Condorcet Jury Theorem, explained.
Condorcet's jury theorem gives conditions under which a majority of independent, sufficiently competent voters becomes more likely to answer a binary factual question correctly.
Why it happens
An odd jury has equal individual correctness p. Independent majority accuracy is an exact binomial tail. With chosen probability c, all jurors instead use one shared Bernoulli(p) signal, giving aggregate accuracy cp+(1−c) times independent-majority accuracy. Reveal one seeded vote.
Condorcet's jury theorem gives conditions under which a majority of independent, sufficiently competent voters becomes more likely to answer a binary factual question correctly.
Read the result
Check individual competence and signal dependence before increasing jury size. More people need not mean more independent evidence.
A worked example
Many votes from the same source
At sixty-percent individual correctness and independent signals, increase the odd jury size and compare majority accuracy.
Set shared-signal chance to one hundred percent. Every vote now copies one Bernoulli signal with the same individual correctness.
The majority accuracy becomes sixty percent regardless of size. Revealing a single vote shows a realisation, not the theorem's guarantee for every jury.
OPTIONAL DEEPER DETAILGo deeper: inside the model
Inside this model
An odd jury has equal individual correctness p. Independent majority accuracy is an exact binomial tail. With chosen probability c, all jurors instead use one shared Bernoulli(p) signal, giving aggregate accuracy cp+(1−c) times independent-majority accuracy. Reveal one seeded vote.
Where this idea is useful
A practical use
More judgments can help when they supply independent information, while many copies of the same signal add little.
A common misconception
“A larger majority must always be more likely to be right.”
The familiar result requires conditions including competence and independence. Below-chance accuracy or shared errors can change or remove the benefit.
What this explanation leaves out
- This authored mixture is not a universal model of correlated votes. Competence, independence and an objectively resolvable binary question are imposed; majority preference does not define factual truth or moral correctness.
Does the theorem make preferences objectively correct?
No. The activity assumes a binary factual question with a known correct answer. Preferences and moral judgments are different objects of aggregation.
How many distinct information sources underlie the apparent number of opinions you are counting?
Associated thinkers
Associations marked provisional are awaiting source review.
Further reading
Explore the original research or the teaching reference behind this experiment.