Central Tendency in Skewed Distributions: A Lesson in Social Justice

I think I'm one of the few academic bloggers in the world who blogs in a discipline that has nothing to do with what I teach at the university. Theology and this blog are my hobby. By profession I'm an experimental psychologist. Which means that my day job is largely about teaching undergraduate and graduate statistics for psychology students. That's what pays the rent.

In short, nothing I write about in this blog is a part of my daily classroom teaching. I've never taught a class in theology. I don't teach in our College of Biblical Studies. I have no contact with our MDiv students. In my entire career at ACU I've guest lectured in a graduate bible class exactly...once.

Basically, I'm living two lives.

But my interest in theology does, from time to time, leak into my statistics lectures. A recent example.

Earlier this semester in my undergraduate statistics class we were talking about measures of Central Tendency and how they behave in skewed frequency distributions. Let me explain this.

A measure of Central Tendency is a number helping you ballpark the "middle" or "center" of a distribution. The most commonly used estimate of Central Tendency is the mean, the arithmetic average. You calculate the mean by adding up all the scores and then dividing by the total number of scores.

The second most common measure of Central Tendency is the median. The median marks the 50th percentile. Fifty percent of the scores are above the median and fifty percent fall below the median.

When a distribution of scores is bell-shaped and balanced (a normal distribution) both the mean and the median sit in the exact center splitting the distribution right down the middle. That is, the mean and median are equal. See the center distribution in the picture below.

Well, if that's the case, if the mean and median have the same value, why have two different measures?

Because this only happens in perfectly symmetrical distributions. When the distribution is skewed and asymmetrical the mean and median take on different values. Which is to say when a distribution is unbalanced there's no consensus on where the "middle" might be located. You could say the middle is where the mean sits. Or you could say the middle is where the median sits.

Okay, so what issues might affect that choice? Well, the key thing to note is that the mean is the most sensitive to the effects of skew. That is, the mean is very sensitive to extreme scores and, thus, is "tugged" more rightward or leftward compared to the median. This can be seen in the left and right distributions of the picture below (Note: the Mode is a third measure of central tendency and is the most frequently occurring score, thus it always sits at the top/highest point of the distribution):

Note how in the left picture (an example of negative skew) the mean is the most leftward measure of central tendency. That is, the mean is the most affected by the extreme scores on the left and is, thus, pulled furthest away from where the scores are piling up to the right. A similar thing is observed in the right picture (an example of positive skew) where the mean has been tugged the furthest rightward.

What is the implication of all this? Basically the following. When a distribution is "normal" people usually report the mean. But when the distribution is skewed we tend to report the median as the median is less affected by the extreme scores.

So where does theology fit into this?

Well, as I was describing all this to my students a month ago I asked the following question:

"When you hear people report the average family income of American households do you hear people say 'mean family income' or 'median family income'?"

A few students respond, "I think I hear people say 'median family income'."

"That's right. The measure of Central Tendency we tend to use in reporting family income is the median. Okay, so what does that tell you about the distribution of family incomes?"

"That it's skewed?"

"Right. When you hear people using the median that's often a clue that the distribution they are trying to describe is skewed. And the distribution of family incomes in America is skewed."

I follow up with another question. "Can you guess if the distribution of American incomes is positively or negatively skewed?" (Refer to the picture above to make your own guess.)

"Is it positively skewed?"

"Yes, it's positively skewed. The great majority of American incomes pile up on the left, on the low end. But there are a few extreme scores--the millionaires and billionaires--that pull the distribution to the right."

I draw this distribution on the board. For you, here is the distribution of American family incomes based on 2005 data (H/T to Visualizing Economics):

Note the positive skew. Note also the behavior of the median and mean (you may need to click on the graph for a closer look). The median is $46,326. The mean is $64,344. Again, the mean is more affected by the presence of the extreme scores, being pulled more rightward by those millionaires and billionaires (who are actually so rightward they are literally off the chart).

Okay, again where is the theology in all this? Well, it has to do with issues related to social justice. I made this point in class a month ago in the following way:

"Note how American family incomes are all piled up on the left. What does that mean? What are the practical implications of that?

Think about it this way. What is the income that officially marks poverty? It's around $20,000. Okay, now imagine a solidly middle class person, someone who makes, say, $50,000.

Given that, what is the distance between the middle class and poverty? About $30,000. Is that a lot of money?

What if someone in the family has a catastrophic illness? Can the hospital bills from a catastrophic or chronic illness run over $30,000 in a year? Oh my yes. Hospital bills from illnesses like that can run in the hundreds of thousands of dollars annually.

And what about disability or injury to the breadwinner? Or divorce? Or layoffs?

Shoot, if your car breaks down you're screwed. Many new cars are well over $30,000. And a good used car can deplete that $30,000 buffer pretty quickly.

The point being, the lesson of the positive skew, is that the distance between being middle class and being poor is very, very small. We're all piled up on the left of the distribution. So a little bit of bad luck--illness, injury, layoffs, something going wrong with the house or car--and a solidly middle class family can fall below the poverty line. Can even become homeless. And if not that, can struggle mightily and will have to forgo things like sending their kids to college. A little bit of bad luck and a family might suffer generational consequences.

Now consider this. If the distance between the middle class and poverty is about $30,000 what is the distance between being middle class and, say, being Donald Trump or Bill Gates?

If the distance between middle class and poverty is $30,000 the distance between middle class and being a millionaire is $950,000. See the difference? There's not really a difference, a few thousand dollars, between the working poor and the middle class. We are all piled up, the great majority of Americans, on the left. And the difference between all those folks and the rich is, well, measured in the millions if not billions of dollars. It's a distance that is hard to compute in your mind.

In short, to be middle class is to live with chronic vulnerability and uncertainty. A real day to day anxiety about waiting for the other shoe to drop. Which is why access to things like universal health care and unemployment benefits are so important, a social safety net for those at or near the bottom. Which, the positive skew tells us, is basically everyone."

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74 thoughts on “Central Tendency in Skewed Distributions: A Lesson in Social Justice”

  1. What does any of this tell us about "justice"?  Or -- how do these numbers indicate an "injustice"?  What appearance does "justice" take in the area of economics and budgets?  No one with any uncertainty in their lives?  Absence of any vulnerability?  Are those with no (apparent) uncertainty or vulnerability commiting a crime which requires the dispensation of some punishment?  How does theology "fix" this?

