Take Five
I heard somewhere that if any five people guess the weight of any individual they will always be right if they pool their answers and average them. Always. I want to find out more about this. Did they find that four people wasn't quite enough? Six too many? How steeply does the effect fall off? Can five people be collectively clever about matters other than body weight? We know that once you get into the 500's -- the size of the US Congress, for example -- the net wisdom is equivalent to that of a box of round rocks. In fact, it seems there comes a point when a group goes from wise to normal to flawed to aggressively stupid. Not only wrong, but destructively so. So if five is wise and 535 is destructive -- there must be some gradations in between. The Supreme Court is nine people, but perhaps this is because in any 5-4 decision we can be confident that the majority of five has nailed it. Our founding fathers were anything but stupid about such things. How many FF's were there, by the way? Adams, Franklin, Hamilton, Jefferson, Washington...hmm.
I happen to serve on the five member board that governs our little town here in Vermont. We're pretty good together. We've never tried to guess anybody's weight, but I think we'd do okay at it. We come up with sound solutions for things like bridge decking, gravel crushing, and employee insurance plans. I think we could do more if given the chance. It might be interesting to try. What if the federal government simply jobbed out a couple of its more nagging issues to five member selectboards around Vermont and New Hampshire? Let's say here in Dummerston we look at the North Korea issue on Wednesday night after the new dump truck bids are opened. Maybe Newfane could take a crack at the Guantanamo thing. How could they possibly make it worse? Lebanon, NH would be perfect for health care reform. They have a hospital there and everything. Climate change? Toss that bone to the farmers up in Rutland. They know their weather. Illegal immigration? St. Albans up on the border -- our front line against the Canadian horde. Education reform? -- look no further than any Vermont town with a school in it. You could bankrupt forty-nine states (not counting California, that's a gimme) with the sheer complexity of Vermont's education funding formula. We know how to overthink education up here and any five of us could fix it. Right after we find Osama. And guess his weight.
posted by Tom Bodett at 9:30 PM
3 Comments:
I didn't realize Canadian hoarding was a problem. Is it as big an issue as that horde coming in from the south?
Sorry. Bet you started blogging to get away from editors.
Kaleymorris -- if I ever truly escaped editors I would certainly perish in the wilderness. Thank you. Late night blogging needs regulating.
In Statistics there's something called the Central Limit Theorem, which implies that when you take a lot of samples of something (such as guessing the weight in your example), the answers tend to form a "normal distribution". The exact method used for each sample doesn't actually matter, only that it's a decent attempt at the answer, and that there are sufficient samples (typically 30+).
A normal distribution gives you two numbers: the mean (the average guess, as you'd expect), plus something called the "standard deviation", which is a measure of how close the guesses tended to be. You use that to decide how confident you can be in the result. If the mean weight guess is 200 lbs, you can be fairly confident of that if the standard deviation is 10 lbs, but not if the standard deviation is 100 lbs! A typical calculator or spreadsheet can do these calculations easily - look up "sample standard deviation".
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