One does not have to know what might happen in order to accurately predict how it would affect a one-dimensional scale of utility, though. It seems intuitively to me, someone who admittedly doesn’t know much about the subject, like unknown unknowns could be accurately modeled most of the time with a long-tailed normal distribution, and one could use evidence from past times that something totally unexpected happened throughout human history (and there were plenty) to get a sense of what that distribution ought to look like.
it seems intuitively to me, someone who admittedly doesn’t know much about the subject, like unknown unknowns could be accurately modeled most of the time with a long-tailed normal distribution
How fat tailed do you make it ? You said you use past extreme events to choose a distribution. But what if the past largest event is not the largest possible event ? What if the past does not predict the future in this case ?
You can say “the largest truck that ever crossed by bridge was 20 tons, therefore my bridge has to be able to sustain 20 tons” but that is a logical fallacy. The fact that the largest truck you ever saw was 20 tons does not mean a 30 ton truck could not come by one day. This amounts to saying “I have observed the queen of England for 600 days and she hasn’t died in any of them, therefore the queen of England will never die”.
One does not have to know what might happen in order to accurately predict how it would affect a one-dimensional scale of utility, though. It seems intuitively to me, someone who admittedly doesn’t know much about the subject, like unknown unknowns could be accurately modeled most of the time with a long-tailed normal distribution, and one could use evidence from past times that something totally unexpected happened throughout human history (and there were plenty) to get a sense of what that distribution ought to look like.
How fat tailed do you make it ? You said you use past extreme events to choose a distribution. But what if the past largest event is not the largest possible event ? What if the past does not predict the future in this case ?
You can say “the largest truck that ever crossed by bridge was 20 tons, therefore my bridge has to be able to sustain 20 tons” but that is a logical fallacy. The fact that the largest truck you ever saw was 20 tons does not mean a 30 ton truck could not come by one day. This amounts to saying “I have observed the queen of England for 600 days and she hasn’t died in any of them, therefore the queen of England will never die”.