    Are you saying that to live with "chronic vulnerability and uncertainty" is more "unjust" than not?  How do you know that those who are "rich" do not have just as many feelings of vulnerability and uncertainty in areas other than employment or healthcare? 

  2. I'm using justice in the broad biblical sense (i.e., the right ordering of creation and human affairs), not a narrow legal sense (crime/wrongdoing).

  3. We're there with the vehicle repair bills. Car goes in the shop Friday (again).  Can't afford a new car, and almost can't afford to drive what we've got with gas prices through the roof.  

  4. I love it when you do a post on statistics!   Although this one is a bit depressing for us middle class folk.  Having a child (or several) with braces can make make the distance shorter as well.

  5. I feel your pain.  We were there last summer and came to the conclusion that the payment for a new car was cheaper than the repair bills.  I think the rule of thumb is that if any repair is more than 20% of the value of the car, it's time to move on.  In our case, each individual repair was less than that but they were so frequent that it was like a car payment.

  6. "Basically I'm living two lives."  -- No, you know that that is not true.  While experimental psychology and statistics may be your area of professional expertise and the source of earning an income, I do not get the sense at all that this facet of your personhood has been compartmentalized or elevated to that of highest form of identity (self-esteem?).  Or, that while you are doing that job, your understanding of God has no bearing on the way that you interact with faculty/peers, parents, and students.

    IMHO, theology might best be kept as only a hobby, because what if "doing" theology and basing one's livelihood on doing it "well" (whatever that means) inadvertently becomes little more than a self-esteem project?  The object of the study (God) becomes the source of our own demise (thinking that we ourselves have become gods, or at least equal to god).  Is that making any sense?

    The deeper truth that I see at work here in the blogging-as-hobby of 'Experimental Theology' is precisely how a person *does* live one whole and seamless life.  All of us wear many hats and fulfill various roles in life.  But what's at the core of our identity?  How do *we* stay centered?

    "Let me explain this."  -- It takes a really good teacher, one who has a deep calling, to bring any subject (experimental psychology, statistics, theology) down to a level that the complete novice can grasp.  It is a gift that not every expert possesses.

    The essence of this post reminded me of the thesis of the book, 'Hearts and Minds: The Anatomy of Racism from Roosevelt to Reagan' by Harry S. Ashmore.  After slavery was abolished, racism was stoked by the crafty rhetoric of haters and politicians within the hearts and minds of the poor and middle class white, whose fears and vulnerabilities were played upon.  The emancipated slaves were made out to be a threat to those in the lower economic brackets.  Promoting a scarcity mindset leads to desperate behaviors, needless competition.  And that is a good example of how the powerful misuse their power with evil consequences.  How the powerful in fact become pawns in powerful dark forces that are hard to pin down to one source or cause.  The evil takes on a life of its own.

  7. We can do the same thing with wealth in the U.S. as you have done with income.

    To make one facet of the injustice more explicit: vast amounts of the total income and wealth available in our country do not serve to protect anyone --- even their rich recipients and owners --- from poverty, while people do in fact live in poverty or in danger of it.  The wealth and income are simply wasted.

  8. Richard....? I'm suspecting that you copped this essay from Focus On the Family. Or maybe the Family Council? Or Families for American Heritage?

    I know the strains of managing two professions plus Chair duties (and dishes) must stretch you to the limits of human possibility. Still, plagiarizing the fine and hard work of the Christian organizations without even a foot note credit, feels a bit unbecoming let alone a bit unChristian.

    There's good news though! other than this little misstep, your work is well on the way!  

  9. " In the grand scheme of things, even the poorest 5% of Americans are better off financially than two thirds of the entire world."

    http://money.cnn.com/2012/01/04/news/economy/world_richest/index.htm

  10. That's a good reminder and a fact which made me think twice about whining about the cost of car repairs and orthodontia in my previous posts.

  11. Mike G., can you expand on this point a bit?  What I hear from and about FOF et al, these orgs are completely against gov't "entitlement programs" (i.e., social programs) of any kind.  In their minds, gov't of that type = evil.  (Though I would suspect that most of their fans are middle class or on the poorer side statistically, they're not advocating for universal healthcare or unemployment benefits and such.)  That is my understanding of the politics these groups espouse.  Further, the theology behind it is, if we work hard, and be real good, then we can trust that God will bless us and take care of us.  I did not read any of that into Dr. Beck's post.   So I'm confused what you meant by your comment.  ~Peace~

  12. There's a positive truth here as well.  Yes, the line between working poor and "middle" class is razor thin.  To that end, the efforts of our current administration for universal health care and social safety nets is important.  I'm not here to debate the workability of the current efforts, but their importance is clear.   The cycle of poverty is vicious, no doubt, and we need organizations and
    individuals who make it their life's work to provide social and
    economic opportunities to escape that cycle. 

    There are also opportunities in these charts. 

    I believe there is also a cycle of "middle class," the psychological mindsets that keep people from pursuing greater economic opportunity.  These are largely psychological tendencies rather than the powers that hold the poor captive to their circumstances.  In short, the opportunities to escape that vulnerability is everywhere in a capitalistic economy and sometimes, even in other economic models (see, for example, the micro-lending successes in socialized or dictatorial economies).  The question for those who are vulnerable is, "What are you going to do about it?  Because you have choices that those in harder circumstances do not."

  13. In the same way that Romney pays 13% in taxes (Soros probably does too, tax loopholes aren't partisan), but I paid 25% as a self employed family man living in middle class suburbia trying to make ends meet. There are no laws being broken, but it still makes you go.......aaughhhh.....sigh.

  14. Wow. Amazing stuff. I'm in a stats class right now (preparing for my Master's), and we just finished up talking about this sort of stuff (though my prof. isn't nearly as well-spoken). As someone who would fall under the net of "poverty" in the US, I would be hopeless without the health care I've been given by the government. And those benefits go beyond just myself and affect my entire family. They may be "middle class," but they're essentially as poor as I am.


    Thanks for the lesson in applied statistics!

  15. "I don't teach in our College of Biblical Studies. I have no contact with our MDiv students. In my entire career at ACU I've guest lectured in a graduate bible class exactly...once."

