Matt_Simpson

00

See also Kreps, Notes on the Theory of Choice. Note that one of these two restrictions are required in order to specifically prevent infinite expected utility. So if a lottery spits out infinite expected utility, you broke something in the VNM axioms.

For anyone who's interested, a quick and dirty explanation is that the preference relation is primitive, and we're trying to come up with an index (a utility function) that reproduces the preference relation. In the case of certainty, we want a function U:O->R where O is the outcome space and R is the real numbers such that U(o1) > U(o2) if and only if o1 is preferred to o2. In the case of uncertainty, U is defined on the set of probability distributions over O, i.e. U:M(O) -> R. With the VNM axioms, we get U(L) = E_L[u(o)] where L is some lottery (i.e. a probability distribution over O). U is strictly prohibited from taking the value of infinity in these definition. Now you probably could extend them a little bit to allow for such infinities (at the cost of VNM utility perhaps), but you would need every lottery with infinite expected value to be tied for the best lottery according to the preference relation.

00

I do this too, though in smaller bites. fitfths? fourths? I'm not sure, actually, but it seems to work.

00

Good point.

100

Funny, I read your post and my initial reaction was that this evidence cuts *against* PUA. (Now I'm not sure whether it supports PUA or not, but I lean towards support).

PUA would predict that this phrase

...while I devote myself to worshiping the ground she walks on.

is unattractive.

30

Well based on your track record there, it seems like a prudent move to avoid making bets with you ;)

(Though I agree with you and should be shaming them rather than defending them.)

00

If the basilisk is correct* it seems any indirect approach is doomed, but I don't see how it prevents a direct approach. But that has it's own set of probably-insurmountable problems, I'd wager.

* I remain highly uncertain about that, but it's not something I can claim to have a good grasp on or to have thought a lot about.

20

I think I understand X, and it seems like a legitimate problem, but the comment I think you're referring to here seems to contain (nearly) all of X and not just half of it. So I'm confused and think I don't completely understand X.

Edit: I think I found the missing part of X. Ouch.

20

I also have this problem and would like to know how to fix it / if dual n-back might help.

10

Politics is the mind killer for a variety of reasons besides ridiculously strong priors that are never swayed by evidence. Strong priors isn't even the entirety of the phenomena to be explained (though it is a big part), let alone a fundamental explanation.

Also, I really like Noah's post (and was about to post it in the current open thread before I found your post). Not only did Noah attach a word to a pretty commonly occurring phenomenon, the word seems to have a great set of connotations attached to it, given some goals about improving discourse.

Since utility functions are only unique up to affine transformation, I don't know what to make of this comment. Do you have some sort of canonical representation in mind or something?