Thanks for the post, Dan and Elliot. I have not read the comments, but I do not think preferential gaps make sense in principle. If one was exactly indifferent between 2 outcomes, I believe any improvement/worsening of one of them must make one prefer one of the outcomes over the other. At the same time, if one is roughly indifferent between 2 outcomes, a sufficiently small improvement/worsening of one of them will still lead to one being practically indifferent between them. For example, although I think i) 1 $ plus a chance of 10^-100 of 1 $ is clearly better than ii) 1 $, I am practically indifferent between i) and ii), because the value of 10^-100 $ is negligible.
Thanks for the post, Dan and Elliot. I have not read the comments, but I do not think preferential gaps make sense in principle. If one was exactly indifferent between 2 outcomes, I believe any improvement/worsening of one of them must make one prefer one of the outcomes over the other. At the same time, if one is roughly indifferent between 2 outcomes, a sufficiently small improvement/worsening of one of them will still lead to one being practically indifferent between them. For example, although I think i) 1 $ plus a chance of 10^-100 of 1 $ is clearly better than ii) 1 $, I am practically indifferent between i) and ii), because the value of 10^-100 $ is negligible.