#USEconomy #GiniCoefficient

The 'Gini Coefficient' is a measure of inequality. 0 means everybody has the same amount of money, 1 means that one person owns everything.
The French Revolution in 1789 happened when the 'Gini' reached 0.82.
This quarter, the US 'Gini' reached 0.83.

#Revolution

Malaysia’s Income Gap Continues to Narrow as Government Adopts Broader Inequality Measures KUALA LUMPUR: Income inequality in Malaysia is continuing on a downward trend, supported by comprehensive monitoring using multiple economic and social indicators, Deputy Economy Minister Mohd Shahar Abdullah said. He noted that findings from the Household Income and Expenditure Survey (HIES) Report 2024 showed the country’s Gini coefficient improved to 0.390 in 2024 from 0.404 …

Malaysia’s Income Gap Continues to Narrow as Government Adopts Broader Inequality Measures #IncomeInequality #Malaysia #EconomicGrowth #SocialEquity #GiniCoefficient

When the rich flaunt their wealth, inequality feels worse, study shows According to new research, people underestimate inequality when they live in segregated social worlds. But when wealth is openly displayed, dissatisfaction rises fast.

No shit, Sherlock!

#inequality
#ginicoefficient

Via Euronews: The rich were quieter after COVID. Now they’re not - and people are noticing
www.euronews.com/business/202...

When the rich flaunt their wealth, inequality feels worse, study shows According to new research, people underestimate inequality when they live in segregated social worlds. But when wealth is openly displayed, dissatisfaction rises fast.

No shit, Sherlock!

#inequality
#ginicoefficient

Via Euronews: The rich were quieter after COVID. Now they’re not - and people are noticing
www.euronews.com/business/202...

US #wealth inequality is shockingly high: the tiny 9%square in the corner? That's half the US population! Poor.

What happens when #AI really kicks in?

#mckinsey #ginicoefficient #wealthinequality #socialism #UBI

Original post on cosocial.ca

Income inequality in Canada, as measured by the Gini coefficient, has changed marginally in the last fifty years, and is lower now than what it was 25 years ago […]

⚖️↔️Resource inequality limits transfer of nutrients from soils to plants in experimental grassland

vist.ly/3y5kj

#EcosystemFunctioning #Ecotron #GiniCoefficient #Grassland #NutrientDynamics #ResourceInequality

T = rSym = (Theil_T[(a,b)] + Theil_T[(a,b)]) / 2 H = zHoover = Hoover inequality ("Robin Hood index") Software to compute theses measures: in https://drive.proton.me/urls/FBYNTG45P4#RafOE8CV1KPf The original source: TheilHooverPlatoGini.hs (Haskell code). I additionally generated TheilHooverPlatoGini.py and TheilHooverPlatoGini.lua using ChatGPT.

Plato_Inequality_Indicator.hs (Haskell code) is here: in https://drive.proton.me/urls/FBYNTG45P4#RafOE8CV1KPf You can use e.g. GhatGPT to convert the code to other languages.

Two experimental inequality measures:
- zPlato
- rAccept and zAccept

The acceptance measure surely is disputable.

#ResearchProposal #TheilIndex #TheilRedundancy #HooverInequality #HooverIndex #RobinHoodIndex #Gini #GiniIndex #GiniCoefficient #PlatoInequality #inequality

