showed that if p is greater than one-half, so that each voter is at least a bit better than a coin flip, then adding more voters increases the chance that the majority is right. As the group grows very large, that chance approaches certainty.
But the theorem cuts both ways. If p is less than one-half, meaning each voter is more likely to be wrong than right, then adding voters makes the group worse. In that case a single voter is the best you can do, and a large crowd is almost guaranteed to be wrong.
That second half is often forgotten. It is why the theorem is a warning as much as a promise. The economist Bryan Caplan has argued that voters' beliefs on some economic questions are systematically biased toward wrong answers, which would put them on the wrong side of Condorcet's line. Later mathematicians have also relaxed the assumption that all voters are equally competent. A 2022 analysis by Romaniega Sancho found that when voters' competence levels are drawn at random, with no built-in tilt toward competence, the theorem's optimistic conclusion fails almost surely. The math, in other words, does not guarantee wise crowds. It tells you exactly what you need for one.
Why averaging works: a plain-English explanation
The statistics behind the wisdom of crowds can be explained without equations.
Imagine every guess as the true answer plus some error. One person guesses too high, another too low. If the errors are random, unrelated to each other, and not tilted in one direction, then when you combine many guesses the highs and lows tend to cancel. The more guesses you add, the more completely they cancel, and the closer the combined answer gets to the truth.
Two words in that explanation carry all the weight: "random" and "unrelated."
Random errors cancel; shared errors do not. If everyone in the crowd shares the same bias, averaging cannot remove it. Suppose every person at Galton's fair had been told the ox was unusually heavy. They would all guess high, and their average would be high too. Averaging removes noise, not systematic bias. The Wikipedia summary of the research puts it plainly: averaging can eliminate random errors but not errors that the whole crowd has in common.
Unrelated errors cancel; connected errors do not. If people's mistakes are linked, because they read the same newspaper, copied each other, or listened to the same loud voice, then their errors move together. A thousand people who all copied one guess are, in effect, one guess counted a thousand times.
There is also a practical lesson about how to combine answers. Galton used the median. Much later research found that for many kinds of estimates, especially those where answers can be wildly large, the ordinary arithmetic average performs badly because a few huge guesses drag it upward. In such cases the median, or the "geometric mean" (an average taken on a logarithmic scale), is usually the better tool. We will see a striking example of this in the Zurich experiment below.
Surowiecki's four conditions
The phrase "wisdom of crowds" became a household term with James Surowiecki's 2004 book The Wisdom of Crowds: Why the Many Are Smarter Than the Few, published by Doubleday. Surowiecki, a financial journalist, argued that aggregated group decisions can beat those of individual members and even experts, and he organized the idea around four conditions that a wise crowd needs.
- Diversity of opinion. Members should hold different private information, even if it is only their own eccentric reading of the facts. Different information produces different errors, and different errors are what cancel out.
- Independence. People's opinions should not be determined by the opinions of those around them. Once people start copying, errors become linked.
- Decentralization. People should be able to specialize and draw on local knowledge. A crowd whose members all see the same narrow slice of the world gains little from being large.
- Aggregation. There must be some mechanism, such as a vote, an average, or a market price, that turns private judgments into a collective decision.
Surowiecki also distinguished three kinds of problems crowds can tackle. Cognition problems have a right answer or a best estimate, such as a market judging the value of a company. Coordination problems involve people fitting their behavior together, such as drivers avoiding collisions or crowds deciding which café to visit. Cooperation problems involve building trust among self-interested people without central control.
Just as useful is his list of ways crowds go wrong. Homogeneity means too little variety in thinking. Centralization means decisions are made at the top while useful knowledge at the bottom is ignored; he pointed to the 2003 loss of the Space Shuttle Columbia, which he blamed partly on a hierarchical NASA bureaucracy that did not listen to lower-level engineers. Division means information is trapped in separate silos, a problem the 9/11 Commission Report described among American intelligence agencies. Imitation means people copy earlier choices, producing information cascades. Emotionality covers peer pressure, herd instinct and collective hysteria.
When crowds shine: prediction markets
One of the best-known practical uses of crowd wisdom is the prediction market. In a prediction market, people buy and sell contracts that pay off depending on whether some event happens, for example whether a candidate wins an election. The market price can then be read as the crowd's estimate of the probability of that event. Traders who think the price is too low buy; those who think it is too high sell. The price is the aggregation mechanism.
