Welfare Reflections: On Duality Conditions in the Theory of Value

Informational invariance conditions in social welfare theory say that the social preference or overall betterness ordering of alternatives should be preserved under certain classes of transformations of individual utility functions. These conditions play a central role in axiomatic characterizations of social welfare functions and in impossibility theorems that are foundational to the subject. This paper studies the neglected flipside of informational invariance conditions, which say that the social preference or overall betterness ordering should be reversed under certain classes of transformations, such as reflections of utilities across the origin. I first draw out some consequences of these "duality" conditions for the ethics of population and distribution. The main theme is that they lead very quickly either to impossibility or to characterizing some form of utilitarianism. I then explore some ways in which the duality conditions might be motivated, having to do with ideas about voting, measurement, and the metaphysics of value relations. Ultimately, the idea of duality emerges as a central distinguishing commitment of utilitarian ethics, though one that proves surprisingly difficult to motivate on independent grounds.