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IneqComps

@ineqcomps.bsky.social

60 followers 200 following 180 posts

This account (by @goetzkluge.bsky.social) mainly is about inequality measures. A special focus is on the symmetrized Theil-T redundancy.

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IneqComps @ineqcomps.bsky.social · Jun 29

That quote gave me the idea to develop the Plato inequality measure. If you compute the Plato measure for some group A devided into a few percentiles, then the Plato measure tells you what kind of group B devided into just two percentiles would have the same Theil Redundancy as group A.

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)

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IneqComps @ineqcomps.bsky.social · 8d

The Dual Challenge of Tolerable Economic Inequality: A Multidisciplinary Analysis of Definition Dilemmas and the Risks of Acceptable Disparities
By Maurizio Bovi
2nd edition, 2025-08-02

https://link.springer.com/book/10.1007/978-3-031-97066-5

Series (Ed. Jaques Silber): Economic Studies in Inequality, Social Exclusion and Well-Being

This book tackles two central challenges in the discourse on economic inequality. First, there is no consensus on what constitutes a morally acceptable inequality, as even philosophers struggle to conceptualize benchmarks for distinguishing between acceptable and unacceptable disparities. Second, while tolerable inequality has the potential to evolve into systemic patterns of polarization, segregation, and discrimination, it can ultimately escalate into unjustifiable inequality. This self-reinforcing cycle complicates efforts to achieve equitable distributions.

The book explores these challenges in two sections through a multidisciplinary lens. Part one discusses distributive justice and philosophical debates surrounding inequality’s acceptable boundaries. Part two employs the concept of social aggregations—such as families, cities, firms, and nations—to examine how even initially tolerable inequality can spread and intensify through interconnected social systems. By emphasizing the relational nature of inequality, the book underscores its systemic complexity and the need for holistic understanding.

1 Introduction

Part I Challenge One: No Consensus on What Constitutes Morally Tolerable Economic Inequality
2 Some Preliminary Considerations on Distributive Justice --- 13
3 Tolerable Inequality According to Radical Egalitarians --- 23
4 Tolerable Inequality According to Desert-Based and Meritocratic Theories --- 31
5 Tolerable Inequality According to Utilitarians -- 45
6 Tolerable Inequality According to John Rawls --- 59
7 Tolerable Inequality According to Amartya Sen --- 73

Part II Challenge Two: Tolerable Economic Inequality Can Turn Intolerable
8 Economic Inequality and the Family --- 93
9 Economic Inequality and the City --- 119
10 Economic Inequality and the Firm --- 139
11 Economic Inequality and the Nation --- 167

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IneqComps @ineqcomps.bsky.social · Jul 23

Yoram Amiel, “Thinking about Inequality”, 2011

What is inequality? In recent years [before 2011] there has been an explosion of interest in the subject that has yielded a substantial body of formal tools and results for income-distribution analysis. But does the standard axiomatic structure coincide with public perceptions of inequality? Or is the economist's concept of inequality a thing apart, perpetuated through serial brainwashing in the way the subject is studied and taught? Amiel and Cowell examine the evidence from a large international questionnaire experiment using student respondents. Along with basic "cake-sharing" issues, related questions involving social-welfare rankings, the relationship between inequality and overall income growth and the meaning of poverty comparisons are considered.

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IneqComps @ineqcomps.bsky.social · Jul 7

Decomposition of Income Inequality by Subgroups

openknowledge.fao.org/server/api/c...

https://openknowledge.fao.org/server/api/core/bitstreams/35c2d071-828b-45bf-97bc-7ba5d817f458/content