The longest-running academic example is the Iowa Electronic Markets (IEM), run by the University of Iowa's Tippie College of Business. It grew out of an earlier project, the Iowa Political Stock Market, developed by the economists George Neumann, Robert Forsythe and Forrest Nelson. The IEM is a not-for-profit, real-money market operated for teaching and research. Because of its academic purpose and tiny stakes, it operates under no-action letters from U.S. regulators rather than being regulated like a commercial exchange, and traders may only risk between $5 and $500.
How accurate has it been? A study by Joyce Berg and colleagues published in 2008 compared the IEM's prices with 964 election polls across the five U.S. presidential elections from 1988 to 2004. The market was closer to the final result than the polls 74 percent of the time. In the 2008 election the IEM predicted the final vote share to within about half a percentage point.
Prediction markets are not magic. They can be thin, with few traders; they can be swayed by people with money and strong opinions; and on some questions they have been badly wrong. But the IEM's track record shows that a crowd with something at stake, combining its views through prices, can rival professional polling.
When crowds shine: forecasting tournaments and "superforecasters"
A second success story comes from the world of intelligence analysis. In 2011 the U.S. Intelligence Advanced Research Projects Activity (IARPA) launched a program called Aggregative Contingent Estimation, or ACE. Its goal was to find better ways of forecasting world events by combining many people's predictions. Competing research teams were asked roughly 100 to 150 questions a year about geopolitical events, such as whether a particular country would hold an election or whether a conflict would escalate.
One of the teams was the Good Judgment Project, led by Philip Tetlock, Barbara Mellers and Don Moore of the University of Pennsylvania. It began in July 2011, and the first contest started that September. Instead of recruiting senior experts, the project gathered amateur volunteers, gave them short tutorials on forecasting, and trained them to recognize and counter common thinking errors. Forecasts were scored using Brier scores, a standard measure that rewards being both right and appropriately confident.
The project combined its forecasters' predictions with a custom algorithm, and it identified a small group of consistently excellent individuals it called "superforecasters." The Good Judgment Project won the tournament, beating other research teams by between 35 and 72 percent in accuracy. By the summer of 2013 it was the only team IARPA was still funding. Its top forecasters were reported to be about 30 percent more accurate than intelligence analysts who had access to classified information. A commercial spin-off, Good Judgment Inc., followed in 2015, along with a public forecasting site called Good Judgment Open.
This story adds an important twist to the simple "average everyone" picture. The best results did not come from treating every forecaster equally. They came from a mix of training, statistics, psychology and, notably, some interaction among forecasters in teams. The crowd was wiser when it was carefully selected, trained and aggregated, not when it was merely large.
When crowds shine: citizen science and Galaxy Zoo
Crowds are not only useful for guessing numbers. They can also do enormous amounts of careful work that no small team could manage.
Galaxy Zoo launched on 11 July 2007. It was created by Kevin Schawinski, then an astrophysicist at Oxford, and Chris Lintott, an Oxford astrophysics professor. The problem they faced was volume. The Sloan Digital Sky Survey, using a telescope at Apache Point Observatory in New Mexico, had photographed close to a million galaxies, far too many for professional astronomers to classify by eye. Computers of the time were not good at telling a spiral galaxy from an elliptical one.
So Galaxy Zoo asked the public. Volunteers looked at images and answered simple questions about each galaxy's shape. The response was overwhelming. More than 100,000 volunteers took part in the first version, and they made more than 40 million classifications in about 175 days. By the project's tenth anniversary in 2017, the total had reached 125 million.
Because each galaxy was classified by many different volunteers, the project could combine their answers and measure how confident the crowd was about each one, which is the wisdom-of-crowds principle applied to labeling. Volunteers also spotted things the professionals had not been looking for. One volunteer flagged a strange glowing cloud that became known as Hanny's Voorwerp ("Hanny's object"), a previously unknown type of astronomical object. Other volunteers drew attention to a class of small, compact galaxies nicknamed "green peas."
Galaxy Zoo's success led to the creation of Zooniverse, a web platform for citizen science that has since hosted around 100 projects, covering everything from wildlife camera-trap photos to historical documents. The same model, many people each contributing small, independent judgments that are then combined, now underpins a great deal of ecological monitoring as well.
A natural crowd: how honeybee swarms choose a home
Long before humans invented polls or markets, honeybees evolved a crowd decision process of their own. It is one of the clearest natural examples of collective intelligence, and it has been studied in detail by the Cornell biologist Thomas Seeley and his colleagues for more than a decade.
When a honeybee colony grows too large, roughly half the colony, about 10,000 bees together with the old queen, leaves the hive and forms a hanging cluster, often on a tree branch. The swarm then has to choose a new permanent home, typically a tree cavity. Choosing badly can be fatal; a cavity that is too small, too exposed or too damp can doom the colony over winter.
