General · EdgepediaSeptember 17, 20268 min read

Wisdom of the crowd

The wisdom of the crowd is the phenomenon in which a statistical aggregate of many individuals' judgments, such as the mean or the majority vote, is more accurate than most or all of the individual judgments that make it up. The name was popularized by journalist James Surowiecki's 2004 book The Wisdom of Crowds, and the effect has been demonstrated in estimation tasks, elections, forecasting tournaments, sports betting, and medical diagnosis.¹^•²

Key fact	Detail
Classic demonstration	At a 1906/1907 county fair, Francis Galton found the crowd's median ox-weight guess of 1,207 lb against a true weight of 1,198 lb, while individual guesses ranged from below 900 to above 1,500 lb³^•²⁵
Original publication	Francis Galton, "Vox Populi," Nature 75 (March 7, 1907), pp. 450–51⁴
Surowiecki's conditions	Diversity of opinion, independence, decentralization, and a mechanism for aggregation⁵
Formal basis	Condorcet's 1785 jury theorem: with independent voters each more than 50% likely to be correct, majority correctness rises with group size and converges to 1⁶
Main failure mode	Social influence makes estimates converge, so errors become systematic rather than canceling⁷
Practical scale	About 10–15 averaged layperson ratings per headline matched the internal agreement of professional fact-checkers, at under $1 per headline⁸
Machine version	Aggregated predictions from large language models on 31 binary questions rivaled a crowd of 925 human forecasters from a three-month tournament⁹

Origins

The founding case study is the ox-weighting competition reported by Francis Galton, a British statistician and polymath, in "Vox Populi" (Nature, March 7, 1907). Visitors to a county fair guessed the weight of an ox, with the closest answer winning a prize. After the animal was slaughtered and weighed, Galton found that the median opinion, 1,207 lb, almost exactly matched the true weight of 1,198 lb²⁵, even though individual opinions varied widely, from below 900 to above 1,500 lb. Galton concluded that in this instance the "vox populi" was correct to within 1 percent of the real value.³^•⁴

The intellectual ancestry is older. Surowiecki's own framing traces the rationale to Aristotle's Politics, which argued that a group pooling many people's knowledge can judge better than its most talented members. The formal mathematical ancestor is the Marquis de Condorcet's 1785 jury theorem.¹⁰^•⁶

Why averaging works, and when it does not

Two classical results justify the averaging procedure. Condorcet's jury theorem treats a binary choice: if each of n independently voting individuals has a probability p greater than 0.5 of being correct, the probability that the majority is correct exceeds p and approaches certainty as n grows. For continuous estimates, Jensen's inequality guarantees that, when error is measured by a convex cost function, the crowd mean performs at least as well as a randomly selected individual; the distance between the truth and the average opinion is always equal to or smaller than the average individual error.⁶^•³

These guarantees depend on assumptions that often fail in practice. If individual errors are biased in the same direction, or correlated because people share information, averaging cancels less error. With non-convex cost functions, Jensen's inequality no longer holds and the average can perform worse in expectation than a randomly chosen individual, a case of negative collective intelligence.³

Conditions. Surowiecki's book states four general conditions for a wise crowd: diversity of opinion, so each person has private information even if only an eccentric interpretation of known facts; independence, so opinions are not determined by those around them; decentralization; and an aggregation mechanism that turns private judgments into a collective decision.⁵

Social influence and the limits of diversity

The independence condition is the most fragile. In experiments on general-knowledge questions, even small amounts of social influence made participants' estimates converge, reducing the diversity of the crowd and making its error more systematic, that is, biased in the same direction. Remarkably little social influence was needed to produce herding and to undermine the statistical mechanism behind crowd wisdom.⁷

