So, as in most such problems, there's an important difference between the epistemological question ("should I pay, given what I know?") and the more fundamental question ("should I pay, supposing this description is accurate?"). Between expected value and actual value, in other words.
It's easy to get those confused, and my intuitions about one muddy my thinking about the other, so I like to think about them separately.
WRT the epistemological question, that's hard to answer without a lot of information about how likely I consider accurate oracular ability, how confident I am that the examples of accurate prediction I'm aware of are a representative sample, etc. etc. etc., all of which I think is both uncontroversial and uninteresting. Vaguely approximating all of that stuff I conclude that I shouldn't pay the oracle, because I'm not justified in being more confident that the situation really is as the oracle describes it, than that the oracle is misrepresenting the situation in some important way. My expected value of this deal in the real world is negative.
WRT the fundamental question... of course, you leave a lot of details unspecified, but I don't want to fight the hypothetical here, so I'm assuming that the "overall jist" of your description applies: I'm paying $1K for QALYs I would not have had access to without the oracle's offer. That's a good deal for me; I'm inclined to take it. (Though I might try to negotiate the price down.)
The knock-on effect is that I encourage the oracle to keep making this offer... but that's good too; I want the oracle to keep making the offer. QALYs for everyone!
So, yes, I should pay the oracle, though I should also implement decision procedures that will lead me to not pay the oracle.
The knock-on effect is that I encourage the oracle to keep making this offer... but that's good too; I want the oracle to keep making the offer. QALYs for everyone!
I think a key part of the question, as I see it, is to formalize the difference between treatment effects and selection effects (in the context where your actions might reflect a selection effect, and we can't make the normally reasonable assumption that our actions result in treatment effects). An oracle could look into the future, find a list of people who will die in the next week, and a l...
If it's worth saying, but not worth its own post (even in Discussion), then it goes here.
Notes for future OT posters:
1. Please add the 'open_thread' tag.
2. Check if there is an active Open Thread before posting a new one. (Immediately before; refresh the list-of-threads page before posting.)
3. Open Threads should be posted in Discussion, and not Main.
4. Open Threads should start on Monday, and end on Sunday.