© FAO December 2006

EASYPol
On-line resource materials for policy making

Policy Impacts on Inequality

Decomposition of Income Inequality by Subgroups

by
Lorenzo Giovanni Bellù, Agricultural Policy Support Service, Policy Assistance Division, FAO, Rome, Italy
Paolo Liberati, University of Urbino, "Carlo Bo", Institute of Economics, Urbino, Italy

for the

Food and Agriculture Organization of the United Nations, FAO

Table of contents
1. Summary..................................................................................1
2. Introduction.............................................................................1
3. Conceptual background............................................................2
3.1. The analysis of variance..................................................................2
3.2. The Gini Index...............................................................................3
3.3. The Theil Index.............................................................................4
4. A step-by-step procedure to decompose inequality..................6
4.1. A step-by-step procedure for the analysis of variance.........................6
4.2. A step-by-step procedure to decompose the Gini Index.......................7
4.3. A step-by-step procedure to decompose the Theil Index......................8
5. A numerical example of how to decompose inequality indexes9
5.1 An example of how to perform the analysis of variance........................9
5.2. An example of how to decompose the Gini Index..............................11
5.3. An example of how to decompose the Theil Index............................15
6. A Synthesis............................................................................15
7. Readers’ notes.......................................................................16
7.1. Time requirements.......................................................................16
7.2. EASYPol links..............................................................................16
7.3. Frequently asked questions...........................................................17
8. References and further reading.............................................17
Module metadata...........................................................................18

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IneqComps @ineqcomps.bsky.social · Jul 6

Not all inequality measures were created equal
The measurement of wealth inequality, its decompositions, and an application to European household wealth

Rita Neves Costa, Sébastien Pérez-Duarte

December 2019

www.ecb.europa.eu/pub/pdf/scps...

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Robert Reich @rbreich.bsky.social · 13d

The 100 lowest-paying US corporations spent $644B on stock buybacks from 2019 to 2024.

Buybacks artificially boost share prices and inflate CEO pay.

The typical worker at these companies earned $35k last year.

Meanwhile, the average CEO was paid $17.2M

See the problem?

370 5.1K 15K

IneqComps @ineqcomps.bsky.social · 23d

#Oxfam, 2025-10-09

#Accountability
#Democracy
#EuropeanUnion
#FiscalJustice
#Governance
#Inequality
#ProgressiveTaxation
#TaxAvoidance
#TaxTheSuperRich
#WealthRedistribution
#WealthTax

policy-practice.oxfam.org/resources/a-...

Oxfem: A European agenda to tax the super-rich: A solution to inequality in the European Union

2025-10-09
53 pages long
Languages: English

Overview: Europe faces a deep inequality crisis: the richest 1% in the EU own nearly a quarter of all wealth while half the population shares just 3%. Decades of tax cuts for the wealthy and corporations resulted in the super-rich paying proportionally less taxes than ordinary citizens, eroding fairness, democracy, and social cohesion. The EU lacks harmonized policies to curb extreme wealth concentration and tax avoidance of the wealthiest. Oxfam calls for bold reforms, such as an EU-wide or national tax on the super-rich and transparency mechanisms like an EU assets registry, to fund social needs, climate action, and development. Taxing the super-rich is widely supported, is feasible and is urgent.
Keywords

Accountability
Democracy
European Union
Fiscal justice
Governance
Inequality
Progressive taxation
Tax avoidance
Tax the super-rich
wealth redistribution
Wealth tax

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Robert Reich @rbreich.bsky.social · 26d

Still waiting for it to trickle down...

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IneqComps @ineqcomps.bsky.social · Sep 15

... consumtion Gini ...

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Surplus | Das Wirtschaftsmagazin @surplusmagazin.bsky.social · Sep 14

Das Statistische Bundesamt beschönigt die Armutszahlen, kritisiert Armutsforscher Christoph Butterwegge. Not und Elend werden sich verschärfen.

