Condorcet's jury theorem states that given an odd number 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 than incorrectly), adding voters
in pairs never decreases 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 more likely to vote incorrectly than correctly), adding voters
in pairs never increases the probability that the
majority chooses correctly and the probability of
a correct decision is maximized for a jury of size one.
