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It is very common in infographics such as the following:

enter image description here

to make a point about wealth inequality by showing a disproportionate amount of money owned by the richest people.

I am slightly skeptical that this is a good measurement of a skewed wealth distribution. In particular, the "what they would like it to be" almost looks paradoxical -- how can the third 20% own the same amount of wealth as the second 20% when by definition the second group earns more income?

I'm particularly curious what such a distribution with a stereotypically "utopian" income distribution, such a normal distribution with identical mean, median, and mode. How about a uniform distribution, with 1 person earning $1000, 1 person earning $2000, up to 1 person earning $10000?

Also, would a distribution graph with wealth on the horizontal axis and percentage of people on the vertical axis give a better picture of income skew?

Sorry if this question belongs more on Math StackExchange.

Source here.

Sklivvz
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ithisa
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  • +1, i've also been very skeptical of this statistic. I'm sick of the porpers using this stupid statistic against us millionaires. – Kenshin Apr 03 '13 at 13:28
  • It might be interesting to do a poll with two questions: 1. "What share of the income do you think the richest 5% own" 2. "Approximately how much richer do you think the riches 5% is compared to the average American". Most people would not realize these questions are approximately equivalent. – ithisa Apr 03 '13 at 13:31
  • These are not the same questions. Let's say average income is 50000, and top 5% is 100 000. Then the answer to question 2 would be 100%, but the answer to question 1 cannot be 100% unless the richest 5% own all the wealth. – Kenshin Apr 03 '13 at 13:33
  • No, but one should be able to derive one from the other given that income is a skewed normal dist which is approximately is. – ithisa Apr 03 '13 at 13:33
  • Yes I agree with that. They are not the same but if you know one, the other is determinable. – Kenshin Apr 03 '13 at 13:34
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    Say the top 5% own 100 000, and the average income is 50000. Say there are 100 people. Their total income is 50000 * 100 = 5000000 dollars, of which 100 000 * 5 = 500000 is owned by the top 5%, so the top 5% own 10% of the wealth. – ithisa Apr 03 '13 at 13:35
  • +1 Yes good example. I think such a survey would be very interesting indeed, to see if people's answers are self consistent. That will put those suckers to the test :p – Kenshin Apr 03 '13 at 13:36
  • Most people I know who are surprised at the top graph would probably agree that the top 20% are 4 times richer than the average... – ithisa Apr 03 '13 at 13:38
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    I'm not understanding what you are skeptical of here. The first chart is based on economic data. The second and third abre based on survey results. They aren't expected to be economically correct. – DJClayworth Apr 03 '13 at 13:46
  • I'm skeptical of whether such graphs represent true inequality. In other words, would the top graph actually represent what an *economist* would think of as a problematically unequal society? – ithisa Apr 03 '13 at 13:47
  • Or in other words, if people were assigned random incomes uniformly would the result look like the top graph? – ithisa Apr 03 '13 at 13:47
  • @EricDong, your graphs refer to "wealth", yet your question refers to "income". Please fix this major discrepancy. – Kenshin Apr 03 '13 at 14:00
  • @Eric: That's not what I am disputing. A company with revenues of $100M can pay a CEO $50k and still pay it's 10 employees $50k each. – RedGrittyBrick Apr 03 '13 at 14:00
  • fixed the title – ithisa Apr 03 '13 at 14:00
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    @EricDong, please fix the graphs too, the graphs display wealth, not income. – Kenshin Apr 03 '13 at 14:01
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    @EricDong It's not an issue whether an economist would consider the top graph problematic. The article shows the differences between what people think it should be (and they may be wrong about whether that is a good thing or not) and what it is. This site isn't for deciding if infographs make a good point or not, it's for deciding if they are true or not. – DJClayworth Apr 03 '13 at 14:02
  • You might want to edit it. I can't find a similar poster-like infographic for income. – ithisa Apr 03 '13 at 14:03
  • @DJClayworth: As I mentioned in the comment above, the lower graphs is what I'm more interested in. x percent earn y percent is inherently a misleading numeric for people to guess or idealize about. Top 20% earn x% more than average is easier to guess. – ithisa Apr 03 '13 at 14:04
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    @EricDong You fixed your question the wrong way. You ask about income distribution, but the source is talking about wealth distribution. – DJClayworth Apr 03 '13 at 14:05
  • @EricDong The lower graphs are about results of a survey. Are you claiming that the figures are wrong? Because asking if people 'should' think that is the ideal wealth distribution isn't on topic here. – DJClayworth Apr 03 '13 at 14:06
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    @Eric: Just change "income" to "wealth" throughout if that specific wealth infographic is the one whose utility you are skeptical of. Also you could weed out all the subsidiary questions which may obscure your main point. – RedGrittyBrick Apr 03 '13 at 14:19
  • This might be better suited to politics.se – Tom77 Apr 03 '13 at 14:24
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    The title and the figure should be made to agree on whether the question is one of wealth or of income as these are not the same thing. – dmckee --- ex-moderator kitten Apr 03 '13 at 14:38
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    What is the question? – Wertilq Apr 03 '13 at 14:46
  • Given the choice between making several of their friends more well off or taking a winfall for themselves, consistantly lottery winners choose to keep it mostly for themselves. So I doubt the accuracy of the last graph for sure. – Chad Apr 03 '13 at 15:18
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    -1 I am not sure whats being asked here. And i would certainly not call a normal distribution to be utopian. – Stefan Apr 03 '13 at 16:09
  • @EricDong+1 Excellent question! I am wondering why are you getting down votes! – Persian Cat Apr 04 '13 at 11:30

2 Answers2

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There is some confusion about the question, so I'll try to answer

I am slightly skeptical that this is a good measurement of a skewed wealth distribution. In particular, the "what they would like it to be" almost looks paradoxical -- how can the third 20% own the same amount of wealth as the second 20% when by definition the second group earns more income?

