Sunday, December 12, 2010

Abilities Chosen -- Effects on Wealth Distribution

I'm baaaack! Sorry it took so long. I've interrupted my study of the super rich to work on a project to efficiently get free money to the poor. (Our current welfare system is inefficient and encourages bad behavior.)

Anyway, in part 3 of my series on the secret of the super rich, commenter Paul suggested I look at the effect of selecting which abilities to employ. That is, Bill Gates did not employ his atheletic abilities to build Microsoft. In fact, limits to athletic ability may have helped since he wasn't distracted in high school by playing football and chasing cheerleaders. True, if he had been severely handicapped athletically, a la Stephen Hawking, he might have had less success. But otherwise, this ability did not particularly factor in.

But it has factored in for many other successful people.

So, maybe it's just a matter of choosing several strengths to put together in order to become a member of the super rich. To test this hypothesis, I looked at multiplying together the best of several distributions. That is, in the previous post I looked at multiplying five abilities together, which each ability was a distribution generated by 5 20 sided dice. The result was:

(This time around I have rescaled my graphs by the bin size, creating proper distributions. The units are population per $1000 income range.)

Now, let's take our five best abilities from among ten abilities rolled with the same distribution. The result is:
Unless I made a programming error, allowing people to pick a subset of available abilities to multiply together reduces the outliers to the right. Yes, when I take the raw numbers, I get more high rolls, but once scaled to population, median income and standard deviation, I end up with a gentler slope on the left side of the curve. The right tail is a bit fatter, but doesn't go out as far.

In other words, abilities chosen, even when multiplied, produces a curve that fits intuitive notions of a meritocracy and not the huge outliers to the right that we see in real life.

Of course, not everyone chooses their best abilities. If the super rich do choose to exercise their best abilities while others allow the whims of fate to set their careers, this might explain some of the wealth gap. But I think other factors are at work. Hopefully, I'll get around to explaining them in a timely fashion.

4 comments:

Paul said...

Huh, very interesting! I'm surprised (and pleased) to see you ended up running this test! Not the results I expected but interesting nonetheless.

I would also like to say that I'm really pleased with all the recent changes to your site -- the blog, commenting system, etc. I would, personally, love to see FB integration on your articles. Sure, I can copy/paste the URL, but that's so Web 1.0 ;)

I have somewhat of an article request for the blog: I recall one of your "books" mentioning your extreme distaste for the public education system, and I'm kind of surprised by this. I'm currently a right-leaning Libertarian (I'm frequently scribbling around the Nolan Chart) but I make a huge "lefty" consession for education. In my mind, one of the few ideal opportunity equalizers.

The problem with free-market education is that the children of the wealthy will always have a higher-quality education purchased for them, whereas the children of the poor will be limited in their options - even with vouchers - due to the inability of their parents to move to a geography with a school that's an ideal match for the student.

Now I'm certainly not a public school apologist and there are so many things wrong with the current system that one can barely begin to list them... but I've thought a lot about it, and I think that with a few simplistic (free-market-inspired) alterations to teacher's compensation and curriculum structure, I could even get the NEA on board with a plan to make our education competitive again... but I'm quite likely being naive to think that. ;)

I'm working on an article that lays out my thoughts the public school system and I'd be interested to know your thoughts on the subject...

Thanks,

-Paul

Carl M. said...

Hi Paul. Public education is better than nothing.But I think vouchers to be a great deal better.

Like any long running government program, education has drifted from the primary purpose of educating the youth to being a jobs program and a source of profits for textbook publishers.

The rich can already buy a better education either by moving or going to private schools. Frankly, I don't worry about the rich winning the self-improvement race. Welfare (including public schools) must always follow behind cutting edge luxury.

My problem with public education is that it is below Wal Mart standards for many districts. Forgetting how to teach phonics or how to spank a bully are unacceptable.

Withing cities vouchers would make excellent education universally available for those who truly want it. In rural areas this would not be the case, but in rural areas, you can live the good life without an excellent academic education.

Paul said...

Thanks for your thoughts. I did also find where you wrote about the public school system: "Evolution IN the Bible" -- a most unlikely place!

I can definitely buy your argument for urban schools, though I am a little surprised at your stance on rural schools. While the sub-par public ed system might be adequate to succeed in a rural lifestyle, not every rural child wants to grow up to inherit the family farm.

Equal opportunity is lacking in this scenario!

(Sorry, I know, this is not the right site for this discussion.)

-Paul

Carl M. said...

Rural schools provide more leadership and diversification opportunities while providing less advanced specialized classes. This is simply a matter of economies of scale. Vouchers vs. public schools has no effect on this phenomenon.

Vouchers may or may not produce better schools in the rural areas. There, school boards are more accountable due to the diseconomies of scale of democracy. To get a high quality prep education when you live in a rural area, you generally need to go to boarding school. Either that, or be into self-study.

I went to a rural public high school by the way. There was no calculus class available, and the physics teacher had only one year of college physics under her belt. On the other hand, I was able to run track, play in the band and be on the debate team at the same time due to the difficulty of filling all the slots for these activities.