No single bee makes the choice. Instead, a few hundred scout bees fly out to search. When a scout finds a promising site, she returns to the swarm and performs a waggle dance, the same kind of dance bees use to advertise food, but now advertising real estate. The dance encodes the direction and distance of the site. Crucially, the strength of the dance reflects the quality of the site. In one experiment, scouts danced around 100 circuits for a first-rate site but only about 12 for a mediocre one.
Because better sites get stronger advertising, more scouts are recruited to visit them. Those scouts inspect the site themselves and, if they agree it is good, dance for it too. Support for weaker sites fades. This is a form of competition among options, not compromise.
The decision is not settled by a full vote. Instead, scouts at each candidate site effectively count how many other scouts are present. Once roughly 15 bees are gathered at one site, they have reached a "quorum." The scouts then return and signal the swarm to warm up its flight muscles, raising body temperature to around 95 degrees Fahrenheit, and the swarm lifts off for the chosen site, even if a few scouts are still dancing for other options.
Seeley's team tested this on Appledore Island, in the Gulf of Maine, where Cornell runs the Shoals Marine Laboratory. The island has few trees, so researchers could offer swarms artificial nest boxes and control the choices. In one set of experiments they labeled all 4,000 bees in a swarm so they could follow individual scouts. When they offered four small, mediocre sites and one superior site, the superior site was never the first to be found, but the swarm almost always chose it. When they offered two equally excellent sites, or five desirable sites, reaching a quorum took much longer. The whole process could take around 16 hours.
The work, published in American Scientist in 2006 by Seeley with Kirk Visscher of the University of California, Riverside, and the engineer Kevin Passino of Ohio State University, shows Surowiecki's conditions in action. The scouts are diverse because they search independently and find different sites. Each scout judges a site for herself rather than simply trusting the dancer who recruited her, which keeps judgments independent. The search is decentralized, with no leader. And the quorum rule is the aggregation mechanism. Seeley remarked that the bees' decision-making rivals that of any university department committee, and that it works through disagreement and competition rather than consensus. For anyone interested in bees, it is a reminder that a hive is not just a factory but also a kind of thinking system.
When crowds fail: information cascades
The bees' process works partly because scouts check sites themselves. Humans often do not. When people can see what others have already chosen, they may ignore their own information and follow the crowd. Economists call this an information cascade.
The concept was formalized by Sushil Bikhchandani, David Hirshleifer and Ivo Welch in a 1992 paper in the Journal of Political Economy titled "A Theory of Fads, Fashion, Custom, and Cultural Change as Informational Cascades." The logic is rational at each step. If the first two people you see choose restaurant A, it may be sensible to assume they knew something, even if your own information pointed to restaurant B. But once you follow them, your choice adds no new information for the next person, who sees three people at restaurant A. The crowd grows, but the information behind it does not. If the first couple of people happened to be wrong, everyone after them can be wrong too.
Lisa Anderson and Charles Holt tested this in a 1997 laboratory experiment. Participants drew a ball privately from one of two urns, one containing mostly "a" balls and the other mostly "b" balls, and announced which urn they thought had been used. Later participants could hear earlier announcements. Cascades, in which people's announcements followed the earlier pattern rather than their own draw, appeared in 41 of 56 rounds. Sometimes these led the whole sequence to the wrong answer, a "reverse cascade."
Cascades help explain fads, bank runs, sudden swings in popularity, and how a handful of early reviews can make or break a product. They are a direct attack on Surowiecki's independence condition.
When crowds fail: the Zurich experiment on social influence
Perhaps the most cited modern study of how crowds lose their wisdom was published in 2011 in the Proceedings of the National Academy of Sciences by Jan Lorenz, Heiko Rauhut, Frank Schweitzer and Dirk Helbing, titled "How social influence can undermine the wisdom of crowd effect."
The researchers recruited 144 students at ETH Zurich and ran 12 sessions of 12 people each. Participants sat in separate cubicles and answered six estimation questions about Swiss geography and crime statistics, such as the length of the border between Switzerland and Italy, the population density of Switzerland, the number of new immigrants to Zurich, and how many murders were officially registered in Switzerland in 2006. Each person gave five estimates per question, in rounds, and was paid in Swiss francs for accuracy in every round: 1.40 francs for being within 10 percent of the truth, 0.70 for within 20 percent, 0.35 for within 40 percent, and nothing otherwise. They were rewarded for being right, not for agreeing.
