Theoretical Model: Condorcet's Jury Theorem, Part 1

number of voters

N

odd

even

both

31

probability bias

ϵ

0.01

This is the first of five Demonstrations about Condorcet's jury theorem (1785). It uses the formula

P(N,p)=

N

∑

k=⌈N/2⌉



N

k

×

k

p

1-p

N-k

)

, where the probability

p=0.5+ϵ

and

N

is the number of voters. The theorem states if the voters are independent and each has probability

p=0.5+ϵ>0.5

of voting for the correct choice, then the probability

P(N,p)

of the majority voting for the correct choice is larger than

p

and converges to one as the population

N

goes to infinity.