Comments on: How to Be an Instrumentally Rational One-Boxer

By: A Pixelated Mind » Oldcomb's Paradox

A Pixelated Mind » Oldcomb's Paradox — Mon, 04 Jun 2007 20:00:01 +0000

[...] This post made me think a bit about the Newcomb paradox. Newcomb’s paradox is basically a prisoner’s dilemma with a sci fi twist. The neat version: [...]

By: Steve C.

Steve C. — Mon, 04 Jun 2007 05:00:09 +0000

Warren,
I think WG is just a framework to discuss the debate and is perfectly neutral between evidential and causal decision theory. The standard two-boxing argument can be given just as effectively in terms of worlds. Either you’re in {W1,W2} or you’re in {W3,W4} (i.e. Either there’s a million in the closed box or there isn’t); if in {W1,W2}, you prefer W1 to W2 (i.e. If there’s a million, you prefer to get it and the thousand as opposed to just getting the million)…

I agree that it is preferable to defend one-boxing in more formal terms. I’ll think about presenting all of this more formally after taking Jim’s course.

On the Adam-related issue, of course I don’t deny his (1) or (2). And yes, you’re certainly right that I’ve given a completely evidentially-laden defense of abandoning the goal of getting $1,001,000.

By: Warren

Warren — Sun, 03 Jun 2007 18:55:29 +0000

I should add that I fully agree with Adam’s comment and see my question as a continuation of his initial critique. If WG entails a denial of Adam’s (2), then it is implausible (and simply stipulates the paradox away). But if WG does not entail a denial of Adam’s (2), then my suggestion is that it doesn’t constitute an alternative to EU. If (2) is true, then why wouldn’t an agent aim at the goal of $1,001,000? Presumably, $1,001,000 isn’t a suitable goal because it is unlikely. But now we’re talking like EU-theorists: we discount the prospect of receiving $1,001,000 because of its low probability. Although the utility of receiving $1,001,000 is high, the expected utility of an unlikely prospect of receiving $1,001,000 is low. That’s why it isn’t a suitable goal: because it presents a low expected utility.

By: Warren

Warren — Sun, 03 Jun 2007 18:41:08 +0000

Steve,
I thought I’d probably overstated your goal. Sorry. But I’m still doubtful that the worlds/goals framework can help you achieve your stated goal (of providing “a fruitful starting point for thinking about the debate”). My reason goes back to what I said in my previous comment. If I’m correct that the worlds/goals framework (I’ll call it “WG”) is nothing more than a heuristic device designed to produce decisions in accordance with expected utility theory (“EU”), then I don’t see what it can contribute. If EU fails as a theory of rational choice in this scenario, and if WG is simply an intuitively presented form of EU, then WG will also fail. If EU succeeds, then WG will also succeed. In either case, the success of WG will be tied to the success of EU. The relevant question will then be why EU succeeds or fails, and clear thought about this matter will require as clear a formulation of the decision theory as possible. Despite it’s flaws, EU is quite clear. I think WG is less clear, and I worry that presenting it as a defense of one-boxing will obscure some important issues. If it doesn’t constitute an alternative to EU, then why discuss it at all? Why not stick with EU? Of course, if it does present an alternative to EU, then there’s good reason to discuss it and none of what I’ve said matters. So my question is still: Does WG differ from EU and, if so, how?

By: Steve C.

