Wisdom of Crowds, explained.
Wisdom of crowds describes how aggregating estimates can improve accuracy when different people's errors partly cancel, while shared biases can persist.
Why it happens
Independent noise averages down as the sample grows. A common offset is added to every estimate and therefore remains in their mean. More people helps with the former, but counting more versions of the same error does not remove the latter.
Averaging diverse estimates can improve accuracy when errors partly cancel. More contributors cannot automatically remove an error shared by everyone.
Read the result
Change crowd size and shared bias separately. Compare average absolute errors across 200 generated crowds. The chart's bands show one analytic noise standard error around the biased mean, not a guarantee that every crowd lies inside them.
A worked example
Independent estimates before discussion
A group estimates a quantity separately, using different observations.
Its high and low errors can partly cancel. If everyone first sees the same misleading anchor, their estimates may all shift together.
Protect independence before aggregation, and check shared assumptions as well as headcount.
OPTIONAL DEEPER DETAILGo deeper: inside the model
Inside this model
The true quantity is 100. Each simulated guess adds a chosen common bias and independent uniform noise from −30 to +30. A batch of 200 crowds reports the mean absolute error for one person and for the crowd mean. The analytic uncertainty band uses noise standard deviation divided by the square root of crowd size; shared bias shifts its center.
Where this idea is useful
A practical use
Ask colleagues to estimate independently before discussion. A shared anchor can make their errors move together even if many people contribute.
A common misconception
“A bigger crowd must produce a more accurate answer.”
Shared bias, bad information and unsuitable aggregation can survive or grow with the crowd. Size alone does not establish wisdom.
What this explanation leaves out
- The guesses are generated, not observed. Equal weighting is not always appropriate, and misinformation, extreme outliers or correlated errors can undermine aggregation.
Why use multiple simulated crowds?
One crowd can happen to be unusually accurate or inaccurate. Repeating the same probability model helps separate the average pattern from one lucky draw.
Which errors are independent, and which assumption could make everyone wrong together?
Associated thinkers
Further reading
Explore the original research or the teaching reference behind this experiment.