Stardate 20030131.0504

(Captain's log): In sports, the difficulty of making your next score is not affected by your current score. The goalposts in football don't move; the size of the soccer or hockey goal doesn't change. But what if they did?

Suppose that in basketball the size of the hoop changed? Suppose that each time you made a score, your hoop got bigger and the other team's hoop got smaller? And each time they score their hoop got bigger and yours got smaller?

Certainly when your hoop was larger it would make it even easier to score again, and when it was smaller it would make it harder. If this was how the sport was truly played, you couldn't necessarily predict which team would win any given game, but you would certainly tend to expect that whoever won did so with a really lopsided score, because once one team got a fair amount ahead (and thus had a substantially easier hoop to hit) it would tend to pull away. The one thing you would not expect to see is a lot of close games.

In fact, what you'd tend to expect was that once one team got enough ahead it would be virtually certain to win, with its score racing away from the other team. After all, once your hoop is smaller than the basketball, you don't even get a chance to score again no matter how hard you try. At that point the game's over even if there's still time on the clock.

That's an example of positive feedback, of a tendency in a system to reinforce differences. Some systems are actually like that, where "even" and "fair" are unstable conditions (a pendulum balanced on top) and that even small differences will magnify themselves and come to dominate the situation.

Of course, a team which was behind could conceivably still come back and win, if its players got a hot streak, but doing so in variable-hoop basketball would be a lot more difficult than in regulation basketball.

It comes as an unpleasant surprise to most people to learn that variable-hoop is actually the norm. The state of "even chance to score the next time no matter the previous score" which we take for granted in sports is an artificial construct which is rarely reflected in the real world.

In most important competitive systems, the winners gain an advantage and the losers tend to have a harder time, which means that the winners are likely to keep winning. This is particularly true in economic competition, for a large number of reasons, but there are three in particular: economy of scale, network effect, reinvesting the profits. Because of these three, what you see is that over time nearly any inequality in an economic system tends to self-reinforce, because they create what are generally referred to as vicious circles and virtuous circles.

Long time readers of this site will have become familiar with discussions of economy of scale and network effect; they're often found together but they're not really the same and each can occur without the other.

Economy of scale refers to cases where doing more of something permits you to do each one cheaper or better. If you are producing fifty widgets per year, each one has to be made by hand. But if you're making fifty thousand widgets per year, you can afford to invest in specialized widget-making machines which are more efficient, for instance. It also means you have a larger sales base over which to amortize your engineering and other fixed expenses. If these are possible, then what it means is that Fifty Thousand Widget Company can sell a widget for a lower price than Mom's Basement Widget Workshop can.

Network effect refers to cases where the perceived value of a product rises as a function of the number of other people who use it. A telephone is worth a lot less to you if only a small percentage of the people in your city also have telephones, and its value rises as a function of penetration. It reaches maximum value when nearly everyone has one.

Providers and customers tend to flock to each other. The web is more valuable to readers as the number of web sites rises, and a provider of material is more attracted to the web as a means of distribution as the number of web users increases.

Languages are subject to network effect. The value to you of a given language is a function of how likely it is that it will permit you to communicate with any given person you meet and need to talk to. (Or of how likely it is to permit you to read a book which contains information you need.) For an author, the value of the language that his book is written in is a function of the number of potential readers who know that language.

Reinvesting the profits refers to the fact that in commercial activities a company which produces fifty thousand widgets makes more money than the fifty-widget company, and thus has a bigger war chest to apply to the future. It can use some of that to buy yet more equipment for its factory, or invest in engineering to design a better widget, or can bank some of it to cover potential future losses if it makes a mistake or has a bad year. But in a more general sense, it refers to the way in which the existence of inequality helps to magnify it in future because the gains feed back in the next round of competition.

If you're on the winning side of any or all of these, you are the happy beneficiary of a virtuous circle, which more or less means that "them as has, gets". As you sell greater volume you make more money. As you sell more volume, the perceived value of y