From a brief glance, it seems to be flawed. It ends up using the expected value of a utility function, since the utility function is regarded as uncertain. But the mathematical nature of a utility function makes this expectation operation meaningless. Utility functions are defined only up to an arbitrary affine transformation, which destroys the ability to take expectations.

I mentioned this problem to my colleague Craig Boutilier, who has done similar things, which resulted in him writing the following paper that attempts to solve the problem:: On the foundations of expectedexpected utility. I believe that, unfortunately, this paper does not actually solve the problem, which is essentially the same as the problem of interpersonal utility comparisons.

I’d be more convinced that they’ve thought of it all already if you gave a reference!

I did some Google searches on things like “amniocentesis” and “Allias Paradox” before posting this, and about the only relevant result was the comment by Dawid that I mentjion in the post.

The focus on the medical decision making literature is on general medical recommendations, in this case what is a good age to recommend testing.

Nobody’s being presumptuous here. Doctors give recommendations, and it’s reasonable for these recommendations to be evidence-based. Of course the decisions are made by the people affected (well, except for the fetuses involved), but said people might well ask their doctor for advice!

Researchers in medical decision making are well aware of utility theory and the value of information and the risks of testing and all these other things. It’s fine for you to work this out on your own; I just wanted to let you know that there are people who have been working in this area for awhile, and they’re not as naive or simplistic as you might think.

However, I think it’s crazy to value “peace of mind” enough to make it a signficant consideration. (This isn’t a mathematical judgement, obviously, but rather a moral one.) If some couples have amniocentesis done for this reason (or even if this is a significant factor in their decision), then I think the medical profession has an ethical problem, since these couples’ uneasiness is probably largely iatrogenic – a result of medical professionals having discussed the issue with them, perhaps too much.

I think “future regret” is not a sensible consideration when making a decision. It’s basically double-counting the bad consequence. To the extent that it might not be explained that way, it’s counting the utility of someone other than the decision-maker, since “you” and “you-in-the-future” are not the same person.

Andrews comments about the medical decision making literature don’t contian references, but if they are about “what is a reasonable age threshold to recommend for the test”, then I think they are far too simplistic. For one thing, recommendations today should not be based just on age, but on non-invasive tests. For another, it’s medically presumtuous to think that a “threshold” can be decided on by medical ethics people, rather than by the people actually affected.