    Let me see if I've got this right... you have no professional expertise or accreditation in theology; no seminary training or official recognition by any denominational governing body; you are not ordained or planning to be. In short, as far as any religious organization is concerned, you have no credibility, and you may in fact be promoting pure heresy over any long accepted "traditions of men." You are not "skewed" towards teaching any particular viewpoint simply because a group of men gathered together and decided what you should teach, and what others "should" believe. You do not feel obligated to accept tradition as undeniable fact, and instead feel compelled to study and think for yourself. You have no fear of rattling or upsetting any theological status quo, and accept no pastor or religious body as having authority over your own ability to seek out and listen to what you feel God is saying to you.

    Good. I trust you more already.

  16. Oh, O:K, thanks Cameron B.  I find that it's just best if I ask for clarification, rather than make assumptions, when it comes to sarcasm and other subtleties, because I'm admittedly just not good at detecting sarcasm from literal meaning...especially minus the face-to-face advantages of body language, facial expression, etc.  Sorry to be so dense!

  17. You mean justice that is flowing with mercy, even toward those deemed undeserving of it?  Generous, restorative justice?  True peace (shalom)?  Living between the hope of it and the bitter reality of "it ain't here yet" is the hardest place to be most of the time.  How not to lay down in despair.

  18. That's an important point. As Sam noted below, capitalism and the opportunities it provides (and the material wealth we enjoy because of it) aren't to be dismissed. I consider myself pro-capitalism (on pragmatic grounds) and pro-safety net.

    I feel strongly that, given that we are the most materially wealthy nation in the history of the world, everyone in this nation should have access to affordable and quality healthcare. This was why I supported (and still support) the Affordable Health Care act.  (Of course, all eyes are on the SCOTUS this month. But still, the US needs universal health care so I'll keep advocating for if the Act is systematically dismantled.)

    I'll go further. Anyone who is pro-Life should be strongly in favor of universal health care with robust provisions for providing free or cheap options for contraception. If you are pro-Life you should be pro-The Affordable Healthcare Act.

  19. Dr. Beck.  Living way close to that line I can certainly feel that, but here is one story.  When Caesar offers something, it comes with Caesar's requirements and it usually chases out private offerings.  Real local example - our church runs a preschool.  We basically used to take everyone regardless of ability to pay.  If you couldn't pay the already low rate, we figured something out.  Then government sponsored Universal Pre-K came.  Of course it didn't cover 100% of the people, cost a lot more, and if you were to be a provider you had to take their curriculum. But it was "free".  The connected and on-the-ball parents signed up and got the free.  Those parents less on-the-ball - not so much.  Church preschools used to be able to make room for those kids - now, not so much - being on-the-ball usually correlates well with ability to pay.  The end point of Caesar's program, less kids in preschool and those in preschool with a materialist only curriculum.  But it is "free".  Which case is closer to social justice?

    Now multiply something like that to a national universal health care.  Do you really see social justice coming from Caesar, or are the social justice cries of the prophets or Jesus for that matter more about equality under the law vs. favoritism?  Just the fact that the government is placed in the position of granting waivers from the law seems to break its social justice.

  20. I agree it's tricky. I wouldn't want to say the Caesar can fix it. But I also think free markets are Caesar. So we have to make discernments, and all solutions while be tainted by sin. For me this post is really about the providing universal health care. It's the last leg of the social safety stool that we should put into place. How best to do that is a matter of debate. But I think the Republican-inspired solution that we've currently enacted is a good start in trying out a possible solution. No doubt it will be glitchy (sin again), but most of our programs need reform over time (see Social Security). For me if it was a choice between the status quo and the Affordable Healthcare Act, I'm going with the one that gets people access to health care. Plus, being pro-Life this was also the right move.

  21. I'd think free markets are Caesar in so far as the government regulates them.  They are definitely under that powers or tainted by sin all by themselves.  But their great advantage in these things is the sin is usually much more dispersed.  And as long as a free market operates, an entity like the Church can establish and offer a solution.  And those church entities hopefully operate with the gospel.  The whole a light shines in the darkness. It is possible to act morally.  Under the Affordable HCA is it going to be possible to be a truly Catholic Hospital?  The bishops don't think so.  And I could be proved wrong, but either every taxpayer is going to be providing for abortions, or it will be the Mexico City Policy - an R wins and the regulations order no abortion coverage, a D wins and the regulations force abortion coverage.  An election issue from here to Kingdom Come. 

  22.  I'm in.  I'd just like to make sure it (and everything else we do) is paid for.

  23. I agree. Stopping foreign wars might be a good place to start. Go get 'em Ron Paul!

  24. http://www.amazon.com/Rational-Optimist-How-Prosperity-Evolves/dp/006145205XWhen Ceasars dreamed, they dreamed of being me. Servants voluntarily offering me goods and services; without even knowing my name. I have 1000 restaurants with everything from junk food and international delicacies available to me, without me having to do a thing.I have more good and services and money available to me through means other than force (the brutal 'powers' behind the social safety net) a government has to employ.

    Because a monopoly always ensures the lowest expense, best service and lowest risk.Rabid ultraconservative George Harrison said it best: "Yet, when the Government's monopolizing, who's gonna send in, you know, this Commission to sort that one out."http://www.beatlesinterviews.org/db1969.1008.beatles.html

  25. I'd agree with Mark here. Economically speaking, by definition free markets would be less "Caesar" (government) than government regulated ones because the government is less involved. Free markets would still certainly be powers and principalities though for sure.

    I've been really struggling with where to plant my feet on this issue. I usually see government intervention/regulation as a last resort, if at all. But, being pro-life in the broadest sense, I must promote policies that reflect the sustaining of life. I guess I would support a minimalist sort of universal healthcare. I would want everyone to have access to free care that is essential to their life and their living. I think that we do have more than two options here though (1. Private, purchased care and 2. Universal free care). There are such things as private and free care (privatized in the sense that it is not a government program, but a regular business or organization). 

    My hesitation is that I do not want to mandate charity. If it is for the sake of saving peoples lives (via healthcare) then so be it. Human life is worth that. But beyond the necessities (I'm sure deciding what is truly necessary may be a can of worms on its own) the ideal I want to strive for is to have neighbor know and help neighbor. That demands a slow, intimate process of change with changes of internal conviction and motivation rather than instant policies changing external behaviors. Again, I think that sometimes those instant law/policy changes are necessary - i.e. women's right, civil rights, universal healthcare - sometimes you can't wait for the slow internal process. But ultimately, we need to remember the deeper goal of changing people's internal desires and motivations - which is rarely on our timing. This is the face-to-face, grassroots sorts of discipleship modeled so well in the Christian tradition. What's more, the grassroots movement is typically characterized more so of individual choice and freedom than are the mandates of law. The point is that I'd rather have the freedom to give and provide for others and do what is right rather than any mandate for orthopraxy. This is why I am usually against government intervention for the most part because it takes the job of helping the poor and the widowed from The Church and its people - no matter how terrible we are at performing those duties. 

