14 November 2005

The Rule Of Twelve Bonks.

Can you explain one of the juiciest equations in the book, "The Rule of 12 Bonks"?

This math helps us answer the question, "How many partners should I have before I settle down?" The background is quite interesting: Despite high divorce rates, when it comes to falling in love, we refuse to take advice. If you were buying a DVD player and you were told there was a 50 percent chance it would break down, you would really think hard before buying it, wouldn't you? You certainly wouldn't buy the first one you came across, and you would probably ask advice from friends. It seems like when it comes to marriage, we're acting all crazy. This mathematician [Peter Todd from the Max Planck Institute for Psychological Research in Germany] said, hold on, maybe there are some mathematical equations that make us act this way. He thought, in this borderless world where we have an almost unlimited number of potential partners, how many partners should we test before we settle down? The math showed a very revealing pattern. If you use this simple rule, it will give you very good results: Test a sample of 12 partners. Then, after you get to 12, continue testing but take the next best partner that comes along (it could be partner number 13 or partner number 40). Todd found that doing this will give you a 75 percent chance of picking someone with the qualities that you want.

Of course, we can't rely upon mathematics to tell us what those qualities are, right? We have to make up our own list of criteria.

That's right. And mind-blowing sex doesn't even have to be one of them. In fact, you don't really need to sleep with 12 partners -- you could be dating platonically, I suppose. But you need to have 12 relationships with 12 partners. I called it the "Rule of 12 Bonks" rule because it's a reflection of my cheekiness. I'm modern woman in a modern world and sex needs to be one of my criteria!

What about all those people in relationships who aren't even close to their 12th partner? Should they dump their current partner and keep looking, just to be sure?

No. This strategy promises a 75 percent chance of success. It's not foolproof. These people could very likely be in that lucky 25 percent. There are some people that would find true love with Number 3, and other who would need to go up to Number 105.

But it's still interesting that this is such a simple strategy. Back in the '80s, a popular idea in mathematics was that our brains worked with strict mathematical rules, and if we could only create a computer to replicate these rules as fast as possible, we could feasibly replicate human thinking. Now they're thinking that our brains actually work with a bunch of very simple strategies that don't always get perfect results. This "12 Bonks Rule" is one of them.

From here, with a hat tip to Diary of a Black Mathematician. (We hope he sticks to his day job, however, his mathematical prowess is impressive, but his poetry prowess is not.)

The rule of twelve bonks may seem odd and counterintuitive. Another rule, however, with a mathematically related answer which is much easier to model, is quite familiar. This is the rule that felony juries must have twelve members who reach a unanimous verdict (which, incidentally, is a common law tradition and is state law in many states, but not a constitutional requirement in non-capital cases, at least). If the twelve jurors were truly independent (they aren't, by design), then the jury has a 50-50 chance of convicting only when 94% of people would agree after having experienced the trial, that the defendant was guilty, a figure quite close to intuitive formulations of the concept of guilt beyond a reasonable doubt. In contrast, the odds of twelve independent jurors reaching a guilty verdict in which any one of them has a 50-50 chance of believing someone to be guilty is a mere one in 4,096.

Of course, reality is a bit more complex. Typically, there is a very strong relationship between a jury's initial poll (in which jurors votes typically are independent of each other) and their final result. Twelve Angry Men is the exception, not the rule. If there are only one or two holdouts either for a conviction or an acquittal, they very, very frequently end up caving in the course of deliberations. But, more than a couple of holdouts significantly increase the chances of an acquittal or hung jury.

Also, jurors are not drawn from a representatives sample of the general population. Generally, they are the hardest twelve people in the jury pools for attorneys for each side to predict the inclinations of, thus they over represent moderates on criminal justice issues in the general population.

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