Last thread you said the problem with the funnel is that it makes the decision arbitrarily dependent upon how far you go. But to stop evaluating possibilities violates the regularity assumption. It seems like you are giving an argument against people who follow solution 1 and reject regularity; it’s those people whose decisions depend hugely and arbitrarily on where they define the threshold, especially when a hard limit for p is selected. Meanwhile, the standard view in the premises here has no cutoff.
> One needs a very extreme probability function in order to make this work; the probabilities have to diminish very fast to avoid being outpaced by the utilities.
I’m no sure what you mean by ‘very fast’. The implausibility of such a probability function is an intuition that I don’t share. I think the appendix 8.1 is really going to be the core argument at stake.
Solution #6 seems like an argument about the probability function, not an argument about the decision rule.
On solution #6: Yeah, it only works if the profiles really do cancel out. But I classified it as involving the decision rule because if your rule is simply to sum up the utilityXprobability of all the possibilities, it doesn’t matter if they are perfectly symmetric around 0, your sum will still be undefined.
Yep, solution #1 involves biting the bullet and rejecting regularity. It has problems, but maybe they are acceptable problems.
Solution #2 would be great if it works, but I don’t think it will—I regret pushing that to the appendix, sorry!
Last thread you said the problem with the funnel is that it makes the decision arbitrarily dependent upon how far you go. But to stop evaluating possibilities violates the regularity assumption. It seems like you are giving an argument against people who follow solution 1 and reject regularity; it’s those people whose decisions depend hugely and arbitrarily on where they define the threshold, especially when a hard limit for p is selected. Meanwhile, the standard view in the premises here has no cutoff.
> One needs a very extreme probability function in order to make this work; the probabilities have to diminish very fast to avoid being outpaced by the utilities.
I’m no sure what you mean by ‘very fast’. The implausibility of such a probability function is an intuition that I don’t share. I think the appendix 8.1 is really going to be the core argument at stake.
Solution #6 seems like an argument about the probability function, not an argument about the decision rule.
On solution #6: Yeah, it only works if the profiles really do cancel out. But I classified it as involving the decision rule because if your rule is simply to sum up the utilityXprobability of all the possibilities, it doesn’t matter if they are perfectly symmetric around 0, your sum will still be undefined.
Yep, solution #1 involves biting the bullet and rejecting regularity. It has problems, but maybe they are acceptable problems.
Solution #2 would be great if it works, but I don’t think it will—I regret pushing that to the appendix, sorry!
Thanks again for all the comments, btw!