We propose an empirically informed measure of the voting power that relaxes the assumptions of equally probable and independent votes. The behavioral power index measures the voter’s ability to swing a decision based on the probability distributions of the others’ behavior. We apply it to the Supreme Court of the United States using roll-call data to estimate voting probability distributions, which lead us to refute the assumption of equally probable and independent votes, and estimate the equivalent number of independent Justices for the Warren, Burger and Rehnquist benches, which turns out to be very low.