The role of diversity itself is debated. The diversity prediction theorem holds that a crowd's error equals the average individual error minus the prediction diversity, so more diversity should reduce collective error. But empirical tests complicate the simple reading. Three experiments on estimating the number of candies in a jar, the length of a paper strip, and the number of pages in a book found no significant correlation between prediction diversity and collective error, and a separate analysis found a positive correlation between the variance of estimates and crowd error, in disagreement with some interpretations of the theorem.¹¹^•¹² Demographic diversity, the kind most often meant by "diversity" in popular discussion, shows only a weak correlation with numerical judgment, so demographically diverse crowds are typically not much wiser than homogeneous ones.¹³

Social influence is not uniformly harmful. Theoretical analysis and reanalysis of four experimental datasets totaling 2,885 subjects show that crowd wisdom depends on the interaction between the centralization of the social influence network and the distribution of initial estimates; under some conditions, influence actually improves the collective result.¹⁴ Allowing discussion before estimates can also improve accuracy at both the group and individual level.¹⁵

Aggregation systems and applications

Prediction markets and polls. Two widely used systems elicit and aggregate crowd judgment. Prediction markets let participants trade contracts whose price reflects the probability of an event; prediction polls directly collect probability estimates and aggregate them statistically. In a large multi-year forecasting competition, the IARPA Aggregative Contingent Estimation (ACE) tournament (2011–2015), market prices were more accurate than the simple mean of poll forecasts in both seasons tested, and a logarithmic market scoring rule (LMSR) market outperformed a continuous double auction market, especially on low-activity questions.¹⁶^•¹⁷ Participation size matters: tennis betting prices became significantly less informative when a clashing soccer tournament reduced participation, suggesting that measures increasing market participation improve forecast accuracy.¹⁸

Elections and sports. Using the 2010 British Election Study internet survey, researchers found that groups of citizens were better election forecasters than individuals, that citizen forecasting correctly predicted the hung parliament of 2010, and that constituency marginality and group size predicted accuracy.¹⁹ In sports, fans predicting UFC fight outcomes over three years of pay-per-view events were right on 85.7 percent of outcomes, against 67.6 percent for expert bookmakers, though the study's authors note the data set was small.²⁰ Analysis of an online community of amateur sports tipsters found that forecast accuracy came from the whole crowd: selecting tipsters by experience or past accuracy did not improve betting returns.²¹

Small crowds and selective aggregation. A crowd need not be large. A partial replication of Kosinski et al. (2012) found that the collective intelligence of 12 randomly selected individuals exceeded that of 99 percent of individuals in the general population. The Good Judgment Project, winner of a major geopolitical forecasting tournament, beat the simple crowd average by training forecasters in debiasing, running team-based polls and markets, selecting top performers into elite "superforecaster" teams, and fine-tuning aggregation algorithms.²²^•²³

Correcting the average. When the plain average is wrong, alternatives exist. The "surprisingly popular" method asks each participant two things: their own answer and what percentage of others they expect to share it; answers that are more popular than people expect are favored, and the method has improved group judgments on factual questions such as US state capitals.² Other procedures include opinion unbiasing, wisdom of the resistant, and select crowds, and machine learning can derive near-optimal aggregation rules from data.³

Content moderation. In a study of news headlines, a politically balanced lay crowd's average truthfulness ratings corresponded to professional fact-checkers' ratings once about 10–15 responses per headline were gathered, and fewer responses sufficed for political articles than for non-political ones. At roughly 30 seconds per rating and pay around $10 per hour, ten ratings per item cost less than a dollar per headline.⁸

Machine crowds

The effect extends to artificial agents. Aggregated predictions from large language models on 31 binary questions matched the accuracy of a 925-person human forecasting tournament, via the simple method of averaging model outputs. Separately, LLM-based agents prompted to role-play partisan personas displayed human-like partisan biases and, like human groups, converged toward more accurate beliefs through deliberation, a "wisdom of partisan crowds" pattern, though chain-of-thought prompting and thin personas interfered with convergence.⁹^•²⁴

References

Initially written Sep 17, 2026 · Reviewed: Sep 30, 2026; Oct 25, 2026 · Edited: Sep 30, 2026; Oct 25, 2026