The influence of behavioral biases on aggregate outcomes depends in part on self-selection: whether rational people opt more strongly into aggregate interactions than biased individuals. In betting market, auction and committee experiments, we document that some errors are strongly reduced through self-selection, while others are not affected at all or even amplified. A large part of this variation is explained by differences in the relationship between confidence and performance. In some tasks, they are positively correlated, such that self-selection attenuates errors. In other tasks, rational and biased people are equally confident, such that self-selection has no effects on aggregate quantities.