Functioning, capability and the standard of living - an axiomatic approach

The standard of living of an agent is viewed as her capability of achieving various functionings (Sen, 1985, 1987). The agent is thus characterized by her capability set that consists of different functioning vectors. The task of measuring the standard of living of the agent formally is therefore to rank different capability sets. This paper explores the problem of ranking capability sets in terms of the standard of living offered to the agent. For this purpose, we consider capability sets that are non-degenerate, compact, comprehensive and convex subsets of the $n$-dimensional real space, propose several intuitively plausible properties for the ranking and give characterizations of some ranking rules.