Or in other words, Are wealth distribution graphs a good measure for wealth distribution inequality?

Yes, they are wealth distribution graphs, show exactly what you want to look at when you talk about wealth distribution. If you want to know how much wealth does the X percent have, look at the graph. The graph also shows the "ideal" wealth distribution, which is taken from a peer reviewed article:

http://pps.sagepub.com/content/6/1/9.short

The graphs doesn't show that the bottom and second bottom 20% percentiles have the same amount of wealth, but very close amounts of wealth, where the second bottom has slightly more the the bottom.

Beware, Here starts the ranty part of the answer.

With all due respect to wealth inequality, it doesn't give a good picture of a person's status, because it doesn't translate the wealth into commodities or services. People don't need money to live, they need food, shelter, education, medical care, safety and so on. Wealth inequality however doesn't tell us if the people in the bottom have those things or not. For example, Uganda's wealth is more evenly distributed that the USA's, but where are the people of the lowest percentiles better off, in Uganda or the USA?

You can see in the Wikipedia article on income inequality (which is sourced well, and organizes everything in a nice table with several different criterion to choose from) that countries like Ukraine, Belarus, Albania and Afghanistan all have more equal wealth distribution than the USA. The question that should be asked is where are people better off, not where are people more equal.

Wealth distribution doesn't tell us if the poorest have food, shelter, medical care etc. and can't really tell us anything about the quality of life of the people.

In other words, if the poorest people have food, housing, education medical care and opportunities in life, why should anyone care the the richest people are pooping in golden toilets?

SIMEL
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  • Wealth distribution may not be able to tell that but it is an indicator. Just like your check engine light. And dismissing an indicator because it doesnt show the entire picture is exactly the type of tactic employed to block any changes to the Status Quo. – Stefan Apr 04 '13 at 15:11
  • Also please compare the US with countries on the same economical level. Like for an example all of the scandinavian countries. Still think people prefer the US? As it stands with the second part i cannot upvote this answer. – Stefan Apr 04 '13 at 15:13
  • @Strafan, I'm not a US citizen, more over, I believe that the poor in the USA don't have access to medical care, housing and sometimes even food. And you are right that the USA is forth last of the OECD countries, with only Chile, Mexico, and Turkey below it. However, I still don't believe that it's a good factor for the state of the people. – SIMEL Apr 04 '13 at 15:43
  • @Stefan, a. You can't exclude other countries from your sample size, if you are saying that wealth inequality is inherently bad, than it should always be bad. b. If you want to talk about hungry people talk about this, if you want to talk about inability to climb the social ladder, Homelessness, education or any other aspect, talk about this. Talk about the buying power of the people, don't tell me that a poor person doesn't have assets, tell me that they can't afford medical care, or food. Why do you need another parameter that doesn't really tell you anything by itself? – SIMEL Apr 04 '13 at 15:44
  • Because it is easier to measure. By itself it doesnt mean much, but like i said its an indicator. And if you compare countries that are roughly equal in term of development you can see that wealth inequality can be used as an indicator of more problems that need fixing. It is no coincidence that most first world countries with lesser inequality also have better health care and social systems than the US. Causation or Correlation is irrelevant. It raises a red flag. Is fixing the inequality going to fix the root issue? That is a different question. – Stefan Apr 04 '13 at 16:52
  • And dont forget that people (or even [monkeys](http://www.youtube.com/watch?v=-KSryJXDpZo)) do not like overly unfair systems. And wealth distribution is a sore point especially for those on the receiving(or better non receiving) end. – Stefan Apr 04 '13 at 16:55
  • @Stefan, there is inequality even in the other countries, rich people are richer, and poor people have less staff. Why is inequality like "the rich person has 2 cars and I have none" is more acceptable, than "the rich person has 2 Rolls-Roys cars, and don't have a car"? After all the monkey was outraged over the difference between a grape and a cucumber, how do you think it would feel if the other monkey got 3 times more food than him, as the "idyllic" difference in wealth shows between the top and bottom 20%? – SIMEL Apr 04 '13 at 17:00
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What you're referring to is defined as Gini coefficient, which measures how far the income distribution curve is from the utopian "line of equality" (uniform distribution). Value of Gini coefficient ranges from 0 (perfect equality) to 1 (perfect inequality as in one person would earn all of country's money).

enter image description here

Not that in countries with progressive tax scheme, there is significant difference between pre-tax and post-tax Gini coefficient.

enter image description here

vartec
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  • Hmm. Then my question might be, what would be the Gini coefficient of normally-distributed wealth, which fits most people's expectation of "utopia", i.e. huge middle class, very little rich, very little poor – ithisa Apr 03 '13 at 13:58
  • Your answer is regarding income, however the graphs in the question display "wealth" not "income". There is huge difference between wealth and income. – Kenshin Apr 03 '13 at 13:58
  • @Chris: yet question talks about income inequality – vartec Apr 03 '13 at 14:01
  • @vartec, the graphs in the question say "wealth" not "income" – Kenshin Apr 03 '13 at 14:01
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    @EricDong _normally-distributed wealth which fits most people's expectation of "utopia"_ [citation needed]. – Stefan Apr 03 '13 at 16:06