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Post self-deleted by United-Viking.
Novoblupolia provides U-V with emergency energy reserve
the best Engineers and IT teams are trying to repairing the algorithms
(Arms T-55s with joyous intent)
What are you up to now?
Alright, I just finished watching Death Note, cuz apparently it was a good anime. I'd say good overall, was happy to binge it in one day, and was feeling good about how the anime was going. Then the ending came, and I changed my mind. Anime is 6/10, its overrated not gonna lie, but the ending was just 0/10.
The Model
Here, we will be using an income inequality model described by two parameters, χ and α. The model is I = χ/(1-P)^α, where I is income, P is proportion of the population are below you in income level, χ is the minimum income for a full-time worker, and α is the inequality parameter. It is closer to 1 with higher inequality, and closer to zero with lower inequality. Using this equation, we can calculate many of the parameters shown in NationStates, and some not shown, but that are important, using χ and α, by applying or integrating the formula shown above. It should be noted that this formula assumes a minimum income level, which is simply the constant χ. These derived formulas are shown in appendix A.
This model comes from a Stanford paper on modelling inequality (see references), the description of which is as follows. "It is well known that the upper tail of the income distribution follows a power law. One way of thinking about this is to note that income inequality is fractal in nature, as we document more carefully below. In particular, the following questions all have essentially the same answer: What fraction of the income going to the top 10 percent of earners accrues to the top 1 percent? What fraction of the income going to the top 1 percent of earners accrues to the top 0.1 percent? What fraction of the income going to the top 0.1 percent of earners accrues to the top 0.01 percent? The answer to each of these questions - which turns out to be around 40 percent in the United States today - is a simple function of the parameter that characterizes the power law." (Jones and Kim, 1786)
Applications
As formulas for the average income (which we will call μ) and the average income of the rich (top 10%) divided by the average income of the poor (bottom 10%) (we will call this massive number ι) can be derived, and these formulas are the ones provided by NationStates, we can use them to derive the values of χ and α, and thus the rest of the formulas in appendix A can be expressed in terms of ι and μ. Unfortunately, the only way to compute these numbers is using numerical methods (such as newton's method), as the system of equations generated cannot be inverted using ordinary mathematical functions. The code required to do this is in appendix C.
Results
As an example, Rho Ophiuchi has an average income of 88,084, and has ι, the "inequality score" equal to 14.2647. Using newton's method, we can calculate that χ = 28,383.9 and α = 0.677764. In contrast, the Municipalities of Antarctica has an average income of 199,607, and an "inequality score" equal to 1.20169. Using newton's method, we can calculate that χ = 177,408 and α = 0.111211. Found in appendix B are the other parameters, calculated form the derived χ and α values.
Notice how both the average income of the poor and the average income of the rich calculated using this model are higher than the displayed value in NationStates, when calculated from the income inequality and mean income. This is due to much less complex modelling being used in the internals of NationStates itself, and the values displayed here are likely more realistic.
References
Jones, Charles, and Jihee Kim. "A Schumpeterian Model of TopIncome Inequality." Journal of Political Economy, 2018, vol. 126, no. 5. https://web.stanford.edu/~chadj/inequality.pdf.
