Resourciv: Social Models, Part 2

Well. How quickly did you expect an update? When I ran my inheritance simulation, I also calculated the Gini coefficient of the population’s wealth distribution. The Gini coefficient expresses relative inequality within a population, where 0% represents total equality and 100% means basically one individual holds all the wealth. Partitive Inheritance Land has a Gini coefficient of 15%, while Primogeniture Land has one around 45%. Modern capitalist societies (and, as far as I can tell, most developed class societies) have Gini coefficients of ~80% with respect to wealth and around ~40% with respect to income. I calculated it by dividing the relative mean average deviance in half, but the typical method is by taking a Lorenz curve and doing some calculus bullshit. I don’t want a Lorenz curve necessarily but I want to know what it means for a Gini coefficient to be such and such.

Here’s a solution: draw a square and bisect it along the diagonal. Then, in the lower right, draw a smaller square who takes a portion of that quadrant proportional to 100% minus the Gini coefficient; in other words, at 0%, the square takes up the whole quadrant, but at 50% the square takes a fourth of that quadrant (having 50% the width/height). Draw two triangles from the adjacent corners. The left triangle along the horizontal axis represents the population’s lower echelon, and the top triangle along the vertical axis represents the higher echelon. Then it’s basic geometry to calculate the percent population of the lower echelon, which you can subtract from 100% to find that of the higher echelon. I messed with the graph to get some sample population compositions, and then I used my brain to arrive at a general formula. Again, it’s only an approximation, but it’s quite insightful since I know (at least) the USA with its ~80% Gini coefficient does indeed see the top 10% own around 90% of wealth.

Gini Coefficient	Lower Class	Upper Class
0%	50%	50%
15%	58%	43%
25%	63%	38%
50%	75%	25%
80%	90%	10%
G	(1 + G) / 2	(1 - G) / 2

But I was like: okay, one abstraction at a time. I need to know how to decompose class composition (or whatever we call it) between multiple sub-populations, because we know that capital picks its favorites. Knowing the USA’s Gini coefficient and its resulting class composition in terms of wealth, I made a spreadsheet to calculate according to this model how different races with different per capita wealth have different internal compositions and (in turn) contribute to society’s overall composition at different ratios. You can see a screenshot below or download the spreadsheet here.

The numbers make sense. White and Asian households are over-represented in society’s highest echelons relative to their population. I’ve also calculated the relative ‘wealthiness’ of the average individual in society at large and within a subpopulation. What's neat is that even if a society has 0% G, if the subpopulations have different per capita wealth, a class division still emerges; the same is if the subpopulations have the same per capita wealth but society has G > 0%. With all this data, barring other open questions of abstraction and game integration, I’d feel pretty equipped to model how populations develop over time both internally and as they are impacted by migration in or out. This approach is much more abstract since we are only looking at the high-level inequality within society, meaning it doesn’t account for division of labor per se. Part of me considers giving each echelon a quality-of-life score which indices their supply of labor and demand of goods (probably given a particular societal mode, e.g. feudalism or capitalism) but I don’t know how much variety that provides. I also wonder how ecological concerns would factor into the thing: will ratios of exploitation define the limits of wealth in/equality? But this feels interesting!