I think I agree that the OP does not follow independence, but everything else here seems wrong.
Actions A and B are identical except that A gives me 2 utils with .5 probability, while B gives me Graham’s number with .5 probability. I do B. (Likewise if there are ~Graham’s number of alternatives with intermediate payoffs.)
I’m not sure how you thought this was relevant to what I said.
What I was saying was this:
Suppose I say that A has utility 5, and B has utility 10. Basically the statement that B has twice the utility A has, has no particular meaning except that if I would like to have A at a probability of 10%, I would equally like to have B at a probability of 5%. If I would take the 10% chance and not the 5% chance, then there is no longer any meaning to saying that B has “double” the utility of A.
I think I agree that the OP does not follow independence, but everything else here seems wrong.
Actions A and B are identical except that A gives me 2 utils with .5 probability, while B gives me Graham’s number with .5 probability. I do B. (Likewise if there are ~Graham’s number of alternatives with intermediate payoffs.)
I’m not sure how you thought this was relevant to what I said.
What I was saying was this:
Suppose I say that A has utility 5, and B has utility 10. Basically the statement that B has twice the utility A has, has no particular meaning except that if I would like to have A at a probability of 10%, I would equally like to have B at a probability of 5%. If I would take the 10% chance and not the 5% chance, then there is no longer any meaning to saying that B has “double” the utility of A.