Armutsforscher Butterwegge: »Not, Elend und Verwahrlosung werden zunehmen«

Das Statistische Bundesamt beschönigt die Armutszahlen, kritisiert Armutsforscher Christoph Butterwegge. Not und Elend werden sich verschärfen.

www.surplusmagazin.de

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IneqComps @ineqcomps.bsky.social · Sep 9

With zPlato you get an inequality measure which behaves quite similar to the Gini index. However, zPlato is much more sensitive to small groups of very poor people. That's not "woke" as it reflects a real risk: Already today's techologies provide horrible weapons to single frustrated individuals.

zSym = 1 - exp(-rSym)

--------------------------

(log is the logarithm with the base e, the natural logarithm.)

Theil_T[(a,b)] + Theil_T[(b,a)]
= a * log (a / b) / aTotal + b * log (b / a) / bTotal
= a * (log a - log b) / aTotal + b * (log b - log a) / bTotal
= a * log a / aTotal - a * log b / aTotal + b * log b / bTotal - b * log a / bTotal
= log a * (a / aTotal - b / bTotal) - log b * (a / aTotal - b / bTotal)
= (log a - log b) * (a / aTotal - b / bTotal)
= log (a / b) * (a / aTotal - b / bTotal)

Theil_sym = rSym = 1/2 * sum( log (a / b) * (a / aTotal - b / bTotal))
Theil_sym = rSym = 1/2 * sum(abs(log (a / b) - k)**(σ=1) * abs(a / aTotal - b / bTotal))
k = log (aTotal / bTotal)

σ is a parameter which controls how "entropic" the indicator is. Default is σ = 1.
If σ = 0, the symmetrized Theil redundancy turns into the Hoover index ("Robin Hood index").

-----------------------------

Keywords: Theil index, Theil redundancy, Theil-T, Theil_sym, Theil_symCDF, inequality, inequity, entropy measures, inequality measures, inequality indicators, Gini index, Gini coefficient, Gini replacement, symmetric Theil redundancy, zSys, rSys, IneqComps

-- ---- zPlato to zSym ---- --
zSym=1-exp(-rSym)=1-((1-zPlato)/(1+zPlato))**zPlato

-- ---- zSym to zPlato (Haskell code) ---- --

-- types --
type ZSym = Double -- Symmetric redundancy measure
type ZPlato = Double -- Plato inequality indicator
type InitialGuess = Double -- InitialGuess of zPlato for Newton-Raphson iteration
type MaxError = Double -- Maximum error for Newton-Raphson iteration
type Iterations = Int -- Number of Newton-Raphson iterations
type IterationsStartValue = Int -- Start value for Newton-Raphson iterations (usually set to 0)

-- zPlato: Convert zSym to zPlato using the Newton-Raphson iteration.
zSym2zPlato :: ZSym -> (ZPlato, Iterations)
zSym2zPlato zSym
| zSym >= 0.99999999999999 = (1,0)
| zSym <= 0 = (0,0)
| zSym < 0.001 = (sqrt (zSym * 0.5), 0)
| otherwise =
let initialGuess = 0.18992 + 0.72791 * zSym
in newtonRaphson initialGuess zSym 0 1e-12
newtonRaphson :: InitialGuess -> ZSym -> IterationsStartValue -> MaxError -> (ZPlato, Iterations)
newtonRaphson a b iter tol
| iter >= 100 || abs (func a b) < tol = (a, iter)
| otherwise = newtonRaphson (a - func a b / deriv a) b (iter + 1) tol
deriv :: Double -> Double
deriv a =
let d = (1 - a) / (1 + a)
in -d ** a * (log d - 2 * a / (1 - a ** 2))
func :: Double -> Double -> Double
func a b = zPlato2zSym a - b
zPlato2zSym :: ZPlato -> ZSym
zPlato2zSym a = 1 - ((1 - a) / (1 + a)) ** a

-- Plato_Inequality_Indicator.hs (Haskell code) also is here:
in https://drive.proton.me/urls/FBYNTG45P4#RafOE8CV1KPf

-- You can use e.g. ChatGPT or other AI services to convert the code to other languages.