Some groups received no information about other people's answers. Others were shown the average of the group's previous estimates. A third set saw everyone's full history of estimates.
The results identified three problems. First, the social influence effect: seeing others' answers made the group's estimates bunch together, reducing diversity, but did not make the group more accurate. Second, the range reduction effect: as answers clustered, the true value tended to end up near the edge of the group's range rather than in the middle, so the crowd became a worse guide to where the truth lay. Third, the confidence effect: people became more confident as their answers converged, even though they were not more accurate. Showing people the group average harmed the crowd's wisdom more than showing them the full set of answers.
The study also gave a vivid lesson about aggregation. Because some people gave enormous overestimates, the ordinary arithmetic average beat the typical individual's first guess only 21.3 percent of the time. When the answers were averaged on a logarithmic scale (the geometric mean), the crowd beat individuals 77.1 percent of the time, and the median performed similarly. Galton's instinct to use the median, it turns out, was sound.
A twist: when talking helps
It would be easy to conclude that any communication ruins a crowd. A 2017 study complicated that picture. Joshua Becker, Devon Brackbill and Damon Centola, also writing in PNAS, recruited 1,360 people online and asked them to estimate quantities from images. Some groups of 40 were connected in decentralized networks, where everyone had the same number of contacts. Others were in centralized networks, where one person was connected to everyone. Control groups revised their answers without seeing anyone else's.
In the decentralized networks, social influence narrowed the spread of answers by 43 percent, yet accuracy improved. Individual error fell by 23 percent, and the error of the group median fell by 12 percent. The authors argued that this happened because people who were more accurate tended to stick to their answers more, so they gained influence as others adjusted toward them. In the centralized networks, by contrast, the group was pulled toward whatever the central person believed. If that person happened to be on the right side, the group improved; if not, it got worse.
The two studies are not as contradictory as they first appear. Together they suggest that how information flows matters more than whether it flows. Broadcasting a single summary number or letting one dominant voice shape everyone's view tends to erode independence. Letting people learn from many peers, in a network without a single hub, can preserve enough diversity for the crowd to improve.
Getting more out of crowds: better aggregation
Researchers have also invented smarter ways to combine answers. One of the most striking is the "surprisingly popular" method, introduced in 2017 in Nature by Dražen Prelec, H. Sebastian Seung and John McCoy in a paper titled "A solution to the single-question crowd wisdom problem."
The method asks each person two questions: what do you think the right answer is, and what share of other people do you think will give each answer? The chosen answer is the one that turns out to be more popular than people predicted.
Their classic example is the question "Is Philadelphia the capital of Pennsylvania?" Many people say yes, because Philadelphia is the state's best-known city. In the example, 65 percent answered yes and 35 percent no. But people also predicted that 75 percent of others would say yes. The "no" answer was more popular than expected (35 percent actual versus 25 percent predicted), so the method picks "no," which is correct: the capital is Harrisburg. The intuition is that people with special knowledge know the answer and also realize that most others will get it wrong, so their answer shows up as a surprise. In tests summarized on Wikipedia, the method reduced errors by around 21 to 24 percent compared with simple majority votes and confidence-weighted votes.
The crowd within your own head
A curious offshoot of this research asks whether a single person can be their own crowd. In 2008 the psychologists Edward Vul and Harold Pashler asked people to estimate quantities such as the percentage of the world's airports located in the United States. Some participants were asked for a second guess immediately; others were asked three weeks later. Averaging a person's two guesses was more accurate than either guess alone, and the delayed second guess helped more, presumably because time made the second guess more independent of the first.
Later work has been mixed. A pre-registered replication by Steegen and colleagues in 2014 mostly confirmed the benefit of averaging two guesses but not the extra benefit of waiting. Rauhut and Lorenz reported in 2011 that asking yourself more than three times made things worse. Stefan Herzog and Ralph Hertwig found in 2009 that a technique they called "dialectical bootstrapping," deliberately assuming your first answer was wrong and reasoning out why before guessing again, improved results more than simply guessing twice, though it still did not match averaging with a different person. The lesson echoes everything above: the value of combining guesses depends on how independent and different those guesses are.
Practical lessons for anyone using a crowd
Pulling the research together gives a short set of working rules.
- Collect judgments before discussion. Ask people for their estimate privately first, then talk. This protects independence and gives you a clean set of answers to combine.
- Seek genuine diversity. A big group of people with the same background and the same sources is less useful than a smaller group with varied knowledge.
