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jimrandomh comments on Making Beliefs Pay Rent (in Anticipated Experiences) - Less Wrong
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But why do beliefs need to pay rent in anticipated experiences? Why can’t they pay rent in utility?
If some average Joe believes he’s smart and beautiful, and that gives him utility, is that necessarily a bad thing? Joe approaches a girl in a bar, dips his sweaty fingers in her iced drink, cracks a piece of ice in his teeth, pulls it out of his mouth, shoves it in her face for demonstration, and says, “Now that I’d broken the ice—”
She thinks: “What a butt-ugly idiot!” and gets the hell away from him.
Joe goes on happily believing that he’s smart and beautiful.
For myself, the answer is obvious: my beliefs are means to an end, not ends in themselves. They’re utility producers only insofar as they help me accomplish utility-producing operations. If I were to buy stock believing that its price would go up, I better hope my belief paid its rent in correct anticipation, or else it goes out the door.
But for Joe? If he has utility-pumping beliefs, then why not? It’s not like he would get any smarter or prettier by figuring out he’s been a butt-ugly idiot this whole time.
They can. They just do so very rarely, and since accepting some inaccurate beliefs makes it harder to determine which beliefs are and aren't beneficial, in practice we get the highest utility from favoring accuracy. It's very hard to keep the negative effects of a false belief contained; they tend to have subtle downsides. In the example you gave, Joe's belief that he's already smart and beautiful might be stopping him from pursuing self-improvements. But there definitely are cases where accurate beliefs are definitely detrimental; Nick Bostrom's Information Hazards has a partial taxonomy of them.
I don't think it's possible for a reflectively consistent decision-maker to gain utility from self-deception, at least if you're using an updateless decision theory. Hiding an unpleasant fact F from yourself is equivalent to deciding never to know whether F is true or false, which means fixing your belief in F at your prior probability for it. But a consistent decision-maker who loses 10 utilons from believing F with probability ~1 must lose p*10 utilons for believing F with probability p.
No, this is not true. Many of the reasons why true beliefs can be bad for you are because information about your beliefs can leak out to other agents in ways other than through your actions, and there is is no particular reason for this effect to be linear. For example, blocking communications from a potential blackmailer is good because knowing with probability 1.0 that you're being blackmailed is more than 5 times worse than knowing with probability 0.2 that you will be blackmailed in the future if you don't.
Oh, sure. By "gain utility" I meant "gain utility directly," as in the average Joe story.
I don't think it's linear in the average Joe story, either; if there's one threshold level of belief which changes his behavior, then utility is constant for levels of belief on either side of that threshold and discontinuous in between.
A rational agent can have its behavior depend on a threshold crossing of belief, but if there's some belief that grants it utility in itself (e.g. Joe likes to believe he is attractive), the utility it gains from that belief has to be linear with the level of belief. Otherwise, Joe can get dutch-booked by a Monte Carlo plastic surgeon.
This doesn't sound right. Could you describe the Dutch-booking procedure explicitly? Assume that believing P with probability p gives me utility U(p)=p^2+C.
An additive constant seems meaningless here: if Joe gets C utilons no matter what p is, then those utilons are unrelated to p or to P--Joe's behavior should be identical if U(p)=p^2, so for simplicity I'll ignore the C.
Now, suppose Joe currently believes he is not attractive. A surgery has a .5 chance of making him attractive and a .5 chance of doing nothing. This surgery is worth U(.5)-U(0)=.25 utilons to Joe; he'll pay up to that amount for it.
Suppose instead the surgeon promises to try again, once, if the first surgery fails. Then Joe's overall chance of becoming attractive is .75, so he'll pay U(.75)-U(0)=.75^2=0.5625 for the deal.
Suppose Joe has taken the first deal, and the surgeon offers to upgrade it to the second. Joe is willing to pay up to the difference in prices for the upgrade, so he'll pay .5625-.25=.3125 for the upgrade.
Joe buys the upgrade. The surgeon performs the first surgery. Joe wakes up and learns that the surgery failed. Joe is entitled to a second surgery, thanks to that .3125-utility purchase of the upgrade. But the second surgery is now worth only .25 utility to him! The surgeon offers to buy that second surgery back from him at a cost of .26 utility. Joe accepts. Joe has spent a net of .0525 utility on an upgrade that gave him no benefit.
As a sanity check, let's look at how it would go if Joe's U(p)=p. The single surgery is worth .5. The double surgery is worth .75. Joe will pay up to .25 utility for the upgrade. After the first surgery fails, the upgrade is worth .5 utility. Joe does not regret his purchase.
You're missing the fact that how much Joe values the surgery depends on whether or not he expects to be told whether it worked afterward. If Joe expects to have the surgery but to never find out whether or not it worked, then its value is U(0.5)-U(0)=0.25. On the other hand, if he expects to be told whether it worked or not, then he ends up with a belief-score or either 0 or 1, not 0.5, so its value is (0.5*U(1.0) + 0.5*U(0)) - U(0) = 0.5.
Suppose Joe is uncertain whether he's attractive or not - he assigns it a probability of 1/3. Someone offers to tell him the true answer. If Joe's utility-of-belief function is U(p)=p^2, then being told the answer is worth ((1/3)*U(1) + (2/3)*U(0)) - U(1/3) = ((1/3)*1 + (2/3)*0) - (1/9) = 2/9, so he takes the offer. If on the other hand his utility-of-belief function were U(p)=sqrt(p), then being told the information would be worth ((1/3)*sqrt(1) + (2/3)*sqrt(0)) - sqrt(1/3) = -0.244, so he plugs his ears.