Summary:
How do we define the standard of living? It's tempting to use a utilitarian (with respect to pleasure, desire-fulfillment, or choice) definition, but using any of these utilitarian measures as the sole basis of the standard of living seems flawed. Against pleasure utilitarianism: if someone is starving and overworked but is satisfied due to heavy social condition, would we consider them to have a good standard of living? Against desire and choice utilitarianism: while desire and choice provide evidence of what people value, it is hard to believe that they are perfectly correlated with value. Instead, Sen prefers to measure the standard of living via functionings (achievements of particular conditions) and capabilities (the ability to achieve).
An approach to evaluating the standard of living of someone or of a population must balance two conflicting factors: relevance (adequately captures the richness of our idea of the standard of living) and usability (practical to actually assess). Also, it is acceptable for an approach to be unable to compare two sets of conditions; an approach can be useful even if it does not generate a total ordering of preferred conditions.
(I only read the two lectures by Sen, "The Standard of Living: Lecture I, Concepts and Critiques" and "The Standard of Living: Lecture II, Lives and Capabilities". These are freely available online as PDFs in the University of Utah's library of Tanner lectures, though these PDFs are missing a couple pages in the beginning. The remaining two-thirds of the 140-page book that this Goodreads listing refers to consists of essays responding to Sen's lectures.)