Condorcet's Jury Theorem

Condorcet's jury theorem states that given a group of voters (a "jury") independently choosing by majority vote between a correct outcome with probability  and an incorrect one with probability :

1. If  (so that each voter is more likely to vote correctly that incorrectly), adding more voters increases the probability that the majority chooses correctly and the probability of a correct decision approaches 1 as the number of voters increases;

2. If  (so that each voter is less likely to vote incorrectly than correctly), adding more voters decreases the probability that the majority chooses correctly and the probability of a correct decision is maximized for a jury of size one.

REFERENCES:

Condorcet, J.-A.-N. de Caritat, marquis de. "Essai sur l'application de l'analyse à la probabilité des décisions rendues à la pluralité des voix." Paris: Imprimerie Royale, 1785.