Steve C. — Sun, 03 Jun 2007 17:02:41 +0000

At the moment, here are the answers I’m inclined to give:
1. Yes. They share the same preference ordering of worlds throughout the decision process.
2. Yes, though different interpretations of “can” lead to divergence.
3. Yes. But I’m inclined to think the one-boxer has the strongest claim to appreciating the preference ordering, given that even two-boxers must admit that acting on the goal of “getting all the money in the room” will almost certainly yield only a thousand dollars, and that acting on the goal of “getting a million” will almost certainly yield a million. All greedy people prefer to be as high on the preference ordering as they can be. One-boxers can grant that our actual choice will not causally affect whether one is in {W1, W2} or {W3, W4}. And of course it is true that, holding it fixed that a million is in the closed box, it would be better if one could take both boxes. The one-boxer has no complaint with that. Unfortunately, that hardly ever happens, and we can see just why that is (while in the room). That is, we can see just why one-boxing pays off as it does, and why two-boxing pays off as it does.
4. To the extent that people fully understand the situation, the disagreement is a normative one (and not descriptive, if I may revert to an old-fashioned distinction). Of course, I wonder if different interpretations of the term “rational” aren’t driving much of the disagreement. I’m not sure. I’m almost exclusively concerned with the question of what to do, given one’s goal.

By: Steve C.

Steve C. — Sat, 02 Jun 2007 20:54:29 +0000

Dustin, thanks for the comment. I’m not inclined to go along with you at present, due to certain cloning cases we’ve discussed. But, of course, there’s much to be said, and I can’t pretend to have a settled view.

Warren, Yes–I agree with most everything you said, though perhaps you did mistake my aim, which was far more modest than “resolving the paradox.” While I presented the above as a defense of the possibility of greedy, instrumentally rational one-boxing, I didn’t mean to imply that causal reasoning can’t provide an equally strong defense for two-boxing. In fact, I think that it can. So yes, I have done nothing in the post to show one reasoning strategy to be superior to the other, and I definitely haven’t resolved the paradox. But, I do think the worlds/goals framework might provide a fruitful starting point for thinking about this debate. Maybe there’s even a satisfactory resolution in the offing.

Here are some questions that interest me, and I’d be curious to get others’ opinions on it:
1. Do you think typical causal and evidential reasoners in the Newcomb game want the same thing?
2. Is the Newcomb debate ultimately a matter of instrumental rationality–what is best to do given the shared goal of “getting as much as you can get”?
3. Could it be that neither two-boxers nor one-boxers are mistaken about the nature of the situation (setting aside facts of rationality for the moment)?
4. To what extent is the debate normative?

By: Dustin

Dustin — Fri, 01 Jun 2007 00:49:24 +0000

I just wanted to add that I fully agree with Adam.

Oh, I’d also like to add that I think it somewhat obvious that the dominance approach is superior to the expected utility approach. Why do I think so? The expected utility approach rests on the following principle:

E: If the thing of value is money, then one should perform the action with the highest “expected value” in terms of money, where the expected value of an action in terms of money is the sum of the probabilities of each possible outcome given the action times the money value of that outcome.

The dominance approach rests on the following principle:

D: If the thing of value is money, then one should perform the action that is guaranteed to get one more money than any other action.

So the question is which of these principle to reject. To me the choice is obvious: although I find (E) very intuitively plausible, the (D) seems to me to border on an analytic truth. Moreover, we can offer a nice explanation of WHY (E) would seem plausible even if it were false: (E) seems plausible because it is very similar to, and often yields the same result as a principle that is true–namely, the basic assumption of causal decision theory:

C: If the thing of value is money, then one should perform the action with the highest “causally expected value” in terms of money, where the causally expected value of an action in terms of money is the sum of the degrees to which each possible outcome is CAUSALLY PROMOTED BY the action times the money value of that outcome.

Whenever we have two conflicting principles P1 and P2 that both seem intuitively plausible, yet A) P2 seems MUCH MORE intuitively plausible and B) we can offer an explanation of why P1 would seem plausible even if it were false, it seems to me that we should reject P1 in favor of P2.

