Many methods have been proposed for making use of multiple experts to predict uncertain events such as election outcomes, ranging from simple averaging of individual predictions to complex collaborative structures such as prediction markets or structured group decision making processes. We used a panel of more than 2,000 forecasters to systematically compare the performance of four different collaborative processes on a battery of political prediction problems. We found that teams and prediction markets systematically outperformed averages of individual forecasters, that training forecasters helps, and that the exact form of how predictions are combined has a large effect on overall prediction accuracy.