Desirable Dispositions and Rational Actions

You need a little more context/priming or to make the joke longer for anyone to catch this. Or you need to embed it in a more substantive and sensible reply. Otherwise it will hardly ever work.

I wasn't sure, so I held off posting my reply (a decision I now regret). It would have been, "Well, hardly ever."

I'm sure it would be Wei-Dai's read as well. The thing is, if Wei-Dai had not mistakenly come to the conclusion that the authors are wrong and not as enlightened as LWers, that admonishment would not be necessary. I'm not saying he condescends to LWers. I say he condescends to the rest of the world, particularly game theorists.

I have taken a graduate level course in game theory (where I got a 4.0 grade, in case you suspect that I coasted through it), and have Fudenberg and Tirole's "Game Theory" and Joyce's "Foundations of Causal Decision Theory" as two of the few physical books that I own.

Ok, so it is me who is convicted of condescending without having the background to justify it. :( FWIW I have never taken a course, though I have been reading in the subject for more than 45 years.

My apologies. More to come on the substance.

Relevance of Subgame perfection. Seldin suggested subgame perfection as a refinement of Nash equilibrium which requires that decisions that seemed rational at the planning stage ought to still seem rational at the action stage. This at least suggests that we might want to consider requiring "subgame perfection" even if we only have a single player making two successive decisions.

Relevance of Footnote #4. This points out that one way to think of problems where a single player makes a series of decisions is to pretend that the problem has a series of players making the decisions - one decision per player, but that these fictitious players are linked in that they all share the same payoffs (but not necessarily the same information). This is a standard "trick" in game theory, but the footnote points out that in this case, since both fictitious players have the same information (because of the absent-mindedness) the game between driver-version-1 and driver-version-2 is symmetric, and that is equivalent to the constraint p1 = p2.

Does Footnote #4 really amount to "they had already argued for [just recalculating the planning-optimal solution]"? Well, no it doesn't really. I blew it in offering that as evidence. (Still think it is cool, though!)

Do they "argue for it" anywhere else? Yes, they do. Section 5, where they apply their methods to a slightly more complicated example, is an extended argument for the superiority of the planning-optimal solution to the action-optimal solutions. As they explain, there can be multiple action-optimal solutions, even if there is only one (correct) planning-optimal solution, and some of those action-optimal solutions are wrong *even though they appear to promise a higher expected payoff than does the planning optimal solution.

I can't see where they made this point. At the top of Section 4, they say "How, then, should the driver reason at the action stage?" and go on directly to describe action-optimality. If they said something like "One possibility is to just recompute and apply the planning-optimal solution. But if you insist ..." please point out where. See also page 108:

In our case, there is only one player, who acts at different times. Because of his absent-mindedness, he had better coordinate his actions; this coordination can take place only before he starts out at the planning stage. At that point, he should choose p1 . If indeed he chose p1 , there is no problem. If by mistake he chose p2 or p3 , then that is what he should do at the action stage. (If he chose something else, or nothing at all, then at the action stage he will have some hard thinking to do.)

If Aumann et al. endorse using planning-optimality at the action stage, why would they say the driver has some hard thinking to do? Again, why not just recompute and apply the planning-optimal solution?

I really don't see why you are having so much trouble parsing this. "If indeed he chose p1 , there is no problem" is an endorsement of the correctness of the planning-optimal solution. The sentence dealing with p2 and p3 asserts that, if you mistakenly used p2 for your first decision, then you best follow-up is to remain consistent and use p2 for your remaining two choices. The paragraph you quote to make your case is one I might well choose myself to make my case.

Edit: There are some asterisks in variable names in the original paper which I was unable to make work with the italics rules on this site. So "p2" above should be read as "p 2"

Yay: honesty points!

For that matter, what's SDT?

I think ADT is only described on Vladimir Nesov's blog (if there) and XDT nowhere findable. ADT stands for Ambient Decision Theory. Unfortunately there's no comprehensive and easy summary of any of the modern decision theories anywhere. Hopefully Eliezer publishes his TDT manuscript soon.

I don't think there are any papers. There's only this ramble:

http://lesswrong.com/lw/15z/ingredients_of_timeless_decision_theory/

As I said, I think your correspondents are in rather a muddle - and are discussing a completely different and rather esoteric PD case - where the agents can see and verify each other's source code.

Yes - but you would still give its skull a lead-lining - and make use of redundancy to produce reliability...

So, you're really interested in this question: what is the best decision algorithm? And then you're interested, in a subsidiary way, in what you ought to do. You think the "action" sense is silly, since you can't run one algorithm and make some other choice.

Your answer to my objection involving the parody argument is that you ought to do something else (not go with loss aversion) because there is some better decision algorithm (that you could, in some sense of "could", use?) that tells you to do something else.

What do you do with cases where it is impossible for you to run a different algorithm? You can't exactly use your algorithm to switch to some other algorithm, unless your original algorithm told you to do that all along, so these cases won't be that rare. How do you avoid the result that you should just always use whatever algorithm you started with? However you answer this objection, why can't two-boxers who care about the "action sense" of ought answer your objection analogously?

I agree that this fact [you can't have a one-boxing disposition and then two box] could appear as premise in an argument, together with an alternative proposed decision theory, for the conclusion that one-boxing is a bad idea. If that was the implicit argument, then I now understand the point.

To be clear: I have not been trying to argue that you ought to take two boxes in Newcomb's problem.

