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Old 10-01-2013, 07:31 PM   #1
Agemegos
 
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Default Index of inequality

I want my world information sheets to provide a useful index of inequality. I suppose that in the end there has to be as set of examples in the key to give most people an understanding of what the numbers mean in social terms. Nevertheless I would like the index listed to be intelligible. Given that there would be some examples in the key that you could refer to, what sort of index of inequality would you find most useful? For instance:

My first thought as an economist is to use the Gini co-efficient, because that's what we use in economics; the economists' "standard of living" is average income times (one minus the Gini coefficient for the distribution of income). The Gini coefficient is a number from zero to one, where the value is zero if everyone has exactly the same income (or whatever is being measures), and one if (and only if) one person has all the income and everyone else none. It is usually reported as a two-digit decimal or as a percentage, and examples would be for instance "Denmark 24%; UK, Indonesia 34%; USA 45%; Brazil 54%; Seychelles 66%". The attraction of the Gini coefficient is that it is sensitive to the entire distribution and that it is easy to find figures for the examples. The repulsion is that the definition is rather abstruse.

The next leading possibility would be the ratio of the combined incomes of the richest 10% to the combined income of the poorest 10%. That would start at 1.0 for perfect equality and range upward without bound. Examples might be "Sweden 6.2; Denmark 8.1; Greece, Spain 10.2; Australia, New Zealand 12.5; UK 13.8; USA 15.9; Nigeria, Rwanda ~18; Uruguay, The Gambia ~20; Swaziland, The Dominican Republic ~ 25; Nicaragua ~30; Brazil ~40; Panama ~50; Colombia ~60; Central African Republic ~ 70; Sierra Leone, Bolivia ~90". It's easier to explain what this measure means, but as you see in the examples it is more sensitive to the existence of rich and poor classes with a wide range between them than the Gini coefficient, and less sensitive to the existence of a very small elite of outstanding wealth ("The 1%"). It's not sensitive to the whole distribution.

Other possibilities would be the percentage of income received by the richest 1% of people, ranging from 1% in complete equality to 100% in extreme inequality. That's directly intelligible, it shouldn't be too hard to get figures to make examples, but it's not sensitive to inequality over most of the range of incomes.

And then I might list the percentage for which 1-x of the people had x% of the income: 50% in perfect equality, 90% where 10% of the people had 90% of the income (e.g. Switzerland, France), 95% where 5% of the people had 95% of the income, and 100% where one person had all the income. That would let users sketch a crude Lorenz curve, but I think it's a bit goofy.

What would work for you?
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Old 10-01-2013, 07:37 PM   #2
sir_pudding
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Default Re: Index of inequality

Since you've explained it the Gini co-efficient seems simple enough to understand and accurate enough to illustrate.
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Old 10-01-2013, 08:16 PM   #3
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Default Re: Index of inequality

To start with, I don't think I want a vector. I want a scalar. You lose a lot of information, but you also get ready understandability.

I agree that the Gini is comparatively unbiased, but also that it's a bit abstruse. On the other hand, your scales that look only at the top N%, or the bottom N%, or a comparison of the two, seem vulnerable to outlier effects. You probably know that a common approach to figuring moments of distributions is to chop off the top and bottom scores, precisely to avoid biasing effects. Or, on the other hand, to rely on the median rather than the mean, because the median inherently eliminates outlier effects.

The trouble, of course, is that the median is a measure of central tendency and not of variation.

There is a way around this, though it's not standard as far as I know. Note that the arithmetic mean is the number N such that the sum of (X-N)^2 over all X is a minimum. That's using the Euclidean measure of distance. If you use |X-N| as the measure of distance, and minimize its sum, I believe you get the median, in the same way. So use the analog of variance based on absolute value of deviations rather than squared deviations, and you have a median-based measure of variation.

Or you could take the ratio of variance to mean.

