I haven’t had time to read the whole thing yet, but I disagree that the problem Wilkinson is pointing to with his argument is just that it is hard to know where to put the cut, because putting it anywhere is arbitrary. The issue to me seems more like, for any of the individual pairs in the sequence, looked at in isolation, rejecting the view that the very, very slightly lower probability of the much, MUCH better outcome is preferable, seems insane. Why would you ever reject an option with a trillion trillion times better outcome, just because it was 1x10^-999999999999999999999999999999999999 less likely to happen than trillion trillion times worse outcome (assuming for both options, if you don’t get the prize, the result is neutral)? The fact that it is hard to say where is the best place in the sequence to first make that apparently insane choice seems also concerning, but less central to me?
Thanks for the comment. I agree that Wilkinson makes a lot of other (really persuasive) points against drawing some threshold of probability. As you point out, one reason is that the normative principle (Minimal Tradeoffs) seems to be independently justified, regardless of the probabilities involved. If you agree with that, then the arbitrariness point seems secondary. I’m suggesting that the uncertainty that accompanies very low probabilities might mean that applying Minimal Tradeoffs to very low probabilities is a bad idea, and there’s some non-arbitrary way to say when that will be. I should also note that one doesn’t need to reject Minimal Tradeoffs. You might think that if we did have precise knowledge of the low probabilities (say, in Pascal’s wager), then we should trade them off for greater payoffs.
I haven’t had time to read the whole thing yet, but I disagree that the problem Wilkinson is pointing to with his argument is just that it is hard to know where to put the cut, because putting it anywhere is arbitrary. The issue to me seems more like, for any of the individual pairs in the sequence, looked at in isolation, rejecting the view that the very, very slightly lower probability of the much, MUCH better outcome is preferable, seems insane. Why would you ever reject an option with a trillion trillion times better outcome, just because it was 1x10^-999999999999999999999999999999999999 less likely to happen than trillion trillion times worse outcome (assuming for both options, if you don’t get the prize, the result is neutral)? The fact that it is hard to say where is the best place in the sequence to first make that apparently insane choice seems also concerning, but less central to me?
Hi David,
Thanks for the comment. I agree that Wilkinson makes a lot of other (really persuasive) points against drawing some threshold of probability. As you point out, one reason is that the normative principle (Minimal Tradeoffs) seems to be independently justified, regardless of the probabilities involved. If you agree with that, then the arbitrariness point seems secondary. I’m suggesting that the uncertainty that accompanies very low probabilities might mean that applying Minimal Tradeoffs to very low probabilities is a bad idea, and there’s some non-arbitrary way to say when that will be. I should also note that one doesn’t need to reject Minimal Tradeoffs. You might think that if we did have precise knowledge of the low probabilities (say, in Pascal’s wager), then we should trade them off for greater payoffs.
Thanks, I will think about that.