    So tread carefully, because once the government fills that role, no one else will need to worry about their neighbor, and then they can just complain about their high taxes by themselves. That last bit was a bit tongue-in-cheek - this is for those of you who are like me and don't get sarcasm very well sometimes. In fact, looking at the federal budget, if certain things, unnecessary in my opinion, were taken out entirely I think we could afford universal healthcare and get rid of income tax entirely - both at the same time! So having the one doesn't have to mean any sort of increase in the other. 

  26. At the risk of going completely off topic, the problem with Ron Paul's vision of isolation is that historically when we have had that attitude, we have been pulled into wars that arguably could have been avoided with a proactive foreign policy that projected US power.  That said, I am not in favor of the current policy (I view the Iraq war as adventurism and a great waste of life and money), but to swing so far the other way would, in the long run, cost more money by pulling us into a major war that would be much more expensive than holding current troop levels and overseas bases at close to the current number.

  27. I love posts like these!  They are like getting a free college lecture!  As someone who fits squarely in the middle class range, I can relate to the feelings of vulnerability that this post suggests are are actually logical and well-founded.  At the same time, I know that as humans, our lives will never be without uncertainty; vulnerability is an inherent feature of the species.  Regarding the practical application to these statistics, I am not sure what would best lessen our vulnerability.  I like the idea of safety nets, even though I also fear big government.  However, history has shown me that free-market capitalism can be coercive and repressive, as well.  While I figure all this out, I take comfort from knowing that my life and the lives of my family members are in God's hands!

  28. Let me add some more thoughts about universal health care.

    I like to think of myself as a pragmatist rather than an ideologue. I think a lot of Independent voters are like that. We see problems in the country and we vote for the best solutions on offer.

    I care a lot about universal health care. Tens of millions of people prior to the Affordable HCA did not have access to basic health care. Many of these were children. That, it seemed to me, was a problem that my great nation should be able to solve.

    And though many are rightfully leery of "big government" we've gotten on just fine with Social Security and MediCare (I recall the sign at a Tea Party rally: "Keep your hands off my MediCare!"). Nor do we seem to object to the Industiral-Military complex and forgein wars (and why Christians don't mind their tax dollars being spent in this way and not for their uninsured neighbors is, well, quite beyond me).

    More, the Affordable HCA was a Republican-inspired idea. And the version passed was in one of it's most conservative forms (e.g., no government run insurance provider). And the idea is based upon free-market logic. Allow groups of people to ban together so that they have bargaining leverage to make the insurance providers fight for our dollar by lowering costs and expanding coverage.

    True, the individual mandate smacks of "tyranny." But it's no more tyrannical than me carrying insurance for driving my car or a host of other things the government makes me do.

    For me, it boils down to this: If the Republicans are successful in repealing the Affordable HCA what is their plan to help the uninsured? As best I can tell, there is no plan. That's not acceptable in my mind. If you don't like the AHCA, fine, but have a damned plan. Show us a better way. I don't see that among the current GOP candidates. They offer no positive way forward.

    So I call bullshit.

    Let's go with the Affordable HCA and reform as needed (as we'll have to do with Social Security and MediCare). It's the only idea on the table. So let's make it work.

  29. Huh. I've honestly never heard of the AHCA until you brought it up. I'll have to check it out and be a bit more informed in that regard. From your description, it fits well with my hope for a "minimalist" universal healthcare. I think that is a very fair point in saying that current GOP candidates do not offer another solution. 

    I think this is debate is largely an issue of dumbfounding where a lot of dialogue is talking about surface level issues while ignoring the fundamental contexts of understanding between people. It's like arguing what to do about the new found water and ignoring why there is a leak in the dam. Both are important, but one takes precedence in order to have productive conversation. Maybe we should spend a good chunk of our time discussing and thinking about the role of government, and what sort of "rights" do people have, as opposed to these hot button issues.

    I'm not a Republican, but I think an answer to your question regarding a plan for the uninsured is important now more than ever because of how messed up healthcare is today. If it wasn't in its current state, it would be much easier to answer that question by saying that we can let not-for-profit organizations and people's neighbors and friends and family take care of them. But only because the system is so inflated is it really necessary to demand universal healthcare for all. It's sort of a catch-22. I think. Though again, there may be more than just the stereotypical two options. There have been very successful free clinics and catholic hospitals that did not turn anyone away. They were able to help the uninsured AND didn't greatly contribute to national debt or inflate the overall costs of healthcare.

    It is entirely unaffordable, as this blog post shows, to pay for your own or other's healthcare without insurance. What seems to be a large contributing factor in this inflation is government's involvement. Because the government mandates it, healthcare companies actually have deals with hospitals and doctors to charge more for procedures simply because a person has the healthcare company to pay for it. If you go to some hospitals without insurance you can pay a lot less out of pocket than your health insurance will pay if they cover it.

    Anyway, the more fundamental issue seems to be how to respond to this unaffordability of our current healthcare system. We either mandate that it should be "free" for all, which doesn't necessarily mean it will actually be free. Or we fix the leak, presumably removing government from the equation. I'd rather it not be so dichotomous. I want to do both; I want to do something about the spraying water, and figure out how to patch the leak. I think that's why I want universal healthcare, as a testament to our current plight, but I also want to fix government involvement and decrease this asinine inflation that no one but government and corporate bigwigs gain from. Unless of course we could figure out a way for the government to cover universal healthcare costs (i.e. getting rid of the military-industrial complex and ending all foreign wars and removing most if not all foreign bases - I heartily agree with you on that!), there's not much point in having it for awhile if it is just going to collapse the entire economy in the process. I think that's the sort of economic pragmatism that many conservatives have at a fundamental level. I think that sort of thinking is very good for us in the long run too. 

    I think we can at least give respect and credence to the fundamental motivations of each side.

  30. I think the Affordable Health Care Act was it's original name. It eventually got changed to something like the Patient Protection and Affordable Care Act.

