This thesis is about the nature of value incommensurability and its significance for judicial reasoning. It argues that there can be incommensurable values and that this incommensurability can have significant implications for judicial reasoning. I argue that incommensurability gives rise to a range of reasonableness, within which it is reasonable but in a sense also arbitrary to decide either way, and that this range is wider than is suggested by the notion that some options are roughly equal, because even a large improvement to one option may not make it the uniquely correct option. The thesis goes on to consider the effect that the authority of law can have on choices between incommensurable options. Although I argue that the authority of law can sometimes provide a conclusive reason to choose one of two incommensurable options, I also argue that it has limits and may not do so in every case of incommensurability. Moreover, the introduction of an authoritative directive may even give rise to incommensurable options where none previously existed. The thesis then draws out the implications of these claims, first, for human-rights adjudication—where my claim is that ‘balancing’ is appropriate both in the specification of rights and in assessing the justification for their infringement, provided we acknowledge the limits of balancing in cases of incommensurability—and, secondly, for adjudication involving common law reasoning and statutory interpretation. Finally, I suggest that we can distinguish between different ideals of the rule of law, and that the arbitrariness of judicial decisions involving incommensurable options has different implications for those different ideals. The arbitrariness involved in choosing between undefeated reasons may be necessary contrary to one ideal of the rule of law, understood as the rule of authority, but not contrary to an ideal of the rule of law understood as the rule of reason.