How does the Rule of Four affect Supreme Court decisions? We show two effects of changing a “hearing pivot” justice who is decisive for case selection. First, a court with more extreme hearing pivots will hear cases with more moderate precedents. For example, as the conservative hearing pivot becomes more extreme, the court hears a broader range of cases with liberal status quo precedents. Second, more extreme hearing pivots shrink dispositional majorities and lead to more polarized rulings. If the median justice becomes more extreme without changing the hearing pivots, then rulings are more extreme. The effect on the range of cases heard, however, is smaller than that from changing hearing pivots. Finally, we show that case selection can also depend on non-median, non-hearing-pivot justices. Replacing an extreme justice with someone even more extreme can lead to a smaller set of heard cases, as final rulings can shift away from the binding hearing pivot, making status quo precedents more appealing.