But I thought this fact [you can't have a one-boxing disposition and then two box] was supposed to be a part of an argument that did not use a decision theory as a premise. Maybe I was misreading things, but I thought it was supposed to be clear that two-boxers were irrational, and that this should be pretty clear once we point out that you can't have the one-boxing disposition and then take two boxes.

Okay, so your dispositions are basically the counterfactual "If A occurred then I would do B" and your choice, C, is what you actually do when A occurs.

In the perfect predictor version of Newcomb's, Omega predicts perfectly the choice you make, not your disposition. It may generate it's own counterfactual for this "If A occurs then this person will do B" but that's not to say it cares about your disposition just because the two counterfactuals look similar. Because Omega's prediction of C is perfect, that means that if a stray bolt of lightning hits you and switches your decision, Omega will have taken that lightning into account. You will always be sad if it changes your choice, C, to two boxing because Omega perfectly predicts C and so will punish you.

Inversely, the rational disposition in Newcomb's isn't to one box. Instead, your disposition has no bearing on Newcomb's except insofar as it is related to C (if you always act in line with your dispositions, for example, what your dispositions matter). It isn't a disposition to one box that leads to Omega loading the boxes a certain way, it's a choice to one box so your disposition neither helps nor hinders you.

As such, your choice of whether to one or two box is what is relevant. And hence, the choice of one boxing is what leads to the better outcome. Your disposition to one box plays no role whatsoever. Hence, based on the maximising utility definition of rationality, the rational choice is to one box because its this choice itself that leads to the boxes being loaded in a certain way (note on causality at the bottom of the post).

So to restate it in the terms used in the above comments: A prior possession of the disposition to one-box is irrelevant to Newcomb's because Omega is interested in your choices not your dispositions to choices and is perfect at predicting your choices not your dispositions. Flukily choosing two boxes would be bad because Omega would have perfectly predicted the fluky choice and so you would end up loosing.

It seems like dispositions distract from the issue here because as humans we think "Omega must use dispositions to predict the choice." But that need not be true. In fact, if dispositions and choices can differ (by a fluke, for example) then it must not be true. Omega must not use dispositions to predict choice. It simply predicts the choice using whatever means work.

If you use dispositions simply to mean, the decision you would make before you actually make the decision then you're denying one of the parts of the problem itself in order to solve it - you're denying that Omega is a perfect predictor of choices and you're suggesting he's only able to predict the way choices would be at a certain time and not the choice you actually make.

This can be extended to the imperfect predictor version of Newcomb's easily enough.

I'll grant you it leaves open the need for some causal explanation but we can't simply retreat from difficult questions by suggesting that they're not really questions. Ie. We can't avoid needing to account for causality in Newcomb's by simply suggesting that Omega predicts by reading your dispositions rather than predicts C using whatever means it is that gets it right (ie. taking your dispositions and then factoring in freak lightning strikes).

So far, everything I've said has been weakly defended so I'm interested to see whether this is any stronger or whether I'll be doing some more time thinking tomorrow.

We're going in circles a little aren't we (my fault, I'll grant). Okay, so there are two questions:

1.) Is it a rational choice to one box? Answer: No. 2.) Is it rational to have a disposition to one box? Answer: Yes.

As mentioned earlier, I think I'm more interested in creating a decision theory than wins than one that's rational. But let's say you are interested in a decision theory that captures rationality: It still seems arbitrary to say that the rationality of the choice is more important than the rationality of the decision. Yes, you could argue that choice is the domain of study for decision theory but the number of decision theorists that would one box (outside of LW) suggests that other people have a different idea of what decision theory would be.

I guess my question is this: Is the whole debate over one or two boxing on Newcomb's just a disagreement over which question decision theory should be studying or are there people who use choice to mean the same thing that you do that think one boxing is the rational choice?

I still don't see how statements about disposition in your sense are supposed to have an objective truth value (what does someone look like in visually simplified?), and why you think this disposition is supposed to better correlate with peoples predictions about decisions than the non-random component of the decision making process (total disposition) does (or why you think this concept is useful if it doesn't), but I suspect discussing this further won't lead anywhere.

Let's try leaving the disposition discussion aside for a moment: You are postulating a scenario where someone spontaneously changes from a one-boxer into a two-boxer after the predictor has already made the prediction, just long enough to open the right hand box and collect the $1000. Is that right? And the question is whether I should regret not being able to change myself back into a one boxer in time to refuse the $1000?

Obviously if my behavior in this case was completely uncorrelated to the odds of finding the $1,000,000 box empty I should not. But the normal assumption for cases where your behavior is unpredictable (e. g. when you are using a quantum coin) is that P(two box) = P ( left box empty). Otherwise I would try to contrive to one-box with a probability of just over 0.5. So the details depend on P.

If P>0.001 (I'm assuming constant utility per dollar, which is unrealistic) my expected dollars before opening the left box have been reduced, and I bitterly regret my temporary lapse from sanity since it might have costed me $1,000,000. The rationale is the same as in the normal Newcomb problem.

If P<0.001 my expected dollars right at that point have increased, and according to some possible decision theories that one-box I should not regret the spontaneous change, since I already know I was lucky. But nevertheless my overall expected payoff in all branches is lower than it would be if temporary lapses like that were not possible. Since I'm a Counterfactual muggee I regret not being able to prevent the two-boxing, but am happy enough with the outcome for that particular instance of me.