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Calling #Theil's #inequality measure an "#entropy" irritated #AmartyaSen. From Amartya Sen's "#OnEconomicInequality" (#OEI) I learned a lot about #InequalityMeasures. But entropy seems not do go down too well with him (1973) and his co-author #JamesEricFoster (1997): When describing the "interesting" "#TheilEntropy" (chapter 2.11), Sen sees a contradiction between entropy being a measure of "#disorder" in #thermodynamics and entropy being a measure for "#equality".
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If you assume that equality is "order" and thus a antonym for "disorder", then you may believe - Sen even calls it a "fact" - that the #TheilCoefficient is computed from an "#ArbitraryFormula".
However, there is no contradiction: The Theil index is a #redundancy, where the actual redundancy (ISO/IEC 2382-16) of a system is computed as the #MaximumEntropy of that system minus the actual entropy of that system. That is the answer to Sen's objection!
«Any city however small, is divided at least into two,
one the city of the poor, the other of the rich;
these are hostile to each other.» (#Plato, #Politeia, 370 BC)
#Phyton2 script https://inequality.snrk.de/oei/ for computing the #inequality measures described in #AmartyaSen's #OEI. I added my own inequality measure to the big zoo of inequality measures. The "Plato index" is hidden in the script.
I wrote this hack many years ago and now would need quite some time to remember, what I did then.
![#!/usr/bin/python2
'''
The following script explains how to compute inequality indices.
First some formulas from Amartya Sen's and James E. Foster's book
"On Economic Inequality" (1973/1997) are implemented:
(1) Entropy of expected information content (2.11 on pg.35, A. Sen)
(2) Theil's measure (redundancy of the expected information content)
(2.12 on pg.35, A. Sen)
(3) Atkinson family (Chapter A.2.2, pg.128, J. E. Foster)
(4) Generalized entropy class (Chapter A.4.1, pg.140, J. E. Foster)
Then further inequality computation routines are shown:
(5) Redundancy R (R[1] = Theil[1])
(6) Gini-Hoover index for societies devided into two a-fractiles:
Gini index and Hoover index computed from Theil index
(7) Gini Index,Hoover Index, three versions of the Theil[1] redundancy
(without any inequality aversion parameters) and the Lorenz curve.
This routine is wrapped into the class GiniHooverTheil(), where I
may add some functionality later.
The last chapter allows you to run experiments with the previous function and
the GiniHooverTheil() class. ...
(8) For your experiments
G.Kluge, Munich, 2008-11-17](https://cdn.masto.host/zirkus/media_attachments/files/109/415/300/860/234/170/original/45bd8b4d54894292.png "#!/usr/bin/python2
'''
The following script explains how to compute inequality indices.
First some formulas from Amartya Sen's and James E. Foster's book
\"On Economic Inequality\" (1973/1997) are implemented:
(1) Entropy of expected information content (2.11 on pg.35, A. Sen)
(2) Theil's measure (redundancy of the expected information content)
(2.12 on pg.35, A. Sen)
(3) Atkinson family (Chapter A.2.2, pg.128, J. E. Foster)
(4) Generalized entropy class (Chapter A.4.1, pg.140, J. E. Foster)
Then further inequality computation routines are shown:
(5) Redundancy R (R[1] = Theil[1])
(6) Gini-Hoover index for societies devided into two a-fractiles:
Gini index and Hoover index computed from Theil index
(7) Gini Index,Hoover Index, three versions of the Theil[1] redundancy
(without any inequality aversion parameters) and the Lorenz curve.
This routine is wrapped into the class GiniHooverTheil(), where I
may add some functionality later.
The last chapter allows you to run experiments with the previous function and
the GiniHooverTheil() class. ...
(8) For your experiments
G.Kluge, Munich, 2008-11-17")