  31. Thanks Richard, I'll start digging!

    I would like to mention that healthcare and poverty a lot of times go hand-in-hand. And fixing poverty is not necessarily a matter of economics. There is an entire lifestyle and culture that keeps people in poverty, even if they win the lottery. The culture of poverty has its own rules, mores, and tendencies that cannot simply change with their amount of income either from work or the government. Being employed as a social worker for a year in a managed care company taught me a lot more than I ever wanted to know - I ended up quitting the job because my conscience wouldn't allow me to remain employed by that sort of business - I'll leave it at that.

    You cannot help the poor simply by throwing money at them - although this is still a necessary ingredient in your casserole of care! But no amount of universal healthcare or government program is going to "fix" poverty - though they try so hard! (I see the function of universal healthcare and relevant govt. programs more so as simply trying to keep people alive rather than helping them achieve a certain level of prosperity; we have a right to life, not the American Dream.) Poverty demands the full-scope of a face-to-face, relational ministry that seeks to invest the kind of resources over a LONG period of time necessary to create a substantial and sustainable change. 

  32. Jim, is there a particular issue brought up that you take issue with?  I believe Dr Beck wrote those to illustrate the usual split between his personal interests and work, to just give a setting for his story about social justice creeping into his lectures.  Additionally, the blog is called Experimental Theology for the reason outlined at the top of the page - "many of the essays here are theological experiments, exploratory and provisional essays that do not necessarily represent my views on matters of faith or ethics."  

    I think you're reading too far into the three short introductory lines to a blog post.

  33. Hi Jesse, thanks for being concerned, but....

    I think you have misunderstood my intent, which is to show my full support for Dr. Beck. I trust that his opinion is honest and sincere exactly because it IS his own, and not simply the repetition of orthodoxy. I'm sorry if my form of humor and sarcasm may have given you the wrong impression. If he was a seminary trained, professional theologian I would have much to question his open-mindedness... but he's not, so I don't.

  34. No, not at all!  I'm sorry for the confusion...I see what you mean now :P

    This is one reason I might not mind the introduction of a sarcasm punctuation mark.  http://en.wikipedia.org/wiki/Irony_punctuation

  35.  I find it is always helpful in this discussion to remember that the concept of "poverty" is a relative one, beyond the fact that there is more than one way way to be "poor". 

    Poverty in the USA does not look anything like poverty in (pick your third world spot).  Then dig deeper and ask yourself why.

  36.  Just as you will never understand how it is "just" for our government to confiscate your money to pay for my defense, I shall never understand how it is "just" for our government to confiscate my money to pay for your healthcare.

  37. Susan, thank you for your peaceful reply when in this case my thoughts weren't clear to you!

    Also, note in the last line my use of "good news" and "the way" which point at Richard's work- which doesn't go by the name "FOF"....

    Peace to you~  Mike

  38. I'd like to offer that when it comes to the concepts of government or corporations, there's a more intelligent conversation to be had than the caveman discussion:

    Governments- BAD. Ugh.

    Corporations- BAD. Ugh.

    Neither exist unless people make them so- right?     A better discussion:

    When we organize ourselves in the enterprise of making society together, what do we like about it when we create what we need through "corporation"? "government"?

    And then ask similarly, what don't we like?

    I'll end with this riddle.

    Q. What's the difference between a democratic society supporting itself through free exchange which fails to spread well-being through out both, human creation and natural creation, and- Heaven?

    A. In Heaven, there'll be adult supervision.

  39. On a more intelligent use of the concept of Caesar.

    To limit the use of Caesar to a stand-in for government, is to blind us to the life and daring of Jesus.

    Jesus isn't the Son of God in a vacuum. Tiberius, in reign as the Caesar during Jesus' time was the SON of Augustus. The Roman senate conferred to Augustus the title, "God". What does this make Tiberius in Jesus' day?

    The historical question posed to human kind is: do you think god is more like Tiberius or Jesus? (Both are "Son's of God.)

    So- when in the corporate structure, we make the work force (i.e. members supporting families) a cost to be driven down, while at the same time, we celebrate the wealth embodied in the CEO persona, are we voting for Tiberius or Jesus?


    I'd say by the looks of the skewing shown in the graph above, our vote has been for Tiberius- not Jesus: maybe not by you- but if I hear nothing said by Focus On the Family about this skewing--which occurred precisely, during its lifetime--how should I read their vote to be?

    The very focus of a family's welfare is ignored by the Christian group embannering itself as the family's champion. Even more goofy, is that in reality, FOF champions the cause of Free Market Fundamentalism--a distortion of Free exchange, as it's a simplistic ideology merely crafted from a dogmatic abstraction of Free Exchange--and because Free Market Fundamentalism in the end, concentrates wealth rather than spreads it, FMF is in the service of Tiberius and not of Jesus isn't it? 

    After all, wasn't Jesus about spreading well being rather than concentrating it to a "deserving" few?.  

  40. I know exactly what you mean Jesse. Without face to face conversation we often miss so much of what another person is trying to convey in their comments. 

    But if everyone was as intelagint as I am then we wouldn't have these problems. ;)

  41. Dr. Beck, thanks for this post. You've made it clear that statistics are moral. Choosing to display the mean or the median in summary stats about peoples' lives is a window into the moral framework of the statistician or the agency etc.

    I'm struggling though -- with the parables of the search for the single lost sheep and coin. (Luke 15:3 ff). Isn't there a hazard to compassion built into the very idea of summary stats? Aren't the outliers just as much a part of the realm of God as the normal ones .. the ones within a couple of sigma of the mean?  Aren't we all outliers before the King on his throne?  (Note: I'm not making an argument here specifically in favor of those folks who make 500x the median household income. This is about pretending to understand actual people by averages.)

    Of course, there's also the moral hazard of self-deception built into using normal distributions to manage risk (Gauss's central value theorem, etc.) as a substitute for covenant relationships with living people.  If you believe Nassim Taleb (The Black Swan), that kind of statistical self-deception is what trashed the economy a few years ago. 

    Thanks for all you do.

  42. Hi Oliver,
    Fantastic point. I do spend some time when lecturing about the mean about the moral hazard inherent in its calculation. How it obliterates diversity, quantifies souls, and enshrines itself as the "norm."

    I quote Mark Twain regularly in my classes: "There are lies, damned lies, and statistics."

  43. The fact that you claim defense for yourself but assume it's only other people who have to worry about healthcare is the reason you will never understand.  We really are all in this together.

  44. No, qb calls BS.  BIG TIME.

    There have been PLENTY of alternatives offered, and several comprehensive plans put forward by conservatives that are based on subsidized premiums for the poor rather than this awful monstrosity, the cost of which (predictably) is already mushrooming out of control even BEFORE its tax implications are felt, a tax impact whose inception was nicely (!) and intentionally delayed until after the 2012 election cycle.