See also ALT-text

-- Part 1 -- -- This Haskell code was sent as a prompt to Meta AI: -- Request to Meta AI: -- Not considering computation errors, -- show that both functions are equivalent. -- --------------------------------------------------------------------------------- type GroupSize = Double type GroupRessources = Double type Percentile = (GroupSize, GroupRessources) type AllPercentiles = [Percentile] type Percentiles = [(GroupSize, GroupRessources)] type TheilRedundancy = Double computeTheilT_1 :: Percentiles -> TheilRedundancy computeTheilT_1 allPercentiles = 0.5 * sum [log (a / b) * ((a / aTotal) - (b / bTotal)) | (a, b) <- allPercentiles] where aTotal = sum [a | (a, _) <- allPercentiles] bTotal = sum [b | (_, b) <- allPercentiles] computeTheilT_2 :: Percentiles -> TheilRedundancy computeTheilT_2 allPercentiles = 0.5 * sum [theilTab a b aTotal + theilTba a b bTotal | (a, b) <- allPercentiles] where aTotal = sum [a | (a, _) <- allPercentiles] bTotal = sum [b | (_, b) <- allPercentiles] theilTab a b aTotal = a * log (a / b) / aTotal theilTba a b bTotal = b * log (b / a) / bTotal -- --------------------------------------------------------------------------------- main :: IO () main = do let percentiles = [(10, 10), (20, 400), (30, 9000), (40, 160000)] let theilT_1 = computeTheilT_1 percentiles let theilT_2 = computeTheilT_2 percentiles print ("Theil T (1): " ++ show theilT_1) print ("Theil T (2): " ++ show theilT_2) {- > .\SymmetricTheilT.exe "Theil T (1): 1.2577697898110196" "Theil T (2): 1.2577697898110196" -}

-- Part 2 -- main :: IO () main = do let percentiles = [(10, 10), (20, 400), (30, 9000), (40, 160000)] let theilT_1 = computeTheilT_1 percentiles let theilT_2 = computeTheilT_2 percentiles print ("Theil T (1): " ++ show theilT_1) print ("Theil T (2): " ++ show theilT_2) {- > .\SymmetricTheilT.exe "Theil T (1): 1.2577697898110196" "Theil T (2): 1.2577697898110196" -} {- Answer from Meta AI: Let's expand theilTab a b aTotal + theilTba a b bTotal: theilTab a b aTotal + theilTba a b bTotal = 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) This is equivalent to the expression in computeTheilT_1. Therefore, both functions are equivalent. The output of your program also confirms this, as both theilT_1 and theilT_2 have the same value. -}

Symmetrized Theil-T Redundancy:

½ (a * ln (a / b) / aTotal + b * ln (b / a) / bTotal)

and

½ ln (a / b) * (a / aTotal - b / bTotal)

are equivalent.

#Theilindex #TheilRedundancy #GiniIndex #Ginicoefficient

Data source: 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 Wealth Distribution (Grouping: Wealth per Income Percentile) Percentiles: Category|Groupsize pct99to100|1.0% pct80to99|19.0% pct60to80|20.0% pct40to60|20.0% pct20to40|20.0% pct00to20|20.0% year|Plato|Gini 1990|42.51%|39.19% 1991|42.91%|39.32% 1992|42.84%|39.27% 1993|43.66%|39.73% 1994|43.96%|39.61% 1995|44.88%|39.78% 1996|45.57%|40.44% 1997|46.50%|41.41% 1998|47.60%|42.64% 1999|48.05%|43.82% 2000|48.24%|44.77% 2001|46.69%|44.13% 2002|46.37%|43.47% 2003|47.35%|43.37% 2004|50.07%|44.43% 2005|51.24%|45.46% 2006|52.68%|46.94% 2007|54.07%|48.42% 2008|52.48%|47.88% 2009|50.52%|47.23% 2010|51.07%|48.40% 2011|52.11%|49.52% 2012|53.18%|50.46% 2013|54.57%|51.61% 2014|55.97%|52.87% 2015|56.60%|53.48% 2016|56.98%|53.76% 2017|57.53%|53.95% 2018|57.60%|53.67% 2019|57.87%|53.64% 2020|56.56%|52.85% 2021|57.28%|53.58% 2022|55.18%|51.88% 2023|55.50%|52.28% 2024|56.48%|53.19%

This is about the distribution of wealth (net worth) in the US from 1990 to 2024. It's not an income distribution even though the percentiles are six income groups (see ALT-Text).

