conchis

Karma: 931

conchis Aug 13, 2009, 10:52 PM
3 points
in reply to: Aurini’s comment on: Deleting paradoxes with fuzzy logic
Warning, nitpicks follow:

The sentence “All good sentences must at least one verb.” has at least one verb. (It’s an auxiliary verb, but it’s still a verb. Obviously this doesn’t make it good; but it does detract from the point somewhat.)

“2+2=5” is false, but it’s not nonsense.

conchis Aug 13, 2009, 8:25 PM
2 points
in reply to: timtyler’s comment on: Utilons vs. Hedons
I was objecting to the subset claim, not the claim about unit equivalence. (Mainly because somebody else had just made the same incorrect claim elsewhere in the comments to this post.)

As it happens, I’m also happy to object to claim about unit equivalence, whatever the wiki says. (On what seems to be the most common interpretation of utilons around these parts, they don’t even have a fixed origin or scale: the preference orderings they represent are invariant to affine transforms of the utilons.)

conchis Aug 13, 2009, 7:35 PM
0 points
in reply to: DanArmak’s comment on: Utilons vs. Hedons
To expand on this slightly, it seems like it should be possible to separate goal achievement from risk preference (at least under certain conditions).

You first specify a goal function g(x) designating the degree to which your goals are met in a particular world history, x. You then specify another (monotonic) function, f(g) that embodies your risk-preference with respect to goal attainment (with concavity indicating risk-aversion, convexity risk-tolerance, and linearity risk-neutrality, in the usual way). Then you maximise E[f(g(x))].

If g(x) is only ordinal, this won’t be especially helpful, but if you had a reasonable way of establishing an origin and scale it would seem potentially useful. Note also that f could be unbounded even if g were bounded, and vice-versa. In theory, that seems to suggest that taking ever increasing risks to achieve a bounded goal could be rational, if one were sufficiently risk-loving (though it does seem unlikely that anyone would really be that “crazy”). Also, one could avoid ever taking such risks, even in the pursuit of an unbounded goal, if one were sufficiently risk-averse that one’s f function were bounded.

P.S.

On my reading of OP, this is the meaning of utility that was intended.

You’re probably right.

conchis Aug 13, 2009, 5:23 PM
1 point
in reply to: DanArmak’s comment on: Utilons vs. Hedons

Utility means “the function f, whose expectation I am in fact maximizing”.

There are many definitions of utility, of which that is one. Usage in general is pretty inconsistent. (Wasn’t that the point of this post?) Either way, definitional arguments aren’t very interesting. ;)

The interesting result is that if you’re maximizing something you may be vulnerable to a failure mode of taking risks that can be considered excessive.

Your maximand already embodies a particular view as to what sorts of risk are excessive. I tend to the view that if you consider the risks demanded by your maximand excessive, then you should either change your maximand, or change your view of what constitutes excessive risk.

conchis Aug 13, 2009, 5:04 PM
0 points
in reply to: DanArmak’s comment on: Utilons vs. Hedons
Crap. Sorry about the delete. :(

conchis Aug 13, 2009, 4:59 PM
1 point
in reply to: DanArmak’s comment on: Utilons vs. Hedons

Redefining “utility” like this doesn’t help us with the actual problem at hand: what do we do if Omega offers to double the f(x) which we’re actually maximizing?

It wasn’t intended to help with the the problem specified in terms of f(x). For the reasons set out in the thread beginning here, I don’t find the problem specified in terms of f(x) very interesting.

In your restatement of the problem, the only thing we assume about Omega’s offer is that it would change the universe in a desirable way

You’re assuming the output of V(x) is ordinal. It could be cardinal.

all this means is that Omega is offering us the wrong thing

I’m afraid I don’t understand what you mean here. “Wrong” relative to what?

which we don’t really value.

Eh? Valutilons were defined to be something we value (ETA: each of us individually, rather than collectively).

conchis Aug 13, 2009, 1:49 PM
3 points
in reply to: DanArmak’s comment on: Utilons vs. Hedons

The logic for the first step is the same as for any other step.

Actually, on rethinking, this depends entirely on what you mean by “utility”. Here’s a way of framing the problem such that the logic can change.

Assume that we have some function V(x) that maps world histories into (non-negative*) real-valued “valutilons”, and that, with no intervention from Omega, the world history that will play out is valued at V(status quo) = q.

Omega then turns up and offers you the card deal, with a deck as described above: 90% stars, 10% skulls. Stars give you double V(star)=2c, where c is the value of whatever history is currently slated to play out (so c=q when the deal is first offered, but could be higher than that if you’ve played and won before). Skulls give you death: V(skull)=d, and d < q.

If our choices obey the vNM axioms, there will be some function f(x), such that our choices correspond to maximising E[f(x)]. It seems reasonable to assume that f(x) must be (weakly) increasing in V(x). A few questions present themselves:

Is there a function, f(x), such that, for some values of q and d, we should take a card every time one is offered?

