Models of decision-making typically assume the existence of some common currency of value, such as utility, happiness, or inclusive fitness. This common currency is taken to allow comparison of options and to underpin everyday choice. Here we explore the ideas that there is no universal value scale, that incommensurability of value pervades everyday choice, and hence that most existing models of decision-making in both economics and psychology are fundamentally limited. We propose an alternative approach. This alternative assumes that choice objects can only be compared with reference to specific but non-universal “covering values”. These covering values may reflect decision-makers’ goals, motivations, or current states. A complete model of choice must accommodate the range of possible covering values. We show that abandoning the common currency assumption in models of judgment and decision-making necessitates rank-based and heuristic models that contrast radically with conventional utility-based approaches. Moreover, the idea that there is no single common currency for object valuation parallels the idea, central to social choice theory, that the welfares of different individuals cannot be combined to represent the welfare of society overall. We note that if there is no universal value scale then Arrow’s Impossibility Theorem places severe bounds on the rationality of individual decision-making, and hence that there is a deep link between the incommensurability of value, inconsistencies in human decision-making, and rank-based coding of value. More generally, incommensurability raises the question of whether it will ever be possible to develop single-quantity-maximizing models of decision-making.