Say we have a treatment of curing hiccups. Or some other inconvenience. Maybe even all medical inconveniences. We have done all the research and experiments and concluded that the treatment is perfectly safe—except there is no such thing as “certainty” in Bayesianism so we must still allocate a tiny probability to the event our treatment may kill a patient—say, a one in a googol chance. The expected utility of the treatment will now have a −ω10100 component in it, which far outweighs any positive utility gained from the treatment, which only cures inconveniences, a mere real number that cannot be overcome the negative ω no matter how small the probability of that ω is nor how much you multiply the positive utility of curing the inconveniences.
I see the problem. I wonder if anyone had already delved and tried formalizing using ordinal numbers. Would be an interesting read, I definitely would need to think about this more.
Say we have a treatment of curing hiccups. Or some other inconvenience. Maybe even all medical inconveniences. We have done all the research and experiments and concluded that the treatment is perfectly safe—except there is no such thing as “certainty” in Bayesianism so we must still allocate a tiny probability to the event our treatment may kill a patient—say, a one in a googol chance. The expected utility of the treatment will now have a −ω10100 component in it, which far outweighs any positive utility gained from the treatment, which only cures inconveniences, a mere real number that cannot be overcome the negative ω no matter how small the probability of that ω is nor how much you multiply the positive utility of curing the inconveniences.
I see the problem. I wonder if anyone had already delved and tried formalizing using ordinal numbers. Would be an interesting read, I definitely would need to think about this more.