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Entry tags:
contest
Pick a number, any number. I'll send the person who picks the number closest to the average of all the entries $5. (Average in this case means the arithmetic mean.)
If more than one person wins I'll pick one of them at random.
The winner will be chosen on Monday, at which point I'll also reveal the numbers that people picked. (For now, for obvious reasons, the results of the poll can only be viewed by me.)
Numbers chosen must be real numbers. Please don't submit entries that make me do complicated calculations, or look things up, etc.
[Poll #838512]
Examples:
If three people enter the contest, and they pick 5, 11, and 23, then the average would be 13.0, and the person who picked 11 would win.
If the only entries were pi, -12, seven billion, and 2 1/2, then the average would be around 175 million and the person who picked pi would win.
Where this idea came from:
I had heard that, in contests of the sort where there is a fishbowl full of jelly beans and people have to guess how many beans are in the bowl, although individual guesses may be off wildly, the average of the guesses is likely to be very close to the number of beans, and indeed will often be closer than any single guess.
So it occurred to me that if you were holding a contest of this kind, it would probably be more practical to calculate the average of the guesses (since you have to go through all the entries anyway) and use that as the assumed number of beans than to actually empty the beans and count them. And then I thought, at that point, why do you need the bowl or the beans to begin with?
Why I am doing this:
I am curious as to what numbers people will pick.
If more than one person wins I'll pick one of them at random.
The winner will be chosen on Monday, at which point I'll also reveal the numbers that people picked. (For now, for obvious reasons, the results of the poll can only be viewed by me.)
Numbers chosen must be real numbers. Please don't submit entries that make me do complicated calculations, or look things up, etc.
[Poll #838512]
Examples:
If three people enter the contest, and they pick 5, 11, and 23, then the average would be 13.0, and the person who picked 11 would win.
If the only entries were pi, -12, seven billion, and 2 1/2, then the average would be around 175 million and the person who picked pi would win.
Where this idea came from:
I had heard that, in contests of the sort where there is a fishbowl full of jelly beans and people have to guess how many beans are in the bowl, although individual guesses may be off wildly, the average of the guesses is likely to be very close to the number of beans, and indeed will often be closer than any single guess.
So it occurred to me that if you were holding a contest of this kind, it would probably be more practical to calculate the average of the guesses (since you have to go through all the entries anyway) and use that as the assumed number of beans than to actually empty the beans and count them. And then I thought, at that point, why do you need the bowl or the beans to begin with?
Why I am doing this:
I am curious as to what numbers people will pick.
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But after a while it can turn into a game of buying and selling where nobody really cares about the underlying business anymore, they're just trying to guess the averages that will come out of the marketplace process... and then that's the situation where you dispense with the jar of jelly beans.
You game has an interesting wrinkle to it if we start thinking about players trying to manipulate the game. If I guess a huge large or small number, much larger than I expect the other players to be guessing, that gives me the opportunity to manipulate the average.
If I'm playing only for myself, there's no advantage to doing that. Say there are a hundred players guessing in the range of 0 to 1000, and I come in and guess a googol. Then I've pretty much set how the game will go - the average will be about 1/100th of a googol, far away from all the other players, and it's obvious I can put the average wherever I want - but I don't win because those other players are much closer. I have to pull my own guess far away from the average in order to be sure of controlling the average. I can't rig the game so that I win, but I can rig it so that the player other than me who guesses the greatest (or least) number wins.
So what happens if I have a confederate, I guess a googol, my confederate guesses 1/1000th of a googol, and everyone else guesses in the range 0 to 1000? Then my confederate wins.
It seems like the game is stable as long as people don't collude - we'll all tend to "cooperate" by guessing numbers near where we think the average of cooperating guesses will be, and that will tend to be close to zero because that's the only really distinguished real number.
But if people attempting to collude in pairs is a common enough thing that we expect it to happen at least once per game, then it seems like it will turn into a contest of who can think of the biggest numbers, because a pair wins if they scale their strategy to be bigger than anyone else's.
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It'll certainly be interesting to see what kind of actual distribution of guesses you get from this.
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If some people did pick large negative numbers, though, it no longer becomes clear that the pair with the highest absolute value will win, although that still seems like the most likely outcome. Still, hedging your bets with a third confederate who picks something in the middle might not be a bad idea, if you can figure out where the middle is.
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I think it makes it more interesting to allow negative and fractional numbers, but that may just be me.
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Near ties would still cause some weirdness even if the biggest manipulations were in the same direction. Suppose my confederate and I choose 1/100th googol and one googol, another pair chooses 1/1000th googol and ten googol, and there are about 98 other guesses all in the range 0..1000. Then the average is about 1/10th googol, and my confederate wins, even though the other pair had the biggest effect on the average.
To make the strategy work, my confederate and I want to guess so that we are sure of having a guess larger in magnitude than anyone else's guess, and a guess larger than that by a factor of more than the number of other guesses, to drive the average into the space between our guesses. We can make our guesses positive or negative and it won't matter as long as they're big enough.
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Probably going with the median would have been a better idea, but I am mostly counting on $5 not being enough money to inspire people to go to those lengths. (I guess actually it would be $5/(number of confederates).)
One of the things I wondered was if different groups of people would tend to pick different numbers, but since I didn't have a very clear picture in my head as to what I meant by 'different groups of people' this contest will probably not provide a good answer to that.
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