Given the discussion, strictly speaking the pill reduces Ghandi’s reluctance to murder by 1 percentage point. Not 1%.
scmbradley
Anyone who can handle a needle convincingly can make us see a thread which isn’t there
-E.H. Gombrich
Any logically coherent body of doctrine is sure to be in part painful and contrary to current prejudices
– Bertrand Russell, History of Western Philosophy p. 98
Bertie is a goldmine of rationality quotes.
Uncertainty, in the presence of vivid hopes and fears, is painful, but must be endured if we wish to live without the support of comforting fairy tales
— Bertrand Russell, History of Western Philosophy (from the introduction)
Hi. I’ll mostly be making snarky comments on decision theory related posts.
I’ve had rosewater flavoured ice cream.
I bet cabbage ice cream does not taste as nice.
There are a couple of things I find odd about this. First, it seems to be taken for granted that one-boxing is obviously better than two boxing, but I’m not sure that’s right. J.M. Joyce has an argument (in his foundations of causal decision theory) that is supposed to convince you that two-boxing is the right solution. Importantly, he accepts that you might still wish you weren’t a CDT (so that Omega predicted you would one-box). But, he says, in either case, once the boxes are in front of you, whether you are a CDT or a EDT, you should two-box! The dominance reasoning works in either case, once the prediction has been made and the boxes are in front of you.
But this leads me on to my second point. I’m not sure how much of a flaw Newcomb’s problem is in a decision theory, given that it relies on the intervention of an alien that can accurately predict what you will do. Let’s leave aside the general problem of predicting real agents’ actions with that degree of accuracy. If you know that the prediction of your choice affects the success of your choices, I think that reflexivity or self reference simply makes the prediction meaningless. We’re all used to self-reference being tricky, and I think in this case it just undermines the whole set up. That is, I don’t see the force of the objection from Newcomb’s problem, because I don’t think it’s a problem we could ever possibly face.
Here’s an example of a related kind of “reflexivity makes prediction meaningless”. Let’s say Omega bets you $100 that she can predict what you will eat for breakfast. Once you accept this bet, you now try to think of something that you would never otherwise think to eat for breakfast, in order to win the bet. The fact that your actions and the prediction of your actions have been connected in this way by the bet makes your actions unpredictable.
Going on to the prisoner’s dilemma. Again, I don’t think that it’s the job of decision theory to get “the right” result in PD. Again, the dominance reasoning seems impeccable to me. In fact, I’m tempted to say that I would want any future advanced decision theory to satisfy some form of this dominance principle: it’s crazy to ever choice an act that is guaranteed to be worse. All you need to do to “fix” PD is to have the agent attach enough weight to the welfare of others. That’s not a modification of the decision theory, that’s a modification of the utility function.
Aha. So when agents’ actions are probabilistically independent, only then does the dominance reasoning kick in?
So the causal decision theorist will say that the dominance reasoning is applicable whenever the agents’ actions are causally independent. So do these other decision theories deny this? That is, do they claim that the dominance reasoning can be unsound even when my choice doesn’t causally impact the choice of the other?
Savage’s representation theorem in Foundations of Statistics starts assuming neither. He just needs some axioms about preference over acts, some independence concepts and some pretty darn strong assumptions about the nature of events.
So it’s possible to do it without assuming a utility scale or a probability function.
I have lots of particular views and some general views on decision theory. I picked on decision theory posts because it’s something I know something about. I know less about some of the other things that crop up on this site…
Signals by Brian Skyrms is a great book in this area. It shows how signalling can evolve in even quite simple set-ups.
we might ask whether it is preferable to be the type of person who two boxes or the type of person who one boxes. As it turns out it seems to be more preferable to one-box
No. What is preferable is to be the kind of person Omega will predict will one-box, and then actually two-box. As long as you “trick” Omega, you get strictly more money. But I guess your point is you can’t trick Omega this way.
Which brings me back to whether Omega is feasible. I just don’t share the intuition that Omega is capable of the sort of predictive capacity required of it.
As I understand what is meant by satisficing, this misses the mark. A satisficer will search for an action until it finds one that is good enough, then it will do that. A maximiser will search for the best action and then do that. A bounded maximser will search for the “best” (best according to its bounded utility function) and then do that.
So what the satisficer picks depends on what order the possible actions are presented to it in a way it doesn’t for either maximiser. Now, if easier options are presented to it first then I guess your conclusion still follows, as long as we grant the premise that self-transforming will be easy.
But I don’t think it’s right to identify bounded maximisers and satisficers.
So I agree. It’s lucky I’ve never met a game theorist in the desert.
Less flippantly. The logic pretty much the same yes. But I don’t see that as a problem for the point I’m making; which is that the perfect predictor isn’t a thought experiment we should worry about.
Elsewhere on this comment thread I’ve discussed why I think those “rules” are not interesting. Basically, because they’re impossible to implement.
According to what rules? And anyway I have preferences for all kinds of impossible things. For example, I prefer cooperating with copies of myself, even though I know it would never happen, since we’d both accept the dominance reasoning and defect.
So these alternative decision theories have relations of dependence going back in time? Are they sort of couterfactual dependences like “If I were to one-box, Omega would have put the million in the box”? That just sounds like the Evidentialist “news value” account. So it must be some other kind of relation of dependence going backwards in time that rules out the dominance reasoning. I guess I need “Other Decision Theories: A Less Wrong Primer”.
See mine and orthonormal’s comments on the PD on this post for my view of that.
The point I’m struggling to express is that I don’t think we should worry about the thought experiment, because I have the feeling that Omega is somehow impossible. The suggestion is that Newcomb’s problem makes a problem with CDT clearer. But I argue that Newcomb’s problem makes the problem. The flaw is not with the decision theory, but with the concept of such a predictor. So you can’t use CDT’s “failure” in this circumstance as evidence that CDT is wrong.
Here’s a related point: Omega will never put the money in the box. Smith act like a one-boxer. Omega predicts that Smith will one-box. So the million is put in the opaque box. Now Omega reasons as follows: “Wait though. Even if Smith is a one-boxer, now that I’ve fixed what will be in the boxes, Smith is better off two-boxing. Smith is smart enough to realise that two-boxing is dominant, once I can’t causally affect the contents of the boxes.” So Omega doesn’t put the money in the box.
Would one-boxing ever be advantageous if Omega were reasoning like that? No. The point is Omega will always reason that two-boxing dominates once the contents are fixed. There seems to be something unstable about Omega’s reasoning. I think this is related to why I feel Omega is impossible. (Though I’m not sure how the points interact exactly.)
Wouldn’t you like to be the type of agent who cooperates with near-copies of yourself? Wouldn’t you like to be the type of agent who one-boxes?
Yes, but it would be strictly better (for me) to be the kind of agent who defects against near-copies of myself when they co-operate in one-shot games. It would be better to be the kind of agent who is predicted to one-box, but then two-box once the money has been put in the opaque box.
But the point is really that I don’t see it as the job of an alternative decision theory to get “the right” answers to these sorts of questions.
– Bertrand Russell