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Friday, May 26, 2006

A MATHEMATICAL THEORY


Mathematician Kurt Godel prevents me from saying so 'completely'—but, there's truth in math. And there's math in music. Modus ponens: there's truth in music. There's also rhythm in music and rhythm in the markets. And lessons in both--you just have to listen.

The Who's Roger Daltry belted out: "we won't be fooled again". Depeche Mode sang "never again is what you swore, the time before.” As is said of history, it doesn't necessarily repeat itself—but it does rhyme. Despite the wisdom from the school of rock, bubble after bubble occurs, separated roughly by the memory of a generation. We seem to fall victims to the same hyperbole disguised through time.

President Reagan wasn’t quite Diogenes, but he had a healthy dose of cynicism and even channeled Depeche Mode with his own Policy of Truth: "Trust, but verify". Here's a story why: A few years ago the founder of a technology company (to remain unnamed) gave a talk to a few of us. He explained the rise in popularity and media coverage behind a technology that he would go on to sell commercially, which I now call the “Secondary Source Fallacy”.

Here’s what happened: This company founder had about 10 really close friends. And one year he noted that two of them were using this particular technology. One year later, he observed that four of his friends were using it.

So he went ahead and wrote a proselytizing article in a small technology journal with a readership of a few hundred people that said usage of this technology was growing 100% annually. Now of course he knew, and we all know that such a sample size (going from n=2 to n=4) is meaningless and insufficient—but it didn’t stop Business Week from running a full cover story on this technology. And the coup for this entrepreneur was that the magazine repeated the statistic and said that this technology was doubling in use every year. Of course they footnoted it “Source: [that little dedicated technology journal]”.

So the entrepreneur then took liberty to go out to investors and market that “according to Business Week, the market is doubling…” The only thing that was really doubling was his unjust credibility. But the credulous investors cut him some pretty large checks and the hype cycle lasted long enough for him to cash out.

Let’s turn to a game:

To play you must pick a number from 0 to 100. But to win you must pick a number that you think will be as close as possible to 2/3 of the average of what everyone else’s guess will be. So, if you think everyone would pick 50, you should pick 2/3 of that which would be 33. But if everyone else realizes this also, then you should pick 22. But if everyone else is thinking this also then you should go down to 14.

You can see taken to its mathematical extension where this is going—all the way to zero. But we know from personal experience and from markets that people don’t behave as mathematical theories predict. In fact, many people in the above game pick numbers of 50, many do in fact pick zero, but the best odds you have of winning typically hover around you picking a number between 15 or 20. That’s because most people go two degrees of what other people think and not further.

I often refer to such games as Keynesian beauty contests. From the man himself:

“...professional investment may be likened to those newspaper competitions in which the competitors have to pick out the six prettiest faces from a hundred photographs, the prize being awarded to the competitor whose choice most nearly corresponds to the average preferences of the competitors as a whole; so that each competitor has to pick, not those faces which he himself finds prettiest, but those which he thinks likeliest to catch the fancy of the other competitors, all of whom are looking at the problem from the same point of view.

It is not a case of choosing those which, to the best of one’s judgment, are really the prettiest, nor even those which average opinion genuinely thinks the prettiest. We have reached the third degree where we devote our intelligences to anticipating what average opinion expects the average opinion to be. And there are some, I believe, who practice the fourth, fifth, and higher degrees.”

Like a game of chess—it’s not enough to think a few moves ahead—you must think at least one move ahead of the number of moves your opponent thinks. Or as I’ve previously recounted more colloquially: two guys are in the woods when a bear comes running. One starts running, the others shouts, “it’s no good—you’ll never outrun a bear.” The running guy turns back and says, “I don’t have to. I only have to outrun you.”

by josh wolf

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