By: waherold

waherold — Thu, 31 May 2007 16:27:48 +0000

Hi Steve,

I’m new to this Newcomb’s Paradox thing, but let me take a shot. From what I can tell, the paradox (if there is one) stems from the apparent conflict between two different decision-making approaches. The “dominance” approach to the problem leads one to reason as follows: no matter what the predictor predicts, I’m better off if I “two-box”, so I should “two-box”. But the “expected utility” approach leads one to make a decision so as to maximize the expected utility of the outcome: assuming the probabilities of W2 and W3 are significantly higher than the probabilities of W1 and W4 (say the first two equal 0.99 and the last two equal 0.01, which seems reasonable, since the predictor is very good at predicting), the expected utility approach seems to endorse the choice of one box. Because both the “dominance” and the “expected utility” approaches seem reasonable, and the two endorse different decisions, we have what looks like a paradox (maybe). In order to resolve the paradox, it is necessary to do one (or more) of the following: (1) explain why one of the decision approaches is actually superior to the other or (2) explain why they don’t really conflict or (3) introduce some other approach that is superior to either of the two.

My question is this: does your “goal” approach do any of these three things? (Perhaps you don’t intend for it to do any of them. I may have completely mistaken your aim.) It seems to me that your approach is really a slightly modified, intuitively presented form of the “expected utility” approach. Basically, you’re a risk-averse individual who wants to maximize your utility (as you said, you’re “just not one for taking great risks”). Because you’re so risk-averse, the strategy of identifying and pursuing an appropriately chosen goal serves as a good rule-of-thumb to help you maximize your expected utility. If this is correct, then it may be a good way of thinking about making a choice, but it doesn’t do much to defend the rationality of “one-boxing” against the arguments in favor of “two-boxing” made by the “dominance” approach. It doesn’t provide an alternative approach, and it doesn’t really show why the “expected utility” approach is superior to the “dominance” approach or that they don’t conflict.

By: Steve C.

Steve C. — Sun, 27 May 2007 04:15:28 +0000

Hey Adam,
I’m definitely not denying (1) or (2). I listed my preference ordering of the worlds and that remains constant throughout the entire deliberation process, and now. And I assume that all greedy people have this same ordering. There’s just a difference between what a person (perhaps fancifully) prefers to be the case, and what she is willing to take as an end in practical deliberation. I’m not willing to do so with 1,001,000 or 0. (Suppose the predictor had been correct in 500 million out of 500 million cases.) So those get bracketed off as potential goals. That leaves two others, and I prefer to aim for 1,000,000 rather than 1,000.

And I don’t think I’ve stipulating away the paradox at all. As I see it, the paradoxical thing about the Newcomb game is that it generates such a clash in our intuitions and nothing I’ve said does away with that. If I were in the room, I am quite sure that I would feel a strong intuitive pull towards two-boxing, even given my strong one-boxing convictions. …so much so that I might even cop out and take both boxes! (But by varying cases, I think you can make either one-boxing or two-boxing win out in the intuition clash, so I’m not inclined to let intuitive pull guide my thinking on this.)

But yes, you’re right–there is still the grand question of “what end to choose.” I haven’t tried to address that here.

By: ajshriver

ajshriver — Sun, 27 May 2007 02:51:01 +0000

I think this whole “Once I take 1,000,000 as my goal…” approach is a bit of a cheat, since it basically stipulates the paradox out of existence. The paradox works (if it does) on the assumption that people have certain preferences: among these are (1) people prefer 1,000,000 to 1,000 and (2) people prefer 1,000 to 0. By saying “1,000,000 is my goal,” you are denying the obvious fact that (2) is true. 1,000 and 0 are both instances of “not 1,000,000″ so a choice between them would be completely negligible if your goal was to get 1,000,000.

Another way of saying this is once you have taken 1,000,000 as your goal, you are no longer fully rational. You would prefer a 1/500 chance at 1,000,000 to a guaranteed 999,999. I suppose you could still be considered instrumentally rational relative to your goal, but this kind of rationality doesn’t seem to be what the paradox is about.

In general, why think that talking about instrumental rationality in this way makes any progress on the paradox? You can be an instrumentally rational one-boxer if your goal is 1,000,000 and an instrumentally rational two-boxer if your goal is to get 1,000; doesn’t the question then just become “what should your goal be?” or, better, “how do you decide between different strategies?” Perhaps this is what you are saying in the last paragraph, but if so then I don’t see how the paradox is addressed.