IneqComps
@ineqcomps.bsky.social
This account (by @goetzkluge.bsky.social) mainly is about inequality measures. A special focus is on the symmetrized Theil-T redundancy.
Pinned
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.
Reposted by IneqComps
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.](https://cdn.bsky.app/img/feed_thumbnail/plain/did:plc:mxbe4sjpwj7pk547n2w3aiki/bafkreiatvn73mxem6rmyikekjzh4k3fott5iiraszejdmxl42dnbaumj6a@jpeg)
July 23, 2025 at 8:32 PM
Yoram Amiel, “Thinking about Inequality”, 2011
Reposted by IneqComps
July 7, 2025 at 9:17 AM
Reposted by IneqComps
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...
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...
July 6, 2025 at 10:21 AM
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...
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...
Reposted by IneqComps
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?
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?
October 19, 2025 at 10:00 PM
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?
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?
Reposted by IneqComps
Still waiting for it to trickle down...
October 6, 2025 at 1:01 AM
Still waiting for it to trickle down...
Reposted by IneqComps
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
September 14, 2025 at 6:00 AM
Das Statistische Bundesamt beschönigt die Armutszahlen, kritisiert Armutsforscher Christoph Butterwegge. Not und Elend werden sich verschärfen.
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](https://cdn.bsky.app/img/feed_thumbnail/plain/did:plc:mxbe4sjpwj7pk547n2w3aiki/bafkreic7dmimzwwqtlkjgsni2v56okplyggrnp473hmlhrncpmv6xvcg4e@jpeg)
September 9, 2025 at 11:08 AM
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.
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.
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.
August 11, 2025 at 7:32 PM
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.
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.
Reposted by IneqComps
Symmetrizing the Theil-T redundancy.
(With σ=0, it turns into the Hoover index.)
(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](https://cdn.bsky.app/img/feed_thumbnail/plain/did:plc:mxbe4sjpwj7pk547n2w3aiki/bafkreif7iomuipczdvtvfqfi4fnqx3ks5tssh4hcfnm5yk5slpsvwbmfoy@jpeg)
July 8, 2025 at 6:37 PM
Symmetrizing the Theil-T redundancy.
(With σ=0, it turns into the Hoover index.)
(With σ=0, it turns into the Hoover index.)
Reposted by IneqComps
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 %.
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 %.
July 9, 2025 at 11:59 AM
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 %.
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 %.
Reposted by IneqComps
The two groups assembly and the eleven groups assembly have the same symmetrized Theil redundancy.
July 24, 2025 at 7:09 AM
The two groups assembly and the eleven groups assembly have the same symmetrized Theil redundancy.
Reposted by IneqComps
Reposted by IneqComps
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
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
June 4, 2025 at 2:58 PM
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
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
Reposted by IneqComps
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
July 6, 2025 at 6:45 PM
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
Reposted by IneqComps
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👇
New Capitalism II:
Compositional vs income inequality
Are all class-based societies unequal?
branko2f7.substack.com/p/new-capita...
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
July 27, 2025 at 11:19 AM
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👇
Reposted by IneqComps
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/p/the-new-ca...
New capitalism III: Capital
Why is capital so concentrated and why so few have it?
branko2f7.substack.com
August 3, 2025 at 12:20 PM
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/p/the-new-ca...
August 6, 2025 at 3:46 AM
Reposted by IneqComps
“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
August 6, 2025 at 12:19 AM
“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...
Reposted by IneqComps
“The lessons he has drawn are often striking: #people are fundamentally #egalitarian but are led to #collapses by enriched, status-obsessed #elites, while past collapses often improved the lives of ordinary citizens.” www.theguardian.com/environment/...
‘Self-termination is most likely’: the history and future of societal collapse
An epic analysis of 5,000 years of civilisation argues that a global collapse is coming unless inequality is vanquished
www.theguardian.com
August 2, 2025 at 1:36 PM
“The lessons he has drawn are often striking: #people are fundamentally #egalitarian but are led to #collapses by enriched, status-obsessed #elites, while past collapses often improved the lives of ordinary citizens.” www.theguardian.com/environment/...
Yoram Amiel, “Thinking about Inequality”, 2011
July 23, 2025 at 8:32 PM
Yoram Amiel, “Thinking about Inequality”, 2011
![https://www.jstor.org/stable/43965822
J-divergence measurements of economic inequality
Nicholas Rohde
Journal of the Royal Statistical Society. Series A (Statistics in Society)
Vol. 179, No. 3 (JUNE 2016), pp. 847-870 (24 pages)
Published By: Oxford University Press
--------------------------------------------------
J. R. Statist. Soc. A (2016)
179, Part 3, pp. 847-870
J-divergence measurements of economic inequality
Nicholas Rohde
Griffith University, Gold Coast, Australia
[Received January 2014. Final revision September 2015]
Summary. The paper uses a symmetric entropy statistic to study income inequality. The index distrition in into mairarion reto ace disay men, and then rant tom original. This alowe
the measure to be interpreted as an average of n income-to-mean divergences such that the inequality estimate can be broken down into contributions across population subgroups. Various properties of the index are analysed and an application comparing the USA, Germany and Britain is provided. We focus on the sensitivity of inequality to the tails of the income distribution and show that the extreme right-hand tail accounts for a large and generally increasing proportion of total inequality. This result holds even if incomes are measured at the household level, averaged over a 5-year period and taken after government taxes and transfers.
Keywords: Distance; Divergence; Inequality; Information theory](https://cdn.bsky.app/img/feed_thumbnail/plain/did:plc:mxbe4sjpwj7pk547n2w3aiki/bafkreiadmctzslltbun4nwwmablwudznjc6gnk362a5ntd3zsry3rke2se@jpeg)