One other suggestion, which isn't so general: If you compare the top to the bottom, you will treat exactly alike a society where nearly everyone is poor and you have some oligarchic lords bestride the economy like colossi, and a society where the great majority are middle class. But those two are different in ways that matter a lot to me, and will matter a lot to many immigrants. How about giving three numbers that express the ratio of the poorest, the median, and the richest? If it's 1:2:100 that's very different from its being 1:20:100—or 1:90:100, though I find it hard to envision how such a society would come about.

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On a different note, you are presenting a static statistic. But it matters to me whether the very wealthy or the very poor are closed classes, or undergo turnover. How about some time of measure of turnover at the extremes? Perhaps you could treat it as a time constant for the decay of wealth—in effect, a mean time to failure of great fortunes.

*****

I want to note, also, though this is going still further afield, that I really, personally, care very little how rich someone is compared to me. I care a lot more how they got rich. Did they make music or movies or write books that entertained a huge number of people? Did they invent something useful? Did they move capital from less to more productive places? Did they get large government grants and subsidies? Did they send an army out to capture and enslave people and exploit their labor? How much of their income derives from coercion, done by them or on their behalf? In GURPS this partly blends into CR, of course, but you aren't doing GURPS.

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Old 10-01-2013, 08:55 PM   #4
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Default Re: Index of inequality

I will be describing the character of social stratification and the ease and means of social mobility separately from the inequality of income.
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Old 10-01-2013, 08:56 PM   #5
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Default Re: Index of inequality

Quote:
Originally Posted by sir_pudding View Post
Since you've explained it the Gini co-efficient seems simple enough to understand and accurate enough to illustrate.
Yeah, I agree.
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Old 10-01-2013, 09:38 PM   #6
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Default Re: Index of inequality

Is it practical to include a basic graphic? You can put quite a lot of information in a rather small line graph.
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Old 10-01-2013, 09:55 PM   #7
whswhs
 
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Default Re: Index of inequality

Quote:
Originally Posted by Agemegos View Post
I will be describing the character of social stratification and the ease and means of social mobility separately from the inequality of income.
I'll grant that that is possible for social mobility, but I don't see how it can possibly work for social stratification. Inequality of income is a key part of social stratification.

In any case, I still want to know not only about the very rich and the very poor, but about where the people in the middle stand in relation to either.

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Old 10-01-2013, 10:17 PM   #8
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Default Re: Index of inequality

Quote:
Originally Posted by sir_pudding View Post
Since you've explained it the Gini co-efficient seems simple enough to understand and accurate enough to illustrate.
Quote:
Originally Posted by Crakkerjakk View Post
Yeah, I agree.
I'll third this.

Really though, the examples are what most people will go by.
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Old 10-01-2013, 10:28 PM   #9
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Default Re: Index of inequality

A single number really wouldn't tell me what I wanted to know, even if that number was a Gini with a series of real-world nations for comparison as you provided.

The top 10% to bottom 10% comparison is one of the two I routinely use, and the second is just a variation (top 20% to bottom 20%). Those two numbers side by side give me an immediate idea of how large the richest class is and how large the underclass is. I suppose for completeness' sake I'd throw in top 50% to bottom 50% if I was taking a first glance at a society about which I knew nothing.

You know your players or target players better than we do, of course. While I personally would also like to see the rate of decay of a fortune as whs suggests, I have to admit most players wouldn't care (in my experience), in part because they expect to be able to personally affect that one ;)
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Old 10-01-2013, 10:46 PM   #10
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Default Re: Index of inequality

Quote:
Originally Posted by patchwork View Post
A single number really wouldn't tell me what I wanted to know, even if that number was a Gini with a series of real-world nations for comparison as you provided.
The most informative multi-number model is probably percentage of the population in certain income brackets. For example, in the US, 8% of households are under $10k, 17% are $10-25k, 25% are $25-50k, 29% are $50-100k, 17% at $100-200k, and 4% for more than $200k.
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Last edited by Anthony; 10-01-2013 at 10:54 PM.
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