We start from the assumption that any realistic reform proposal must not require a constitutional amendment. We then suggest that hyperpoliticization arises out of a feedback loop between appointments and decision-making: Politicized decisions beget politicized appointments, and vice-vernal. We thus propose a change to the Court's decision-making process, which we believe will incentivize useful changes in the appointments process. Our proposal involves an application of what mathematicians and game-theorists call "fair division theory." To begin, we suggest a new decision-making process in which a three-Justice panel--not the entire Court--would hear and decide each case. Appeal to an en banc sitting owed be available only upon the unanimous vote of the remaining six Justices. The parties themselves would engage in a fair division process to select the decisive panel: (1) Petitioner partitions 3 possible panels, using each Justice once; (2) Respondent eliminates 1 panel, then repartitions the remaining Justices into two new panels; (3) Petitioner chooses one panel. We offer a mathematical proof that this will result in a panel close to the parties perception of the Court's ideological center relative to their case. We offer reasons to think that this would (1) produce less politicized opinions and more stable doctrine; and (2) discourage outlier appointments, as such Justices would serve on fewer decisive panels. Over time this would lead to a more moderate, centrist Court.