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evand comments on "I don't know." - Less Wrong
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There's no rational reason to do this. If you think that X has more than a 25% chance of being true given that the market is at 25%, you'd buy at 25%. If you think it has less than a 25% chance of being true, you'd sell at 25%.
There's no way you're going to think that it has exactly an 8% chance of being true given that the market is at 8% and exactly a 44% chance of being true given that the market is at 44%. If you're really more sure of the market than yourself, it will be close, but you can always improve it slightly.
Really? What about the Kelly Criterion
The Kelly Criterion is when you're betting with something that you value logarithmically. That is, doubling it gives you a constant utility. As such, it's not an even bet. For example, if you have $1500, and you've already bet $500 and you're considering betting another $1, you're comparing gaining $1 when you have $2000 with losing $1 when you have $1000. Since the dollar is twice as valuable in the second case, you're actually betting at 1:2 odds.
Also, the Kelly Criterion limits the amount you're betting based on your certainty. You still bet something.