We are grateful to the commentators for their close reading of our article 1 and for their challenging and interesting responses to it. We do not have space to respond to all of the objections that they raise, so in this reply, we address only a selection of them. Some commentaries question the usefulness of developing an account of the sort we provide, 2 or of revising the Standard Account (SA) in doing so. 3–5 Our schema is intended to provide (...) a framework for developing a full account of invasiveness that captures existing uses of the term. On the assumption that the term is used somewhat reliably and consistently–and we are inclined to agree with some of our commentators 3 4 that people are not terribly confused or mistaken in how they employ the term–an account that captures these... (shrink)

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. Here, we focus 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—e.g., 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. We attempt 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, we think, more perspicuous—conception of measurement opens an array of possibilities for aggregation across disparate scale types. (shrink)