    When AHCA was voted through by a hegemonic Democrat party, it was rammed through with cynical bribes to co-opt some wavering Democrats with religious objections (see also "Bart Stupak"), without full knowledge of what was in it (see Madam Pelosi's famous "we have to pass it so we can then see what's in it" BS), and using the threat of heavy-handed parliamentary tactics (aka "reconciliation," which bypasses the Senate's filibuster rules).  That such a litany of tactics was required to get it passed is a pretty clear and compelling case that it was bad national policy.

    The equivalence you posit between the individual mandate and other government mandates has been repeatedly shown to be spurious; you need to do more homework on that, because your dog won't hunt.

    To repeat:  there are credible, safety-net GOP plans that never saw the light of day, legislatively speaking, when the AHCA was being rammed through by a two-branch Democrat bully in 2009.  But the plans have been there all along.  You may have to spend some quality time with Paul Ryan and his gutsy brand of policy wonks if you want to learn what they are.

    This presidency has been an utter disaster, both practically and constitutionally.  It's time the American people pulled their heads out of the MSNBC/CNN/HuffPo sand and reckoned with the reality that the GOP-led House has been faithfully putting forward credible, liberty-preserving plans for both budget and health insurance ever since they earned the right to put Paul Ryan in the Budget Committee's chair.  In the meantime, the yellow-bellied Majority Leader (!) from Nevada, Harry Reid, has hid behind the skirt of little rhetorical and parliamentary maneuvers for nearly three years, refusing to offer a comprehensive budget proposal of his own.

    So, qb calls BS.  Big time.

  45. Just so you know, Paul Ryan's latest budget proposal seeks to change this scenario by reducing the availability of tax-shelter dodges, which are available primarily to the wealthier, precisely so that lowering rates across the board is approximately revenue-neutral.

  46. Paul Ryan has a nasty habit of sticking his neck out with affirmative proposals while other people duck for cover and hide in the weeds.  His health-care proposals, for those who really wish to dig in, can be found at http://paulryan.house.gov/Issues/Issue/?IssueID=9978 .  qb

  47. "[F]ree markets are Caesar in so far as the government regulates them."

    This is silly.  Some power will rule them, and absent a more-or-less democratic government, that power will be the rich.

  48. Yes, alternative proposals have been floated. What I said here in my comment is about the proposals on offer by the current GOP candidates, the people I'm currently evaluating for the coming election. I'm asking about their proposals, the ones I, myself, can vote on in November.

  49. In looking over Ryan's most recent budget it still seems he's ignoring MediCare. Which, per my comment above, is both ironic and philosophically inconsistent with the "big government" rhetoric.

  50. Please specify/link to the alternatives and comprehensive plans you mention.  The ones I've seen have offered nothing like this - so if they exist, I'd like to take a look.  The Paul Ryan plans I've seen so far, including that got pushed out within the last day or so, cut social services dramatically at the same time as cutting upper-income tax rates dramatically.  That doesn't seem like much of a safety net to me.
    Also... your last paragraph (or second-to-last if you count the final six words) brings your comments out of the "potentially helpful to the discussion" realm and into the "unhelpful and meaningless partisan rhetoric" realm.  There are lots of other places we can go for the latter, so it'd be nice if you stuck to the former here.

  51. Adding on to Stephen above, if I'm attempting to think theologically which is way too tough, all the law does is compound sin.  The more and the bigger the law, the more sin. (Romans 5:20)  The government is an entity of the law.  It is the rightly established authority, but it is still part of the law. (Romans 13:4) The best government as regard to sin is then that one which governs least or at least realizes its proper sphere.  Are the works of mercy the proper sphere of an institution of the law?  (I think of health care as fundamentally a work of mercy.)  Government mandated health care is a fundamental confusion of law and gospel that can't but lead to grief. (And health care is fundamentally different from Auto Insurance in that it is a work of mercy and not just personal responsibility.  As person without insurance can be told you can't drive and nobody gets upset.  A person without health insurance that gets sick still calls for mercy.)

    Jeff W, instead of calling something silly because of less than thought out ad hominem toward "the rich", please sit and think for a second.  Absent government regulation of who can enter, leave or participate in a market, it is open to anyone.  Can the rich attempt to corner the market?  Yes they could.  And the vast majority of examples of rich attempting to corner an open market end poorly with the rich being much poorer. (Pop culture reference Trading Places which takes some of its comedy from the real life Bass brothers.)  What "The Rich" can corner and do very well is when the government regulates.  Regulatory Capture and using government entities to erect barriers to entry are business school 101.

    What you can look at the Health Care Act as is major barrier to entry to Catholic hospitals and essentially a theft of two centuries of work of that church.  In a free market politically liberal protestants are just as free to get together and start hospitals or offer insurance plans.  Instead, allied with a secular group they are using the government to regulate out and declare beyond the pale what they didn't do.  There are all kinds of sins of omission from Christians not stepping up to help with health care for the poor.  None of those sins are grounds for mandating as part of the law what should be a function of the gospel.  What they are is the Lazarus outside our gate that will testify against us.

  52.  In the little book 'The Real Worlds of Welfare Capitalism', which studies how people fare through longitudinal data over the decade 1985-1994 in the USA, the Netherlands and Germany, one of the things they look at is the chances of a person from a 'privileged' social class (white males in the USA) who is well-off at the beginning of the decade of being poor by the end of it.

    I don't remember quite how they defined 'well-off', but I believe it was around $50k, so about your 'solidly middle class' person.  Poverty was defined at half the median income, which was about $20k again.(*)

    There was a surprisingly large chance of impoverishment in the USA. I think it was around 10%.  That's a lot higher than things we'd usually take care to insure against, like house fires.

    They noted that a common cause for impoverishment was medical costs.

    (For women, the most common cause was divorce)

     (*) prices were adjusted for inflation - not that it'd make that much difference, because the median income in the USA hasn't changed much in the last 30 years.

