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Dagon comments on Open Thread for February 11 - 17 - Less Wrong Discussion
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I participated in an economics experiment a few days ago, and one of the tasks was as follows. Choose one of the following gambles where each outcome has 50% probability Option 1: $4 definitely Option 2: $6 or $3 Option 3: $8 or $2 Option 4: $10 or $1 Option 5: $12 or $0
I choose option 5 as it has the highest expected value. Asymptotically this is the best option but for a single trial, is it still the best option?
Clearly option 5 has the higest mean outcome. If you value money linearly (that is, $12 is exactly 3 times as good as $4, and there's no special utility threshold along the way (or disutility at $0), it's the best option.
For larger values, your value for money may be nonlinear (meaning: the difference between $0 and $50k may be much much larger than the difference between $500k and $550k to your happiness), and then you'll need to convert the payouts to subjective value before doing the calculation. Likewise if you're in a special circumstance where there's a threshold value that has special value to you - if you need $3 for bus fare home, then option 1 or 2 become much more attractive.