The power of a cohesive subgroup within a voting body

We examine the power of a subgroup within a voting body as a function of its size and cohesiveness. The measure of cohesiveness is the probability that an arbitrary member of the subgroup will vote the same way as the leader of the subgroup. All voters are assumed to vote independently, and those not in the subgroup vote “for” or “against” with probability 1/2 in each case. The power of the subgroup is the probability that its vote differential exceeds the vote differential of the members of the body not in the subgroup. Tradeoffs between relative subgroup size and its follow-the-leader probability are considered.