Inequality indicators, #Ginicoefficient, #Platoinequality

The gini-coefficient (measure of income inequality) is so high in San Francisco (at 0.5172) that only developing countries with high levels of corruption are as unequal, e.g. Colombia (0.539), Eswatini (0.546). #economics #ginicoefficient #sanfrancisco

Gintropy: Gini Index Based Generalization of Entropy by Tamás S. Biró [ORCID] and Zoltán Néda [ORCID] Wigner Research Centre for Physics, 1121 Budapest, Hungary Complexity Science Hub, 1080 Vienna, Austria Department of Physics, Babeş-Bolyai University, 400084 Cluj-Napoca, Romania Author to whom correspondence should be addressed. Entropy 2020, 22(8), 879; https://doi.org/10.3390/e22080879 Submission received: 9 July 2020 / Revised: 7 August 2020 / Accepted: 8 August 2020 / Published: 10 August 2020 Abstract Entropy is being used in physics, mathematics, informatics and in related areas to describe equilibration, dissipation, maximal probability states and optimal compression of information. The Gini index, on the other hand, is an established measure for social and economical inequalities in a society. In this paper, we explore the mathematical similarities and connections in these two quantities and introduce a new measure that is capable of connecting these two at an interesting analogy level. This supports the idea that a generalization of the Gibbs–Boltzmann–Shannon entropy, based on a transformation of the Lorenz curve, can properly serve in quantifying different aspects of complexity in socio- and econo-physics. Keywords: entropy; Gini index; socio-economic inequalities; econophysics

Gintropy: Gini Index Based Generalization of Entropy
by Tamás S. Biró [ORCID] and Zoltán Néda [ORCID]

@orcid.org

#entropy #entropymeasures
#Giniindex #Ginicoefficient #Gini
#socioeconomicinequalities
#econophysics

www.mdpi.com/1099-4300/22...

# Example in Python for how to compute the Plato inequality indicator: # Goetz Kluge, 2025-06-25 import math # Compute rSym (symmetrized Theil redundancy) from a table of pairs (a,b). def compute_theil_redundancy(pairs): a_total = sum(a for a, _ in pairs) b_total = sum(b for _, b in pairs) return 0.5 * sum(math.log(a / b) * ((a / a_total) - (b / b_total)) for a, b in pairs) def theil2atkinson(redundancy): return 1 - math.exp(-redundancy) # Compute zSym (symmetrized Atkinson inequality indicator) def plato2atkinson(a): return 1 - ((1 - a) / (1 + a)) ** a # zPlato: Convert zSym to zPlato using the Newton-Raphson iteration.def atkinson2plato(z_sym) def deriv(a): d = (1 - a) / (1 + a) return -d ** a * (math.log(d) - 2 * a / (1 - a ** 2)) def func(a, b): return plato2atkinson(a) - b def newton_raphson(a, b, iter, tol): if iter >= 100 or abs(func(a, b)) < tol: return a, iter else: return newton_raphson(a - func(a, b) / deriv(a), b, iter + 1, tol) if z_sym >= 0.99999999999999: return 1, 0 elif z_sym <= 0: return 0, 0 elif z_sym < 0.001: return math.sqrt(z_sym * 0.5), 0 else: initial_guess = 0.18992 + 0.72791 * z_sym return newton_raphson(initial_guess, z_sym, 0, 1e-12) # -- Usage example: def main(): data_points = [(50, 2.5), (40, 47.5), (9, 27), (1, 23)] r_sym = compute_theil_redundancy(data_points) z_sym = theil2atkinson(r_sym) z_plato, steps = atkinson2plato(z_sym) print(f"rSym: {r_sym}") print(f"zSym: {z_sym}") print(f"zPlato: {z_plato}") print(f"Newton-Raphson iterations: {steps}") if __name__ == "__main__": main() # rSym: 1.161710269336159 # zSym: 0.6870495067042661 # zPlato: 0.6880377297113732 # Newton-Raphson iterations: 3

