ABSTRACT
Many values in least upper bound models have subvalues that are themselves values. This chapter defines subvalues and considers the extent to which values of various kinds can be analyzed into their subvalues. Every value has itself and zero as subvalues. In least upper bound models, the positive and negative parts of a value are also subvalues of it. Values have unions and intersections, and the unions and intersections of some (maybe all) subvalues of a value are also subvalues of it. Any nonzero value that has only itself and zero as subvalues is elemental; it cannot be further analyzed. All elemental values are either positive or negative. None are incomparable with zero. A complete analysis breaks a value down into elemental values, but this is not always possible. Section 13.5 describes a procedure for analysis that works for many least upper bound value structures. In value structures whose values are all analyzable, it may be possible to define dimensions, but many questions about the scope and limits of analyzability remain open.
Value analysis breaks values down into subvalues. On an objective list conception of welfare, for example, an individual’s welfare is assessed along a number of dimensions, which are combined into an overall welfare assessment. A subvalue of that assessment corresponds to assessment by some subset of items on the list. Similarly, Cartesian values are lists of component values, and partial lists of those components are subvalues.
