Thursday, April 1, 2021

Going against currently expected utilities

Today I am making an important decision between A and B. The expected utilities of A and B depend on a large collection of empirical propositions p1, ..., pn. Yesterday, I spent a long time investigating the truth values of these empirical propositions and I calculated the expected utility of A to be much higher than that of B. However, today I have forgotten the results of my investigations into p1, ..., pn, though I still remember that A had a higher expected utility given these investigations.

Having forgotten the results of my investigations into p1, ..., pn, my credences for them have gone back to some sort of default priors. Relative to these defaults, I know that B has higher expected utility than A.

Clearly, I should still choose A over B: I should go with the results of my careful investigations rather than the default priors. Yet it seems that I also know that relative to my current credences, the expected utility of B is higher than that of A.

This seems very strange: it seems I should go for the option with the smaller expected utility here.

Here is one possible move: deny that expected utilities are grounded in our credences. Thus, it could be that I still hold a higher expected utility for A even though a calculation based on my current credences would make B have the higher expected utility. I like this move, but it has a bit of a problem: I may well have forgotten what the expected utilities of A and B were, and only remember that A’s was higher than B’s.

Here is a second move: this is a case where I now have inconsistent credences. For if I keep my credences in p1, ..., pn at their default levels, I have a piece of evidence I have not updated my credences on, namely this: the expected utility of A is higher than that of B relative to the posterior credences obtained by gathering the now-forgotten evidence. What I should do is update my credences in p1, ..., pn on this piece of evidence, and calculate the expected utilities. If all goes well—but right now I don’t know if there is any mathematical guarantee that it will—then I will get a new set of credences relative to which A has a higher expected utility than B.


Alexander R Pruss said...

I think the math does work out and the second solution is right.

David Gordon said...

Who does "you" and "your" in the first and third paragraphs ("you still remember" and "your current credences"0 refer to?

Alexander R Pruss said...

I got "I" and "you" confused. I think I fixed it.