IneqComps @ineqcomps.bsky.social · Aug 20

How did the USA sink into its current state? By allowing a narcissistic felon and sociopath to assemble an incompetent administration and to troll the US citizens and the rest of the world?

IneqComps @ineqcomps.bsky.social · Aug 12

Journalistisch seriöser wäre: "Sogenannte Wirtschaftsweise will Soziales kürzen und den Reichtum pflegen."

IneqComps @ineqcomps.bsky.social · Aug 11

I just found a "The Plato Index", a measure of tax progressivity devised by Valpy FitzGerald, Oxford University and presented in 2006.
www.taxjustice.net/cms/upload/p...

I devised my Platon Inequality in 2004.

Valpy FitzGerald and I probably both think that Plato was a wise man.

The Plato Index
a new international comparative
measure of tax progressivity
Valpy FitzGerald, Oxford University
Intertax Workshop “Tax, Poverty and Finance for
Development” Essex University 6/7 July 2006
https://www.taxjustice.net/cms/upload/pdf/Valpy_Fitzgerald_06_Plato_Index.pdf

Reposted by IneqComps

IneqComps @ineqcomps.bsky.social · Jul 8

Symmetrizing the Theil-T redundancy.

(With σ=0, it turns into the Hoover index.)

(log is the logarithm with the base e, the natural logarithm.)

Theil_T[(a,b)] + Theil_T[(b,a)]
= a * log (a / b) / aTotal + b * log (b / a) / bTotal
= a * (log a - log b) / aTotal + b * (log b - log a) / bTotal
= a * log a / aTotal - a * log b / aTotal + b * log b / bTotal - b * log a / bTotal
= log a * (a / aTotal - b / bTotal) - log b * (a / aTotal - b / bTotal)
= (log a - log b) * (a / aTotal - b / bTotal)
= log (a / b) * (a / aTotal - b / bTotal)

Theil_sym = rSym = 1/2 * sum( log (a / b) * (a / aTotal - b / bTotal))
Theil_sym = rSym = 1/2 * sum(abs(log (a / b) - k)**(σ=1) * abs(a / aTotal - b / bTotal))
k = log (aTotal / bTotal)

σ is a parameter which controls how "entropic" the indicator is. Default is σ = 1.
If σ = 0, the symmetrized Theil redundancy turns into the Hoover index ("Robin Hood index").

-----------------------------

Keywords: Theil index, Theil redundancy, Theil-T, Theil_sym, Theil_symCDF, inequality, inequity, entropy measures, inequality measures, inequality indicators, Gini index, Gini coefficient, Gini replacement, symmetric Theil redundancy, zSys, rSys, IneqComps

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IneqComps @ineqcomps.bsky.social · Jul 9

With zPlato you can present an inequality indicator in a ratio format.

Example: In the case below zPlato of an assembly with 11 groups is 52%. There is an assembly with just two groups where in the 1st group 76% of people own 24% of all ressources, while in the 2nd group 24% of people own 76 %.

$> .\IneqComps.exe "17906784,7517963|56209266,4941934|133272817,6690138|432264597,12033448| 473801090,6954766|272745562,1968380|71047533,213679|34457325,51702|23561458,16199|10801357,3178|22796674,1798" IneqComps V23 rSym ≥ 0.60044 (symmetric Theil redundancy) zSym ≥ 45.143% (zSym=1-exp(-rSym)) zPlato ≥ 52.040% (Plato inequality, Theil & zSym & Plato equivalent ratio: 76.020:23.980) zGini ≥ 51.086% (Gini inequality, Gini equivalent ratio: 75.543:24.457) zHoover ≥ 35.902% (Hoover inequality, Hoover equivalent ratio: 67.951:32.049)$

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IneqComps @ineqcomps.bsky.social · Jul 24

The two groups assembly and the eleven groups assembly have the same symmetrized Theil redundancy.

