It might be useful to distinguish between the actual total utility experienced so far, and the estimates of that which can be worked out from various view points.
Suppose we break it down by week. If during the first week of March 2014, Bob finds utility (eg pleasure) in watching movies, collecting stamps, and in owning stamp collections, and in having watched movies (4 different things), then you’d multiply the duration (1 week) by the rate at which those things add to his utility experienced to get how much you add to his total lifetime utility experienced.
If, during the second week of March, a fire destroys his stamp collection, that wouldn’t reduce his lifetime total. What it would do is reduce the rate at which he added to that total during the following weeks.
Now let’s take a different example. Suppose there is a painter whose only concern is their reputation upon their death, as measured by the monetary value of the paintings they put up for one final auction. Painting gives them no joy. Finishing a painting doesn’t increase their utility, only the expected amount of utility that they will reap at some future date.
If, before they died, a fire destroyed the warehouse holding the paintings they were about to auction off, then they would account the net utility experienced during their life as zero. Having spent years with owning lots of paintings, and having had a high expectation of gaining future utility during that time, wouldn’t have added anything to their actual total utility over those years.
How is that affected by the possibility of the painter changing their utility function?
If they later decide that there is utility to be experienced by weeks spent improving their skill at painting (by means of painting pictures, even if those pictures are destroyed before ever being seen or sold), does that retroactively change the total utility added during the previous years of their life?
I’d say no.
Either utility experienced is real, or it is not. If it is real, then a change in the future cannot affect the past. It can affect the estimate you are making now of the quantity in the past, just as an improvement in telescope technology might affect the estimate a modern day scientist might make about the quantity of explosive force of a nova that happened 1 million years ago, but it can’t affect the quantity itself, just as a change to modern telescopes can’t actually go back in time to alter the nova itself.
It might be useful to distinguish between the actual total utility experienced so far, and the estimates of that which can be worked out from various view points.
Suppose we break it down by week. If during the first week of March 2014, Bob finds utility (eg pleasure) in watching movies, collecting stamps, and in owning stamp collections, and in having watched movies (4 different things), then you’d multiply the duration (1 week) by the rate at which those things add to his utility experienced to get how much you add to his total lifetime utility experienced.
If, during the second week of March, a fire destroys his stamp collection, that wouldn’t reduce his lifetime total. What it would do is reduce the rate at which he added to that total during the following weeks.
Now let’s take a different example. Suppose there is a painter whose only concern is their reputation upon their death, as measured by the monetary value of the paintings they put up for one final auction. Painting gives them no joy. Finishing a painting doesn’t increase their utility, only the expected amount of utility that they will reap at some future date.
If, before they died, a fire destroyed the warehouse holding the paintings they were about to auction off, then they would account the net utility experienced during their life as zero. Having spent years with owning lots of paintings, and having had a high expectation of gaining future utility during that time, wouldn’t have added anything to their actual total utility over those years.
How is that affected by the possibility of the painter changing their utility function?
If they later decide that there is utility to be experienced by weeks spent improving their skill at painting (by means of painting pictures, even if those pictures are destroyed before ever being seen or sold), does that retroactively change the total utility added during the previous years of their life?
I’d say no.
Either utility experienced is real, or it is not. If it is real, then a change in the future cannot affect the past. It can affect the estimate you are making now of the quantity in the past, just as an improvement in telescope technology might affect the estimate a modern day scientist might make about the quantity of explosive force of a nova that happened 1 million years ago, but it can’t affect the quantity itself, just as a change to modern telescopes can’t actually go back in time to alter the nova itself.