Abstract: Multidimensionality is everywhere: in ethics, epistemology, philosophy of science, philosophy of language, and philosophy of mind, as well as a host of domains outside philosophy. Many ethicists are pluralists about value, holding that whether one state of affairs is better than another depends on how the two compare in terms of well-being, equality, autonomy, and various other values. Many epistemologists are pluralists about theoretical virtues, holding that your confidence in a theory should depend on how it fares with respect to simplicity, strength, and fruitfulness. And so on. We need a way to aggregate these various dimensions to yield all-things-considered judgments. Things get worse when we notice that underlying dimensions may often be measured on different types of scale: some ordinal and some cardinal (including various types of cardinal scales). How, if at all, can this be done? We are in uncharted territory as far as social choice theory goes