Flippant Juror

During lunch I exercised on the "Flippant Juror Problem"

1. a jury of 3 jurors decides by majority
2. two jurors are serious experts, they make a right decision with the probability p
3. one is a jerk, he just flips a coin with probability for head q=1/2 to decide

Is this jury better than a single person who also makes a right decision with the probability p?

The solution is they are equal. Thats indeed counterintuitive! The jerk sabotages the jury.

Annotation: If they would all flip a coin with majority vote it would be also equal to one flip

This leads to a question related to the electoral process with majority vote in general.

Given N voters, how many "coinflippers" M it takes to reduce their probability for right decision to one decision, hmm try to solve that....