Yes. f(x)=V(x) gives this result for all d<q. This is the standard approach.

Is there a function, f(x), such that, for some values of q and d, we should never take a card?

Yes. Set d=0, q=1000, and f(x) = ln(V(x)+1). The card gives expected vNM utility of 0.9ln(2001)~6.8, which is less than ln(1001)~6.9.

Is there a function, f(x), such that, for some values of q and d, we should take some finite number of cards then stop?

Yes. Set d=0, q=1, and f(x) = ln(V(x)+1). The first time you get the offer, its expected vNM utility is 0.9ln(3)~1 which is greater than ln(2)~0.7. But at the 10th time you play (assuming you’re still alive), c=512, and the expected vNM utility of the offer is now 0.9ln(1025)~6.239, which is less than ln(513)~6.240.

So you take 9 cards, then stop. (You can verify for yourself, that the 9th card is still a good bet.)

* This is just to ensure that doubling your valutilons cannot make you worse off, as would happen if they were negative. It should be possible to reframe the problem to avoid this, but let’s stick with it for now.

conchis Aug 13, 2009, 11:06 AM
0 points
in reply to: Psychohistorian’s comment on: Utilons vs. Hedons
Interesting, I’d assumed your definitions of utilon were subtly different, but perhaps I was reading too much into your wording.

The wiki definition focuses on preference: utilons are the output of a set of vNM-consistent preferences over gambles.

Your definition focuses on “values”: utilons are a measure of the extent to which a given world history measures up according to your values.

These are not necessarily inconsistent, but I’d assumed (perhaps wrongly) that they differed in two respects.
1. Preferences are a simply binary relation, that does not allow degrees of intensity. (I can rank A>B, but I can’t say that I prefer A twice as much as B.) In contrast, the degree to which a world measures up to our values seems capable of degrees. (It could make sense for me to say that I value A twice as much as I value B.)
2. The preferences in question are over gambles over world histories, whereas I assumed that the values in question were over world histories directly.
I’ve started calling what-I-thought-you-meant “valutilons”, to avoid confusion between that concept and the definition of utilons that seems more common here (and which is reflected in the wiki). We’ll see how that goes.
What links here?
- conchis's comment on Utilons vs. Hedons by Psychohistorian (Aug 13, 2009, 1:49 PM; 3 points)

conchis Aug 13, 2009, 10:07 AM
0 points
in reply to: timtyler’s comment on: Utilons vs. Hedons

since Hedons are a subset of Utilons

Not true. Even according to the wiki’s usage.

conchis Aug 13, 2009, 10:04 AM
0 points
in reply to: PhilGoetz’s comment on: Utilons vs. Hedons
We can experience things other than pleasure.

conchis Aug 13, 2009, 9:22 AM
0 points
in reply to: Vladimir_Nesov’s comment on: Exterminating life is rational
Agreed. My point is simply that one particular (tempting) way of resolving the underspecification is non-useful. ;)

conchis Aug 13, 2009, 9:15 AM
2 points
in reply to: PhilGoetz’s comment on: Exterminating life is rational

if we see that we’re acting in ways that will probably exterminate life in short order, that doesn’t necessarily mean it’s the wrong thing to do.

Well, I don’t disagree with this, but I would still agree with it if you substituted “right” for “wrong”, so it doesn’t seem like much of a conclusion. ;)

conchis Aug 13, 2009, 9:10 AM
1 point
in reply to: Vladimir_Nesov’s comment on: Exterminating life is rational

it’s just a parameter of the tool.

It’s also an entity in the problem set-up. When Omega says “I’ll double your utility”, what is she offering to double? Without defining this, the problem isn’t well-specified.

conchis Aug 13, 2009, 8:52 AM
0 points
in reply to: Vladimir_Nesov’s comment on: Exterminating life is rational
I argue that the thought experiment is ambiguous, and that for a certain definition of utility (vNM utility), it is trivial and doesn’t solve any problems. For this definition of utility I argue that your example doesn’t work. You do not appear to have engaged with this argument, despite repeated requests to point out either where it goes wrong, or where it is unclear. If it goes wrong, I want to know why, but this conversation isn’t really helping.

For other definitions of utility, I do not, and have never claimed that the thought experiment is trivial. In fact, I think it is very interesting.

conchis Aug 12, 2009, 8:10 PM
2 points
in reply to: Adventurous’s comment on: Utilons vs. Hedons
We can value more than just our emotional states. The experience machine is the classic thought experiment designed to demonstrate this. Another example that was discussed a lot here recently was the possibility that we could value not being deceived.

conchis Aug 12, 2009, 6:08 PM
1 point
in reply to: Vladimir_Nesov’s comment on: Exterminating life is rational

As the tool’s decision in this thought experiment is made invariant on the tool’s settings (“utility” and prior), showing that the tool’s decision is wrong according to a person’s preference (after “careful” reflection), proves that there is no way to set up “utility”

My argument is that, if Omega is offering to double vNM utility, the set-up of the thought experiment rules out the possibility that the decision could be wrong according to a person’s considered preference (because the claim to be doubling vNM utility embodies an assumption about what a person’s considered preference is). AFAICT, the thought experiment then amounts to asking: “If I should maximize expected utility, should I maximize expected utility?” Regardless of whether I should actually maximize expected utility or not, the correct answer to this question is still “yes”. But the thought experiment is completely uninformative.