-- Example in Haskell for how to compute the Plato inequality indicator -- Goetz Kluge, 2025-06-25 -- Compute rSym (symmetrized Theil redundancy) from a table of pairs (a,b). type PairsTable = [(Double,Double)] type RSym = Double computeTheilRedundancy :: PairsTable -> RSym computeTheilRedundancy pairs = 0.5 * sum [log (a / b) * ((a / aTotal) - (b / bTotal)) | (a, b) <- pairs] where aTotal = sum [a | (a, _) <- pairs] bTotal = sum [b | (_, b) <- pairs] -- Compute zSym (symmetrized Atkinson inequality indicator) theil2Atkinson :: Double -> Double theil2Atkinson redundancy = 1 - exp (-redundancy) -- zPlato: Convert zSym to zPlato using the Newton-Raphson iteration. atkinson2Plato :: Double -> (Double, Int) atkinson2Plato 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 :: Double -> Double -> Int -> Double -> (Double, Int) 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 = plato2atkinson a - b plato2atkinson :: Double -> Double plato2atkinson a = 1 - ((1 - a) / (1 + a)) ** a -- Usage example: main :: IO () main = do let dataPoints = [(50,2.5),(40,47.5),(9,27),(1,23)] let rSym = computeTheilRedundancy dataPoints let zSym = theil2Atkinson rSym let (zPlato, steps) = atkinson2Plato zSym putStrLn $ "rSym: " ++ show rSym putStrLn $ "zSym: " ++ show zSym putStrLn $ "zPlato: " ++ show zPlato putStrLn $ "Newton-Raphson iterations: " ++ show steps

Alternative to: #Gini #GiniIndex #GiniCoefficient

The basic operations to compute the Platon inequality indicator from a set of data pairs now are explained not only in Haskell, but also in Python.

web.archive.org/web/20250625...

#inequality #Theil #Atkinson #Plato #Platoinequality #Hoover

Wealth of the top 0.0001% in the US as a share of total US wealth. (Top 0.0001% = 19 richest American households in 2024, 4 richest households in 1913)

#inequality | inequality | #oligarchs | oligarchs | This also might be interesting for people who search for #Gini or #GiniCoefficient

Image from image_1.jpg

In Q4 2024, the top 10% in the eurozone owned 57.3% of household wealth, up from 54.5% in 2009. The Gini index, with Sweden at 75 and Belgium at 46, shows increasing inequality. Experts advise considering wealth distribution for a clearer picture.

#WealthInequality #Eurozone #GiniCoefficient

With #DAO , we see voting power inevitably ends up with founders and big backers, not the public. www.dlnews.com/articles/def...

The #GiniCoefficient (rating #Equality ) rates DAOs as 99/100 (highly unequal): The most-corrupt countries average 60-70/100. ccaf.io/defi/protoco...

We are not the richest country on the face of the Earth…. We rank at number 20 on the #HDI #HumanDevelopmentIndex and on the #GINICoefficient even worse as “medium inequality.” We must resist #populism and focus on educating the electorate. Populism is what’s leading to #fascism. #Canada is richer.

#OECD chart showing #Canada had one of the smallest gains in its #GiniCoefficient from the mid 80s to the early 2020s
#inequality

I discovered that the #wealthdisparity we're seeing today versus where it was at the time of the #FrenchRevolution as of 2023 [using the #GINIcoefficient scale]:

Scale is 0-1:
0=perfect, 1=worst

US (2023): .47 or 47%
France (1780s): .59 or 59%

We REALLY need to stop this from going up further.🥺

I discovered that the #wealthdisparity we're seeing today versus where it was at the time of the #FrenchRevolution as of 2023 [using the #GINIcoefficient scale]:

Scale is 0-1:
0=perfect, 1=worst

US (2023): .47 or 47%
France (1780s): .59 or 59%

We REALLY need to stop this from going up further.🥺

#LamborghiniReform + #ginicoefficient = #Lamborghinicoefficient ? #dkpol #finderselvud

#LamborghiniReform + #ginicoefficient
= #Lamborghinicoeffient ?
#dkpol #finderselvud

A better number to celebrate than #Dow20k would be if we got our pre-tax #GiniCoefficient below 40%. Unfortunately it's still above that