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Computational representation of everyday emotional states is a challenging task and, arguably, one of the most fundamental for affective computing. Standard practice in emotion annotation is to ask people to assign a value of intensity or a class value to each emotional behavior they observe. Psychological theories and evidence from multiple disciplines including neuroscience, economics and artificial intelligence, however, suggest that the task of assigning reference-based values to subjective notions is better aligned with the underlying representations. This paper draws together the theoretical reasons to favor ordinal labels for representing and annotating emotion, reviewing the literature across several disciplines. We go on to discuss good and bad practices of treating ordinal and other forms of annotation data and make the case for preference learning methods as the appropriate approach for treating ordinal labels. We finally discuss the advantages of ordinal annotation with respect to both reliability and validity through a number of case studies in affective computing, and address common objections to the use of ordinal data. More broadly, the thesis that emotions are by nature ordinal is supported by both theoretical arguments and evidence, and opens new horizons for the way emotions are viewed, represented and analyzed computationally.