Do you understand my argument for this conclusion? (Fourth para of my previous comment.) If you do, can you point out where you think it goes astray? If you don’t, could you tell me what part you don’t understand so I can try to clarify my thinking?

On the other hand, if Omega is offering to double something other than vNM utility (hedons/valutilons/whatever) then I don’t think we have any disagreement. (Do we? Do you disagree with anything I said in para 5 of my previous comment?)

My point is just that the thought experiment is underspecified unless we’re clear about what the doubling applies to, and that people sometimes seem to shift back and forth between different meanings.

conchis Aug 12, 2009, 4:02 PM
1 point
in reply to: Vladimir_Nesov’s comment on: Exterminating life is rational
I’m struggling to figure out whether we’re actually disagreeing about anything here, and if so, what it is. I agree with most of what you’ve said, but can’t quite see how it connects to the point I’m trying to make. It seems like we’re somehow managing to talk past each other, but unfortunately I can’t tell whether I’m missing your point, you’re missing mine, or something else entirely. Let’s try again… let me know if/when you think I’m going off the rails here.

If I understand you correctly, you want to evaluate a particular decision procedure “maximize expected utility” (MEU) by seeing whether the results it gives in this situation seem correct. (Is that right?)

My point was that the result given by MEU, and the evidence that this can provide, both depend crucially on what you mean by utility.

One possibility is that by utility, you mean vNM utility. In this case, MEU clearly says you should accept the offer. As a result, it’s tempting to say that if you think accepting the offer would be a bad idea, then this provides evidence against MEU (or equivalently, since the vNM axioms imply MEU, that you think it’s ok to violate the vNM axioms). The problem is that if you violate the vNM axioms, your choices will have no vNM utility representation, and Omega couldn’t possibly promise to double your vNM utility, because there’s no such thing. So for the hypothetical to make sense at all, we have to assume that your preferences conform to the vNM axioms. Moreover, because the vNM axioms necessarily imply MEU, the hypothetical also assumes MEU, and it therefore can’t provide evidence either for or against it.*

If the hypothetical is going to be useful, then utility needs to mean something other than vNM utility. It could mean hedons, it could mean valutilons,** it could mean something else. I do think that responses to the hypothetical in these cases can provide useful evidence about the value of decision procedures such as “maximize expected hedons” (MEH) or “maximize expected valutilons” (MEV). My point on this score was simply that there is no particular reason to think that either MEH or MEV were likely to be an optimal decision procedure to begin with. They’re certainly not implied by the vNM axioms, which require only that you should maximise the expectation of some (positive) monotonic transform of hedons or valutilons or whatever.*** [ETA: As a specific example, if you decide to maximize the expectation of a bounded concave function of hedons/valutilons, then even if hedons/valutilons are unbounded, you’ll at some point stop taking bets to double your hedons/valutilons, but still be an expected vNM utility maximizer.]

Does that make sense?

* This also means that if you think MEU gives the “wrong” answer in this case, you’ve gotten confused somewehere—most likely about what it means to double vNM utility.

** I define these here as the output of a function that maps a specific, certain, world history (no gambles!) into the reals according to how well that particular world history measures up against my values. (Apologies for the proliferation of terminology—I’m trying to guard against the possibility that we’re using “utilons” to mean different things without inadvertently ending up in a messy definitional argument. ;))

*** A corollary of this is that rejecting MEH or MEV does not constitute evidence against the vNM axioms.

conchis Aug 12, 2009, 2:22 PM
3 points
in reply to: Wei Dai’s comment on: Exterminating life is rational

No one has proposed a form of utilitarianism that is free from paradoxes (e.g., the Repugnant Conclusion).

I’d be interested to know what you think of Critical-Level Utilitarianism and Population-Relative Betterness as ways of avoiding the repugnant conclusion and other problems.

conchis Aug 12, 2009, 9:40 AM
0 points
in reply to: SilasBarta’s comment on: Deleting paradoxes with fuzzy logic
Apology likewise accepted! ;)

conchis Aug 12, 2009, 1:48 AM
2 points
in reply to: Nanani’s comment on: Utilons vs. Hedons
Hedons won’t be a subset of utilons if we happen not to value all hedons. One might not value hedons that arise out of false beliefs, for example. (From memory, I think Lawrence Sumner is a proponent of a view something like this.)

NB: Even if hedons were simply a subset of utilons, I don’t quite see how that would mean that this post “doesn’t really make sense”.