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Yeah, I'm pretty sure my usage is entirely consistent with the wiki usage, if not basically identical.
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.
- 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.)
- 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.
If you are still talking about Hedons and Utilons - and if we go by the wiki, then no difference - since Hedons are a subset of Utilons, and are therefore measured in the same units.
Then what's the difference between "pleasure unit" and "experiential utility unit"?
We can experience things other than pleasure.
Certainly, you need to resolve any underspecification. There are ways to do this usefully (or not).
Agreed. My point is simply that one particular (tempting) way of resolving the underspecification is non-useful. ;)
What you just said seems correct.
What was originally at issue is whether we should act in ways that will eventually destroy ourselves.
I think the big-picture conclusion from what you just wrote is that, 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.
However, in our circumstances, time discounting and "identity discounting" encourage us to start enjoying and dooming ourselves now; whereas it would probably be better to spread life to a few other galaxies first, and then enjoy ourselves.
(I admit that my use of the word "better" is problematic.)
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. ;)
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.
If by "your example" you refer to the setup described in this comment, I don't understand what you are saying here. I don't use any "definition of utility", it's just a parameter of the tool.
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.
You argue that the thought experiment is trivial and doesn't solve any problems. In my comments above I described a specific setup that shows how to use (interpret) the thought experiment to potentially obtain non-trivial results.
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.
What's the difference between 1 and 2? If we're being selfish then surely we just want to experience the most pleasurable emotional states. I would read "values" as an individual strategy for achieving this. Then, being unselfish is valuing the emotional states of everyone equally... ...so long as they are capable of experiencing equally pleasurable emotions, which may be untestable.
Note: just re-read OP, and I'm thinking about integrating over instantaneous hedons/utilons in time and then maximising the integral, which it didn't seem like the OP did.
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.
You are placing on a test the following well-defined tool: expected utility maximizer with a prior and "utility" function, that evaluates the events on the world. By "utility" function here I mean just some function, so you can drop the word "utility". Even if people can't represent their preference as expected some-function maximization, such tool could still be constructed. The question is whether such a tool can be made that always agrees with human preference.
An easy question is what happens when you use "hedons" or something else equally inadequate in the role of utility function: the tool starts to make decisions with which we disagree. Case closed. But maybe there are other settings under which the tool is in perfect agreement with human judgment (after reflection).
Utility-doubling thought experiment compares what is better according to the judgment of the tool (to take the card) with what is better according to the judgment of a person (maybe not take the card). 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't preference (after "careful" reflection), proves that there is no way to set up "utility" and prior so that the "utility" maximization tool represents that person's preference.
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.
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If you accept that you're maximizing expected utility, then you should draw the first card, and all future cards. It doesn't matter what terms your utility function includes. The logic for the first step is the same as for any other step.
If you don't accept this, then what precisely do you mean when you talk about your utility function?
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.