  53. Excerpted:

    "The House-passed budget repeals the President’s disastrous new health care law and protects the health and retirement security of those who need it. With the creation of Medicare in 1965, the United States made a commitment to help fund the medical care of elderly Americans to ensure that a serious illness would not exhaust their life savings or the assets and incomes of their working children and younger relatives. Medicare’s structural imbalance threatens beneficiaries’ access to quality, affordable care. A flaw in the structure of the program is driving up health care costs, which are, in turn, threatening to bankrupt the system – and ultimately the nation. Unless Congress fixes what’s broken in Medicare, without breaking what’s working, the program will end up causing exactly what it was created to avoid – millions of American seniors without adequate health security and a younger working generation saddled with enormous debts to pay for spending levels that cannot be sustained.It is morally unconscionable for elected leaders to cling to an unsustainable status quo with respect to America’s health and retirement security programs. Current seniors and future generations deserve better than empty promises and a diminished country. Current retirees deserve the benefits around which they organized their lives. Future generations deserve health and retirement security they can count on. By making gradual structural improvements, Congress can preserve America’s social contract with retired workers.Recognizing the problems facing Medicare, the House Budget Proposal:Saves Medicare for current and future generations while making no changes for those 55 and older. For younger workers, when they reach eligibility, Medicare will provide a list of guaranteed coverage options from which recipients can choose a plan that best suits their needs, the same way members of Congress chose their plans today.  Then, Medicare will provide a premium payment directly to the plan of the beneficiaries’ choice.  Medicare will also provide additional assistance for lower-income beneficiaries and those with greater health risks.
    Ensures that the cost of frivolous litigation is not passed on to consumers in the form of higher health-care premiums by capping non-economic damages in medical liability lawsuits.
    Stops the raid on the Medicare trust fund that was going to be used to pay for the new health care law. Any current-law Medicare savings must go to saving Medicare, not financing the creation of new open-ended health-care entitlements.
    Fixes the Medicare physician payment formula for the next ten years so that Medicare beneficiaries continue to have access to health care.Allowing the federal government to break its promises to current seniors and to future generations is unacceptable. The reforms outlined in the budget passed by the House protect and preserve Medicare for those in and near retirement, while saving and strengthening this critical program so that future generations can count on it to be there when they retire."---------------------------Yes, Rep. Ryan has virtually ignored Medicare!  LOL.Of course, one must actually go to the text of the legislative proposal itself to find out how these things are implemented; that would take up too much space, as if this wasn't already doing that.qb

  54. As the Saviour said, "ask, and ye shall receive; seek, and ye shall find."  To that end, qb has done some homework for anyone who is interested in the answer to the challenge Richard has posed:

    http://amzn.to/GDLxOt (Ron Paul's proposals on many fronts)

    http://www.newt.org/solutions/healthcare/

    http://www.mittromney.com/issues/medicare

    http://www.ricksantorum.com/repeal-and-replace-obamacare-patient-centered-healthcare

    Now, let's get one thing straight:  saying "I disagree with the approaches the candidates are taking" is a far cry from saying "But as best I can tell, there is no plan. That's not acceptable in my mind. If you don't like the AHCA, fine, but have a damned plan. Show us a better way. I don't see that among the current GOP candidates. They offer no positive way forward."  The former is, of course, acceptable; and qb will gladly concede that Santorum, in particular, does not meaningfully address Medicare in his platform.  But to say that the four remaining candidates have not offered a plan is simply to have failed to seek their plans where one might expect to find them, that is, on this newfangled thing known as the World Wide Web.

    Stump speeches are not the place to get into the weeds on this stuff.  But if you want details, details you may have.

    Your cheerful servant,

    qb

  55. Matt, the polemics began with "have a damned plan" and "I call BS."  My reply is:  "I call BS; and don't be a coward, Harry."

  56. Much of what we find in the candidates' proposals can be found in utero at the Heritage Foundation's health-care strategy briefing:  http://www.candidatebriefing.com/health-care/

  57. Any current-law Medicare savings must go to saving Medicare, not
    financing the creation of new open-ended health-care entitlements.


    You don't see the irony in that?

  58. I'm still calling BS. The soon-to-be GOP nominee, Mitt Romney, is not making these proposals (i.e. privatize MediCare) in front of American senior citizens.

  59. Once again, you may find the proposals ironic, distasteful, or otherwise without merit, but that is a far cry from your original complaint, to wit, that there are no alternative plans on the table.  You may have wished to present yourself as open to conservative alternatives, but your continued misdirection in the face of substantive challenges to your central, polemically reinforced complaint has been exposed for what it is:  an exercise in crawfishing.  You're better off just admitting that you wouldn't really consider voting for any GOP candidate who presents a health-care alternative that involves repealing BHOcare, which is to say, any GOP candidate at all.  In veritas libertas, and all that.

  60. Yes, of course, which is why Romney resoundingly carried the primary in Florida, the home of snowbirds a-plenty, who may have been Romney's stoutest supporters.

    http://www.cbsnews.com/8301-503544_162-57369367-503544/how-mitt-romney-won-the-florida-primary/

    Either that, or Florida's retirees are all senile and haven't any idea where Romney stands on MediCare.

    /chuckle

    qb

  61. I'll admit that Paul Ryan has a plan.

    But two points in this regard:

    Point #1:
    To quote my comment where "damned" and "bullshit" are used:

    They can have my vote this year if they show me a better way to solve
    this problem. But as best I can tell, there is no plan. That's not
    acceptable in my mind. If you don't like the AHCA, fine, but have a
    damned plan. Show us a better way. I don't see that among the current
    GOP candidates. They offer no positive way forward.

    So I call bullshit.


    "They" as in reference to the "current GOP candidates." As in, "they can have my vote this year if they show me a better way to solve this problem."

    Point #2:
    Even Ryan is afraid of messing with MediCare to be accused again by Newt Gingrich of "right wing social engineering." So the ironies abound.

    Big government is bad. And please keep your hands off my MediCare and Social Security. (And don't cut defense.)

  62. 1.  You fancy yourself a pragmatist, right?  Would it surprise you to learn that one of the central tenets of pragmatism is incrementalism?  

    2.  If you are really paying open-minded attention to what conservatives mean when they engage in the necessary practice of sloganeering in this ADHD society, "big government is bad" really means "extraconstitutional government is a dangerous and ultimately ruinous road."  They are not going after undifferentiated government in the abstract, and they are not anarchists.  (The Rothbardian libertarians ARE anarchists, but conservatives disavow Rothbard on pragmatic grounds:  we have no clean slate to begin with.)