Appendix A
Value Type | Formula using χ and α | Formula using ι and μ |
Average income | χ/(1-α) | μ |
Average income of poor (bottom 10%) | (1-0.9^(1-α))∙10χ/(1-α) | N/A |
Average income of rich (top 10%) | 10χ∙0.1^(1-α)/(1-α) | N/A |
Lowest income for a full-time job | χ | N/A |
10th percentile income | χ/0.9^α | N/A |
Median income | χ/0.5^α | N/A |
90th percentile income | χ/0.1^α | N/A |
99th percentile income | χ/0.01^α | N/A |
Income of rich divided by income of poor | (0.1^(1-α))/(1-0.9^(1-α)) | ι |
Appendix B
Value Type | Rho Ophiuchi: (ι, μ) = (14.2647, 88,084) | The Municipalities of Antarctica: (ι, μ) = (1.20169, 199,607) |
α | 0.677764 | 0.111211 |
χ | 28,383.9 | 177,408 |
Average income | 84,084.2 | 199,606 |
Average income of poor (bottom 10%) | 29,403.5 | 178,433 |
Average income of rich (top 10%) | 419,432 | 257,861 |
Lowest income for a full-time job | 28,383.9 | 177,408 |
10th percentile income | 30,484.9 | 179,499 |
Median income | 45,404.5 | 191,624 |
90th percentile income | 135,156 | 229,184 |
99th percentile income | 643,576 | 296,090 |
Income of rich divided by income of poor | 14.2647 | 1.20169 |
Appendix C
i = 14.2647#this is inequality
m = 88084.0#this is average income
import numpy as np
def f1x(x,y):
f1x = 0
return f1x
def f1y(x,y):
f1y = (((0.1**(1-y)) + (0.1**(1-y) * y * np.log(10))) / (1-(9/10)**(1-y))) + (((0.09**(1-y) * y * np.log(10 / 9))) / (1-(9/10)**(1-y)) ** 2)
return f1y
def f1(x,y):
f1 = (0.1**(1-y))/(1-0.9**(1-y)) - i
return f1
def f2(x,y):
f2 = x/(1-y) - m
return f2
def f2x(x,y):
f2x = 1/(1-y)
return f2x
def f2y(x,y):
f2y = x/(1-y)**2
return f2y
def j(x,y):#jacobian
j = np.array([[f1x(x,y),f1y(x,y)],[f2x(x,y),f2y(x,y)]])
return j
def fv(x,y):#vector function
fv2 = np.array([f1(x,y),f2(x,y)])
return fv2
def newton_i(xn,j,fv):# iteration of multivariable newton method
x = xn[0]
y = xn[1]
x1 = x - np.matmul(np.linalg.inv(j(x,y)),fv(x,y))[0]
y1 = y - np.matmul(np.linalg.inv(j(x,y)),fv(x,y))[1]
xn1 = np.array([x1,y1])
return xn1
xn = np.array([0.5,0.5])#starting point
x = [xn]# all x
xnm1 = [0,2]#previous estimate of x
iteration = 0
while iteration < 500:
xnm1 = xn
xn = newton_i(xn,j,fv)
iteration += 1
x.append(xn)
error = np.linalg.norm(xn-xnm1)
print('The solution is',xn[0],xn[1],', which took',iteration,'iterations to produce. The 2-norm of the residual is',np.linalg.norm(fv(xn[0],xn[1])),'.')
[I have done a mathematical analysis of inequality.]
Penguinya is ranked 50,445th in the world and 1,592nd in the Pacific for Most Income Equality, scoring 57.8 on the Marx-Engels Emancipation Scale.
c a p i t a l i z e d
You watched the 2nd half? I usually stop after Light wins against L.
Novoblupolia is ranked 37,765th in the world and 1,278th in the Pacific for Most Income Equality, scoring 63.7 on the Marx-Engels Emancipation Scale.
This reminds me - a while ago, a troll account posted a black-and-white photo of a dude with a beard and said "Can we get a HELL YEAH for our confederate ancestor?" and a ton of republicans commented "HELL YEAH!"... The man on the photo was Engels.
True Europa State and Blaricia
cool
hi
Hello there
Yeah. Wanted the full story. To put it in censored, my reaction was this
*it finishes*
Me: Bro what the [REDACTED] [REDACTED]. Are you [REDACTED] serious right now? What type of a [REDACTED] ending is that?
To be clear, I put in the redacted, so I'm good because no swearing has been made. But irl? Yes. I swore.
so much communists here ... :s whats wrong with capitalism?
Post self-deleted by Blaricia.
CAPITALISM SUCKS
Near is not L's replacement. He only got lucky because Light got too reckless.
how do i leave a region to join this one
You watched the actual ending too? I thought you said you stopped after L is beaten
this is Ny sarim (player)
[My nation is capitalist.]
>:(
but i like mommy and daddy buy my nice precious things ^^ or daddy bought for mommy a new Porsche in her favorite color
We are from the Pacific, it does not matter if we are communists, capitalists or monarchies.
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