From revealed preference to preference revelation

Utility functions are regarded as elements of a linear space that is paired with a dual representation of choices to demonstrate the similarity between preference revelation and the duality of prices and quantities in revealed preference. With respect to preference revelation, quasilinear versus ordinal utility and choices in an abstract set versus choices in a linear space are distinguished and their separate and common features are explored. The central thread uniting the various strands is the subdifferentiability of convex functions.