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IneqComps @ineqcomps.bsky.social · Jul 24

Plato_Inequality_Indicator.hs (Haskell code) is here:
in https://drive.proton.me/urls/FBYNTG45P4#RafOE8CV1KPf

You can use e.g. ChatGPT or other AI services to convert the code to other languages.

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Reposted by IneqComps

Jia-Bin Huang @jbhuang0604.bsky.social · Jun 4

Kullback–Leibler (KL) divergence is a cornerstone of machine learning.

We use it everywhere, from training classifiers and distilling knowledge from models, to learning generative models and aligning LLMs.

BUT, what does it mean, and how do we (actually) compute it?

Video: youtu.be/tXE23653JrU

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Alon (they/them) @alonlevy.bsky.social · Jul 6

20. @brankomilan.bsky.social calls the transition to the more modern form of inequality homoploutia: the top earners of wages are also often top earners of capital; in the 19th century, they weren't - wage and capital income correlated negatively, because if you have money, why work at all? /end

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Marco Ranaldi @marcoranaldi.bsky.social · Jul 27

Just read @brankomilan.bsky.social's latest on income & compositional inequality. One more point: if AI pushes up the capital share by replacing jobs across skill levels, reducing compositional inequality can help capital complement labor—and prevent income inequality from rising👇

Branko Milanovic @brankomilan.bsky.social · Jul 26

New Capitalism II:
Compositional vs income inequality
Are all class-based societies unequal?
branko2f7.substack.com/p/new-capita...

New Capitalism II: Compositional vs income inequality

Are all class-based societies unequal?

branko2f7.substack.com

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Branko Milanovic @brankomilan.bsky.social · Aug 3

While capitalism rules alone, 85% of the (adult) people in the world have no income from property.
New capitalism III: Capital
Why is capital so concentrated and why so few have it?
branko2f7.substack.com/p/the-new-ca...

New capitalism III: Capital

Why is capital so concentrated and why so few have it?

branko2f7.substack.com

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IneqComps @ineqcomps.bsky.social · Aug 6

Zu hohe #Ungleichverteilung von Resourcen ist Gift für die #Demokratie. Aber was ist eine zu hohe Ungleichverteilung?

bsky.app/profile/ineq...

IneqComps @ineqcomps.bsky.social · Jul 23

Yoram Amiel, “Thinking about Inequality”, 2011

IneqComps @ineqcomps.bsky.social · Aug 6

"What other numbers would he try to fake?"
And what other numbers would he try to hide?

bsky.app/profile/ineq...

IneqComps @ineqcomps.bsky.social · Aug 5

Next: The GOP will let Trump force the FED to hide the statistics of wealth distribution (like DFA: Distributional Financial Accounts, www.federalreserve.gov/releases/z1/...) in the U.S. provided since 1989.

#inequality #wealth #wealthdistribution #FED #JeromePowell #Powell

https://www.federalreserve.gov/releases/z1/dataviz/dfa/distribute/chart/#range:1990.3,2024.4;quarter:142;series:Net%20worth;demographic:income;population:all;units:levels

Keywords: inequality | wealth | wealth distribution | FED | DFA | Distributional Financial Accounts | Jerome Powell | GOP | Republicans | Trump

IneqComps @ineqcomps.bsky.social · Aug 6

List of countries by income inequality

en.m.wikipedia.org/wiki/List_of...

Reposted by IneqComps

Sam Pizzigati @sgp.bsky.social · Aug 6

“Countries with higher levels of income inequality are associated with higher rates of adult obesity and child overweightness, diabetes, mental illness, asthma, drug use and infant mortality.” @lseinequalities.bsky.social @profkepickett.bsky.social blogs.lse.ac.uk/inequalities...

The wealth gap – and the health trap

What drives the differences in population health among rich nations? Kate Pickett on the lower “wellbeing-adjusted” life expectancy of more unequal countries

blogs.lse.ac.uk

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