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Rationality is prized by lawyers. The 'rational review' test provides the constitutional minimum for due process and equal protection analysis. Unfortunately, even in an idealized world populated by perfectly rational people not all causes of irrational decision-making can be avoided. The basic nature of group decision-making inevitably creates the possibility of certain kinds of irrationality. The core of the problem is that, while deciding which party prevails is a binary decision [either one side or the other wins], there are often multiple issues that need to be decided in any particular case. The task of creating a system for selecting among multiple options presents an intractable problem for any group, including the Supreme Court. Kenneth S. Arrow has proven that no reasonable group-voting system for resolving multiple issues can avoid all inconsistency. Specifically, Arrow showed that under certain conditions, there always exists the potential for what is known as a 'lack of transitivity.' Transitivity requires that preferences between several options be consistent, so that if one prefers coffee to soda, and soda to tea, that person also prefers coffee to tea. Arrow's Theorem establishes that such a conclusion does not necessarily follow in the context of group decision-making. That is, given a similar choice of the three beverages, the group might prefer coffee to soda, and soda to tea, but also prefer tea to coffee. While the scholarly discussion of Arrow's Theorem is voluminous, until now, no one has identified a lack of transitivity in Supreme Court opinions. This Article presents the first such example, but it also explains why Arrow's Theorem is not a significant cause of "irrational" Supreme Court opinions. The article shows that there is a second form of irrational group decision-making exists, which has occurred far more frequently. It occurs when one party in a case receives the votes of a majority of the Justices of the Court on every relevant issue yet loses the case anyway. In these cases: (i) the Court agrees that if all of the relevant issues are decided in one party's favor, that party will win; (ii) at least five of the nine Justices rule in favor of that same party on all relevant issues; but, (iii) the other party wins. This phenomenon can be explained using what this Author has termed the 'Irrationality Theorem.' Stated generally, the Irrationality Theorem proves that there is no way to eliminate the possibility that a majority of the Supreme Court (or any other multi-member tribunal) will vote that one party should lose on every relevant issue yet win the case anyway. Several cases embodying this irrationality are discussed in detail.