Friday, December 07, 2007

Why are Klingons getting screwed?

In the Galaxy there are 1 billion people of different species; 30% of people are Klingon, and the other 70% we call Federation.

Everyone in the Galaxy gets an IQ test. The tests are set up so that the average score is 100 and the standard deviation is 15. (For those who need a refresher, this means that 68% of people will score between 85 and 115 with the average being 100.)

When you sort the test results into Klingon and Federation, you find that Klingons don't do as well; their scores come out with a mean of 91 and a standard deviation of 13. Federation scores come out with a mean of 104 and a standard deviation of 14.

The Galaxy is a loathsome managerial socialism, but it IS speciesblind. The result of your IQ test, and that result only, determines your career, no matter what your inclination or talents run to... there are three basic careers, scientist, bureaucrat, menial. The Galaxy firmly believes that test scores to some extent reflect fitness for careers, though the extent is argued.

Scientists are all those who score 125 or better. Bureaucrats score 95 or better, up to 124. Menials are all those who score under 95.

Scientists have a mean IQ of 131; they make up 5.1% of the total population.

Bureaucrats have a mean IQ of 107 with a standard deviation of 8, and 59.2% of people are bureacrats.

Menials are 35.7% of the population, with a mean IQ of 84.

So how do Klingons do?

Klingons are 51.2% of the Galaxy's menials, and 61% of all Klingons end up as menials--but only 24.9% of Federations have to worry about ending up as menials.

Klingons are 20% of the Galaxy's bureaucrats, and only 38.7% of Klingons can expect to have that career; but 68% of Federations can look forward to eternal job security and petty displays of power.

Only 2.2% of scientists are Klingons; only 0.4% of Klingons can hope to become a scientist. Only 7% of Federations get to be scientists; but scientists are 97.8% Federations.

Nonetheless it is true that 42 million Klingons are smarter than the average Federation. In other words, 14% of Klingons are smarter than 50% of Federations. But it is the very same thing to say that 86% of Klingons are dumber than 50% of Federations.

Given Klingon aggressiveness and irritability, I think it is safe to conclude the Galactic society is not going to last long!

Society is very FAIR, even if it's not reasonable; everyone takes the same test and everyone who gets the same score gets the same result. But imagine you are a Klingon. 3 out of 5 Klingons are doing the scut work; 98% of scientists are NOT Klingons. It would take a remarkable sort of person who wouldn't feel that the deck was purposely stacked against them in some way.

(Incidentally there is a counter-intuitive effect here: the average score for Klingon scientists is slightly higher than for the average Federation scientist. The average for Klingons is 134 and for Federations it is 131. But among scientists the distribution is not Gaussian; far more scientists are at 125 than at 160. At the tails of the bell curve "average" no longer means "typical". The "typical" scientist is nearer 125 no matter his species. More on this later.)

Suppose we want to make careers in society "look like the Galaxy" at 30% Klingon. We could do this in several ways.

1) Throw out the tests. Now you get your career based on what school you went to, or who you know, or who your parents are, or how much you bribe the career assigners, or where you live, or by lottery, or whatever--or maybe if you're Klingon or not, whatever way gets you to 30% of professions being Klingon. But of course now profession will correlate much less with intelligence than it did. We expect that scientists really ought to be smarter than bureacrats, and they in turn smarter than menials (or better at paperwork at least), and this solution is unsatisfactory.

2) Keep the tests but reduce the standards until scientists are 30% Klingon. We can't actually get this without making everyone a scientist, so let's settle for about 10% Klingon. We have to lower the scientist score to 105. If we do this, scientists are now 11.0% Klingon. Leaving the other scores the same, bureaucrats are now 28.8% Klingon, looking like the Galaxy, and menials are unchanged at 51.2%. 61% of Klingons are menials and 14% of them are scientists, compared with 25% of Federations as menials and 50% as scientists.

But this alludes to our next problem: the percentage of scientists has to go from 5.1 under the old system to 38.2 under the new system. The Galaxy probably can't afford that many; and there may not be enough for all of them to do! The other issue is that the mean IQ of scientists drops from 131 to 115, massively concentrated at the low end. (Bureaucrats go from 107 to 100, due to so many of the smartest ones getting bumped up to scientists; however, their numbers drop from 59.1% of the Galaxy to 21.6%, probably a good thing.)

Under this system, expect a lot of Departments of Klingon Studies to pop up.

3) Keep the test, and the numbers of scientists and bureaucrats the same, but reserve 30% of scientist and bureacrat positions to the smartest Klingons available.

Federations now need a score of 127 to be a scientist; Klingons only need 112. Federations now need a score of 100 to be a bureaucrat, and Klingons only need 87. The numbers of scientists and bureaucrats are about the same and the percentages of Klingon scientists and bureaucrats is almost 30% (27.6% for scientists and 30.5% for bureaucrats). The change negatively affects only 13% of Federations, 2% of whom could have been scientists and 11% of whom could have been bureaucrats.

But now we have a new problem. 94.3% of Klingon scientists have scores below ANY Federation scientist. Under the old system, Klingon scientists were rare but they had the same test scores, with their average slightly higher. Now "Klingon scientist" becomes nearly synonymous with "lower test score". The problem of unequal test scores has been made more acute among scientists than among the Galaxy at large. The problem is not so bad for the bureaucrats, with only 65% of Klingons doing worse than ANY Federation bureaucrat.

Remember where we started: we had species unequally distributed among the professions due to Klingons having lower scores. We distributed them equally across the professions; but now ALL professions have Klingons dominating the lower end, much MORE unequally than they did in society as a whole.

Under the old system, most Klingons you saw were menials. Under the new system, 30% of all professions are Klingons, and they are nearly always the worst-scoring 30% no matter their career. We have replaced one problem with another, arguably worse one.

Conclusion: If we really can measure fitness for the careers, AND if there really is nothing anyone can do to make Klingons more fit for the careers, THEN Klingons are either going to dominate the lower rungs of whatever we group we put them in, OR we are going to have to abandon the idea of assigning careers according to merit.

I would hesitate to draw many parallels between my parable and our society. I've made things very simple, and I never attempted to address whether the test really is or isn't prejudiced against Klingons in some way. Option 1 sounds vaguely like the system we had before standardized testing. Our system today seems like a combination of all three options.

What I do think my parable shows is this: if we do have a system that is supposed to reward merit, and there really is some identifiable subset of the population that really, for some reason that is no one's fault, doing less well under that system, then that group is going to feel really screwed over, and the only solution will be to give up meritocracy to some extent.