Multidimensional Concepts and Disparate Scale Types

Multidimensional concepts are everywhere, and they are important. Examples include moral value, welfare, scientific confirmation, democracy, and biodiversity. How, if at all, can we aggregate the underlying dimensions of a multidimensional concept F to yield verdicts about which things are Fer than which overall? Social choice theory can be used to model and investigate this aggregation problem. This article focuses on a particularly thorny problem made salient by this social choice-theoretic framework: the underlying dimensions of a given concept might be measurable on different types of scales-for example, some ordinal and some cardinal. An underappreciated impossibility theorem due to Anna Khmelnitskaya shows that seemingly plausible constraints on aggregation across scale types are inconsistent. This impossibility threatens to render the notion of overall Fness incoherent. This article attempts to defuse this threat, arguing that the impossibility depends on an overly restrictive conception of measurement and of how measurement constrains aggregation. Adopting a more flexible-and, the authors think, more perspicuous-conception of measurement opens an array of possibilities for aggregation across disparate scale types.