The study of representation has been a major research field in quantitative political science, and it has been accompanied by a range of conceptual innovations by political theorists working on the topic. Yet, although many quantitative scholars are familiar with the conceptual literature, even the most complex quantitative studies have tended to rely on a simplistic and unidimensional modelling of representative processes, refusing to operationalize the more sophisticated conceptions of representation theorists have developed. In this project, we develop four remodelled conceptions of representation that are both sensitive to theorists’ conceptual impulses and operationalizable for quantitative scholars. In doing so, we advance a new research agenda on representation that moves significantly beyond the status quo of the field.