What is the Condorcet jury theorem in simple terms?

If each person is even slightly better than a coin flip at getting the right answer and nobody copies anyone else, a majority vote becomes almost certain to be right as the group gets larger.

Does the theorem prove that democracy works?

No. If independence or individual competence fails, or people vote strategically, the conclusion may not hold, so it is best seen as a conditional argument for democracy's epistemic strengths.

Condorcet Jury Theorem

🏛️ Politics & Public Administration By CampusDown Wiki Editorial Team Last updated October 27, 2026

The Condorcet jury theorem, proved by the French mathematician and philosopher the Marquis de Condorcet in 1785, states that when one of two options is objectively correct, each voter chooses correctly with probability greater than 1/2 and votes are independent, the probability that the majority is right rises with the number of voters and approaches 1 as the group grows without limit. It is widely cited as an epistemic argument for majority rule and democracy.

Contents

1. The theorem and its intuition
2. Limits of the assumptions and generalizations
3. Strategic voting and epistemic democracy
4. FAQ
5. References

The theorem and its intuition

Condorcet (1785) presented the theorem alongside the voting paradox in his treatise on the probability of majority decisions. If each of three voters is right with probability 0.6, the majority is right with probability about 0.65; with 101 voters it rises to about 0.98. By the law of large numbers, independent errors cancel out. Conversely, if individual accuracy is below 1/2, a larger group makes the majority almost certainly wrong. Black (1958) rediscovered Condorcet's work and presented it as a founding text of social choice theory, and Grofman, Owen and Feld (1983) gave the theorem a modern formulation and catalogued its generalizations.

Limits of the assumptions and generalizations

The theorem relies on strong assumptions that voters judge independently and have similar competence. Berg (1993) and Ladha (1992) showed that the conclusion can survive correlated votes if the correlation is not too strong, and Estlund (1994) analyzed how reliance on opinion leaders undermines independence. List and Goodin (2001) extended the theorem to more than two options. Dietrich (2008) argued that the independence and competence premises are hard to justify at the same time. Galton's (1907) report that the median of a crowd's guesses at an ox's weight was remarkably close to the truth is often discussed with Surowiecki's (2004) wisdom of crowds as an instance of similar information-aggregation logic.

Strategic voting and epistemic democracy

Austen-Smith and Banks (1996) showed that if voters act strategically by conditioning on being pivotal, voting according to one's private information may not be an equilibrium. Feddersen and Pesendorfer (1998) applied this to juries, finding that a unanimity rule can actually raise the probability of convicting the innocent. In political philosophy, Landemore (2013) combined the theorem with diversity arguments to defend democratic reason, the claim that rule by the many can outperform rule by a few experts. At the same time, scholars stress that the theorem's optimistic conclusion fails when independence breaks down, as in groupthink.

FAQ

What is the Condorcet jury theorem in simple terms?: If each person is even slightly better than a coin flip at getting the right answer and nobody copies anyone else, a majority vote becomes almost certain to be right as the group gets larger.
Does the theorem prove that democracy works?: No. If independence or individual competence fails, or people vote strategically, the conclusion may not hold, so it is best seen as a conditional argument for democracy's epistemic strengths.

Sources reviewed: 2026-10-26

References

Condorcet, M. J. A. N. de C., marquis de. (1785). Essai sur l'application de l'analyse à la probabilité des décisions rendues à la pluralité des voix. Paris: Imprimerie Royale.
Black, D. (1958). The Theory of Committees and Elections. Cambridge: Cambridge University Press.
Grofman, B., Owen, G., & Feld, S. L. (1983). Thirteen theorems in search of the truth. Theory and Decision, 15(3), 261–278.
Ladha, K. K. (1992). The Condorcet jury theorem, free speech, and correlated votes. American Journal of Political Science, 36(3), 617–634.
Austen-Smith, D., & Banks, J. S. (1996). Information aggregation, rationality, and the Condorcet jury theorem. American Political Science Review, 90(1), 34–45.
Feddersen, T., & Pesendorfer, W. (1998). Convicting the innocent: The inferiority of unanimous jury verdicts under strategic voting. American Political Science Review, 92(1), 23–35.
Estlund, D. M. (1994). Opinion leaders, independence, and Condorcet's jury theorem. Theory and Decision, 36(2), 131–162.
Berg, S. (1993). Condorcet's jury theorem, dependency among jurors. Social Choice and Welfare, 10(1), 87–95.
List, C., & Goodin, R. E. (2001). Epistemic democracy: Generalizing the Condorcet jury theorem. Journal of Political Philosophy, 9(3), 277–306.
Dietrich, F. (2008). The premises of Condorcet's jury theorem are not simultaneously justified. Episteme, 5(1), 56–73.
Landemore, H. (2013). Democratic Reason: Politics, Collective Intelligence, and the Rule of the Many. Princeton, NJ: Princeton University Press.
Surowiecki, J. (2004). The Wisdom of Crowds. New York: Doubleday.
Galton, F. (1907). Vox populi. Nature, 75(1949), 450–451.

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This article was last updated on October 27, 2026. It is based on widely recognized original works and textbooks; when citing it in a paper, please check the original sources listed in the references.