IneqComps

(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

Symmetrizing the Theil-T redundancy.

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

> .\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)

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 %.

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

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.

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

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

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 III: Capital Why is capital so concentrated and why so few have it?

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...

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

bsky.app/profile/ineq...

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

bsky.app/profile/ineq...

List of countries by income inequality

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

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

“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...

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

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

bsky.app/profile/ineq...

‘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

“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/...

Thank you for the video.

(D_KL(p||q)+D_KL(q||p))/2 is a symmetrized D_KL. Do you know applications where it is used?

You’re welcome.

What exactly do you think I am “defending”?

You don’t know my way.

Anyway, it’s your claim that we want equality. So it’s on you to prove that. But it also could be that a zero income Gini isn’t what you want. Right?

Do we want equality?

You might like this; bsky.app/profile/ineq...

The Indian propaganda did not make clear that the World Bank used consumption data for computing a Gini index. Thus, that index isn’t about income distribution.

What is a morally virtuous Gini coefficient? bsky.app/profile/ineq...

As the graph shows, that was the Gini index for the income distribution.

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.

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

That seems to be the Gini index for income distribution. Below 0.4 is not terribly bad.

The Indian propaganda does not make clear, that the World Bank data used to compute the Gini index are about consumption, not about incomes.

The Worldbank computed the Gini for the distribution of consumption, not from the distribution of incomes.

In dem Zusammenhang auch interessant: bsky.app/profile/ineq...