Save 400 lives, with certainty.
Save 500 lives, with 90% probability; save no lives, 10% probability.
I’m surprised how few people are reacting to the implausibility of this thought experiment. When not in statistics class, God rarely gives out priors. Probabilities other than 0+epsilon and 1-epsilon tend to come from human scholarship, which is an often imperfect process. It is hard to imagine a non-contrived situation where you would have as much confidence in the 90⁄10 outcome as in the certain outcome.
Suppose the “90/10” figure comes from cure rates in a study of 20-year-old men, but your 500 patients are mostly middle-aged. You have the choice of disarming a bomb that will kill 400 people with probability 1-epsilon, or of taking that “90/10″ estimate, really, really seriously; I know which choice I would make.
Save 400 lives, with certainty. Save 500 lives, with 90% probability; save no lives, 10% probability.
I’m surprised how few people are reacting to the implausibility of this thought experiment. When not in statistics class, God rarely gives out priors. Probabilities other than 0+epsilon and 1-epsilon tend to come from human scholarship, which is an often imperfect process. It is hard to imagine a non-contrived situation where you would have as much confidence in the 90⁄10 outcome as in the certain outcome.
Suppose the “90/10” figure comes from cure rates in a study of 20-year-old men, but your 500 patients are mostly middle-aged. You have the choice of disarming a bomb that will kill 400 people with probability 1-epsilon, or of taking that “90/10″ estimate, really, really seriously; I know which choice I would make.