    3.  Below, I have pionted to FIVE places - other than Paul Ryan's plan, that is - where you can find more or less comprehensive approaches to health insurance reform from a more or less conservative perspective.  FOUR of those five places happen to be - surprise!! - the campaign sites, or in Ron Paul's case the most recent book, of the four remaining GOP candidates.  Don't try to convince qb that you don't have access to the GOP candidates' respective plans for health insurance reform.

    4.  Finally, let's take your statement below and deal with it practically.  You said, "...I'm asking about their proposals, the ones I, myself, can vote on in November."  Let's say for the moment that the GOP retains the House and Paul Ryan remains Chair of House Budget.  If you vote for one of the GOP candidates and he happens to win, then it doesn't matter whether the plan is Romney's or Rand Paul's or Heritage's or Paul Ryan's; you will have voted to consider a comprehensive plan that someone in the conservative wing has put forward as a starting piont.  And your vote in November will, in effect, have been a vote on one or more of the conservative proposals currently on the table.

    If you vote for BHO and he (heaven forfend!) is returned to the White House, you get what we have now:  a disaster.

    qb

  63. On those points.

    1. Agreed. Which is why I gave props to the POTUS for bucking the liberal voices in his party (who still feel betrayed) and going with the Republican plan of the 90's.
    2. I disagree. I think they are playing politics with older white voters. Philosophically, we know the GOP doesn't like Social Security. But their base is getting older. Not that Obama is any less a politician.
    3. I'm on my iPhone and can't see the links. I'll get back to you. But see #4.
    4. Ryan doesn't have a plan. How many people will his plan cover? At what cost? Point me to an independent analysis of his plan. I'd like to see something more specific that talking points from candidates and conservative think tanks. Show me where Ryan's plan covers every American.
    As for disasters, I'm grateful BHO has cleaned up the mess the last president left us. I'd say: disaster averted.

  64. Well, to complicate things, a church pre-school wouldn't be 'free' either, necessarily. Not costing money is hardly the equivalent of not costing anything. What about the children whose parents have a different religion than yours, or no religion at all? How would they rest comfortably, knowing you felt an obligation to guide their children's spiritual life, perhaps in directions they disagree with? How would a trans child's parents feel about sending their child into an church environment? How would gay parents feel about sending a child into a church environment? What would it cost them, mentally and emotionally, to send their children to your preschool?
    And suppose your church hadn't run a pre-school. If government did not provide one, who would? Who would be obligated? And what allegiances would they have, that parents and children might be uncomfortable with?
    Government programs certainly could benefit from reform. (An area your church might help with, if you're inclined. If you're no longer running the pre-school, why not devote your freed up time to helping the less-on-the-ball parents sign up?) But a materialist curriculm is a good thing. Spiritual matters should be a matter for a child, their family, and their religious heritage to shape and determine. Religious education is fine as an opt-in thing, but it shouldn't be the only option available.
    To be frank, I can't trust a church to provide social justice. I've seen what churches have done to my brothers and sisters in the name of god, and remember what has been done to me. Justice was not involved. Before any argument that religion is uniquely suited to providing social justice can be taken seriously, religious people have to quit their support for policies and actions that support the oppression of women and QUILTBAG folk.

  65. I have seen several evangelical Christian church schools, inclusive of pre-schools, that began and still exist today as 'white flight' schools. You better believe that parents who can barely afford other private school institutions are given every kind of financial 'help' by the churches and extended family members (grandparents, etc.) just so those babies and the other primary school aged children would not have to get on a bus ride to attend the inner-city schools down-town. The evangelical Christians in these churches starting up these white flight bastions of evangelical Christian education find legal ways to keep the government from forcing their precious children from mixing with children of color. I was so naĆÆve that this could even happen even 30 years after the Civil Rights Act that when I discovered I was teaching at one of these schools I fell physically ill. 

    Oh, BTW, many evangelical Christian church schools do nothing to insure their staff, teaching or otherwise, have any medical care. Full stop. The salaries they pay are rarely if ever adequate enough enable anyone to afford viable health care. Many of the young teachers who go to work for these schools who pay at or below poverty wages with no healthcare benefits are praised up and down for their magnanimous commitment, Christian 'sacrifice' and altruistic sense of social justice. 

    This is not to say many evangelical Christian church schools in America do not do great things. But they still charge fees to prop up an exclusivity-based agenda. When they take in a few scant charitable 'projects' how many of these are tokens only, used for PR? And what kind of government system do these schools give homage to? Because whatever they system they sign on to does not have Christ at the center.

  66. I'm awfully sorry about calling you or your argument silly.  My thinking here is, to me, an elementary power calculation, but my reaction towards you was just flat-out impatient and inconsiderate.  I ask forgiveness.

    I'll say that I'm not terribly interested in the particulars of the debate about the health-care act, but instead about a general awareness of power relationships outside government.  However, I'd rather ask for a "reset" on the conversation given my tone earlier, so I'll defer such a conversation to a later time.

    Again, I'm sorry.

  67. While true, I find such arguments most akin to: a Baron rides by a peasant lying in the road and when told of their destitution merely says "Hey, at least your not covered in shit..."

  68.  And that power will, inevitably, *become* Caesar.  Citizens United will see to that.

  69. Wow.  /tilt

    Taxation = _a priori_ claim on [what is said to be] another's property.  But...it's not confiscation.

    Wow.

  70.  Still, no.  First, one has to consider how one even has "property" in the first place.  Since the world was created by God, and He handed out no deeds, then the ONLY reason you can lay any claim of ownership on any *thing* is the agreement by everyone else that we won't pound on you and take it away and say it is ours.  So your "property" is merely an illusion created by social contract.

    Second, taxation is merely the means by which society says that a part of your labor output must be put towards the commons so that we can do in common those things no individual can do.  Like build roads, make sure all children are educated, keep those not wanting to agree to the "no pounding on others" compact from pounding on others, and, yes, seeing to the health and welfare of the least among us.  So not property, but works.

  71. Of course, by definition the mean is that income which everyone (all households in this case) would have if all had the same income. So if we took all the high earner's income (actually, everyone's income) and divided it up equally, we'd move everyone to $64,344. The median income earner currently at $46,326 would gain $18,018. This is a used car away from the mean. On the other hand, a mere $250,000 year income household (where it seems like the wealth re-distributors think obscene wealth begins) would lose $185,656. This assumes, of course, that there's no commensurate value added by the high income earners and hence that societal wealth and income production could just roll on as usual.

    Another observation is that, unless everyone makes the same, the incomes will certainly be positively skewed since they are bounded on the bottom by zero and unbounded above.

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