- Watch for a single dominant voice. Whether it is a boss, a celebrity or the first reviewer, one influential source can turn a crowd into an echo.
- Choose the right summary. For estimates that can be wildly large, prefer the median or geometric mean over the plain average.
- Reward accuracy, not agreement. Prediction markets and scored forecasting tournaments work partly because people gain from being right.
- Measure and select. As the Good Judgment Project showed, tracking who is reliably accurate, and weighting or training accordingly, can beat treating everyone equally.
- Remember that crowds share biases. No amount of averaging fixes an error that everyone makes.
These rules apply to company planning meetings, to online reviews, to citizen science surveys of insects and plants, and to the growing practice of combining many people's ratings to train and evaluate computer systems. In each case, the question is not "how many people agree?" but "how independent, diverse and well-combined were their judgments?"
Frequently asked questions
Does the wisdom of crowds mean the majority is always right? No. It means that, under certain conditions, combining many independent and diverse judgments tends to produce a good estimate. Condorcet's jury theorem shows that if individuals are more likely to be wrong than right, a larger majority is more likely to be wrong.
What was Galton's ox experiment? At a livestock fair in Plymouth, England, in 1906, about 800 people guessed the weight of a dressed ox. Francis Galton found that the median guess, 1,207 pounds, was within 1 percent of the actual weight of 1,198 pounds. He published the result in Nature in 1907.
What are the conditions for a wise crowd? James Surowiecki's 2004 book lists four: diversity of opinion, independence, decentralization, and a good aggregation mechanism.
Why does social influence hurt crowds? When people see others' answers, they tend to adjust toward them. A 2011 ETH Zurich study found this reduced diversity without improving accuracy, and made people more confident. However, a 2017 study found that in decentralized networks without a central figure, sharing information could improve accuracy.
Do animals show wisdom of crowds? Yes. Honeybee swarms choose new nest sites through independent scouting, waggle dances whose strength reflects site quality, and a quorum of roughly 15 scouts at one site. In Thomas Seeley's experiments, swarms almost always chose the best available site.
Is averaging always the best way to combine answers? Not always. When some guesses are extreme, the median or geometric mean is often better. Methods like the "surprisingly popular" algorithm can also find the right answer even when the majority is wrong.
Conclusion
The wisdom of crowds is real, but it is conditional. Galton's fairgoers, Iowa's traders, Galaxy Zoo's volunteers and Seeley's bees all succeeded because their judgments were varied, made largely independently, drawn from different pieces of the world, and combined through a sensible rule. The Zurich experiment and the study of information cascades show what happens when those conditions are removed: groups converge, grow confident, and drift from the truth together.
The practical message is encouraging. We do not need perfect experts to make good collective decisions. We need to design the process well: ask people separately, include different perspectives, avoid letting one voice dominate, and combine answers with care. A beehive manages this without a leader. With a little thought, human groups can too.
Sources and further reading
- Wikipedia, "Wisdom of the crowd": https://en.wikipedia.org/wiki/Wisdom_of_the_crowd
- Wikipedia, "The Wisdom of Crowds" (Surowiecki's book): https://en.wikipedia.org/wiki/The_Wisdom_of_Crowds
- Wikipedia, "Condorcet's jury theorem": https://en.wikipedia.org/wiki/Condorcet%27s_jury_theorem
- Wikipedia, "Information cascade": https://en.wikipedia.org/wiki/Information_cascade
- Wikipedia, "Iowa Electronic Markets": https://en.wikipedia.org/wiki/Iowa_Electronic_Markets
- Wikipedia, "The Good Judgment Project": https://en.wikipedia.org/wiki/The_Good_Judgment_Project
- Wikipedia, "Galaxy Zoo": https://en.wikipedia.org/wiki/Galaxy_Zoo
- Wikipedia, "Surprisingly popular": https://en.wikipedia.org/wiki/Surprisingly_popular
- Lorenz, J., Rauhut, H., Schweitzer, F., and Helbing, D. (2011), "How social influence can undermine the wisdom of crowd effect," PNAS (full text via PubMed Central): https://pmc.ncbi.nlm.nih.gov/articles/PMC3107299
- Becker, J., Brackbill, D., and Centola, D. (2017), "Network dynamics of social influence in the wisdom of crowds," PNAS (PubMed Central): https://pmc.ncbi.nlm.nih.gov/articles/PMC5495222
- Cornell Chronicle, "How 10,000 bees decide where to go when they fly the coop" (2006): https://www.news.cornell.edu/stories/2006/04/honeybee-decision-making-ability-rivals-any-department-committee