I learned a lot from Sen's and Foster's book. It is an important key to the understanding of inequality measures. Especially the welfare funcion seems to be a much better measure to describe income than the average per capita income or the median.
I, however, have one objection. Sen is careful enough not to completely reject Theil's formula (see formula 2.11 in "On Economic Inequality"). And although Sen and James E. Foster are puzzled by the application of entropy to economics, they seemingly also feel, that it is interesting enough to be discussed.
Unfortunately though, Sen called Theil's formula not only "interesting", but also "arbitrary". Here is an example for how Sen's further comments on Theil's measure successfully inhibited other researchers to develop an understanding for entropy measures. "Sen ... describes the major flaw in T very nicely when he states that it 'is not a measure that is exactly overflowing with intuitive sense'. Why then would econometricians - or anyone else - want to use T?" This response (from a participant from Macquarie University, 1991 Conference of the Australian Association for Research in Education) is regrettable. I wish, Sen and Foster would reevaluate entropy measures and their application to the measurement of inequality.
(Sen is not completely wrong. He is puzzled by the non-entropical behaviour of the "Theil-Entropy". What is wrong here is calling Theil's index an entropy. That is a popular mistake. The index is not an entropy. It is an redundancy (ISO/IEC DIS 2382-16:1996), that is, the difference between the maximum entropy and the presently effective entropy of a system.)
"Intuitive" understanding of entropy is rare. (That is why confusing entropy problems with energy problems is common.) The major flaw in evaluating entropy measures often is lack of common knowledge in physics as well as lack of intuition. If sociologists and economists don't trust physicists or engineers, they at least should observe how the "Shannon index" is used in statistical ecology.
As for economics, you find excellent examples for how to use Theil's measure in James K. Galbraith's "Created Unequal" (1998, ISBN 0-684-84988-7).