Now suppose that I am so unfortunate as to forget the value of the utility-ratio u(salmon)/u(tuna).
But, on reflection, the possibility of forgetting knowledge is probably a can of worms best left unopened. For, one could ask what would happen if I remembered that I was highly confident that I would choose salmon over tuna, but I forgot that I was absolutely certain about this. It would then be hard to see how to avoid inconsistent utility functions, as you describe.
Perhaps it’s better to suppose that you’ve shown, by some unspecified means, that u(salmon) > u(tuna), but that you did so without computing the exact utility-ratio. Then you become certain that you choose salmon over tuna, but you no longer have the prior subjective uncertainty that you need to compute the ratio u(salmon)/u(tuna) directly. That’s the kind of case where you might be able to find some other piece of prior subjective uncertainty, as I describe in the above paragraph.
I wrote,
But, on reflection, the possibility of forgetting knowledge is probably a can of worms best left unopened. For, one could ask what would happen if I remembered that I was highly confident that I would choose salmon over tuna, but I forgot that I was absolutely certain about this. It would then be hard to see how to avoid inconsistent utility functions, as you describe.
Perhaps it’s better to suppose that you’ve shown, by some unspecified means, that u(salmon) > u(tuna), but that you did so without computing the exact utility-ratio. Then you become certain that you choose salmon over tuna, but you no longer have the prior subjective uncertainty that you need to compute the ratio u(salmon)/u(tuna) directly. That’s the kind of case where you might be able to find some other piece of prior subjective uncertainty, as I describe in the above paragraph.