Comments on: Asymmetric Death in Damascus

By: Ralph Wedgwood

Ralph Wedgwood — Wed, 14 Jan 2009 14:06:13 +0000

P. S. Obviously, the kind of answer that I want to give about these asymmetric “Death in Damascus” cases will constrain what I can consistently say about the original Death in Damascus case.

So I say that in the original Death in Damascus case, both of the available options are rational. It’s a ghastly situation to be in, but that is just because of the virtual certainty of imminent death, not because rational choice is impossible!

By: Ralph Wedgwood

Ralph Wedgwood — Wed, 14 Jan 2009 12:54:28 +0000

I’ve been working on an answer to exactly this problem, in a paper that I’m now calling “Gandalf’s Solution to the Newcomb Problem”:

http://users.ox.ac.uk/~mert1230/gandalf.ltr.pdf

Basically my approach is a version of Brian’s Answer 3.

I deny that picking Box B in Brian’s example is the slightest bit irrational. Of course, it’s quite true that “choosing B involves doing something that you know, when you do it, is less rewarding than something else you could just as easily have done”. But the crucial point is that choosing A would involve doing something that you know, when you do it, would be atrociously suboptimal. So B is to be preferred to A, and choosing the option that is to be preferred is rational.

Kenny’s objection seems to me the crucial one that I have to answer. I think that what I have to do is to argue that only a one-boxer can really view this objection as having any force.

By: Avrom

Avrom — Fri, 12 Dec 2008 19:41:46 +0000

So, I think I have a potential solution to this problem:

http://avromandina.net/avrom/2008/12/dealing-with-asymmetric-death-in-damascus/

Thoughts?

By: Avrom

Avrom — Fri, 12 Dec 2008 08:05:57 +0000

The thing that really gets to me about this, and what might be the source of your intuitive “ugh” about answer 2, is this: Unlike with the “one-boxing” answer in Newcomb’s Paradox, there’s no direct counterargument to the “Box B” argument here. In Newcomb’s paradox, you really do have these two arguments that both look good prima facie, and which pull in opposite directions, and you have to decide which one you find more convincing. But here, there’s no reason not to buy the argument for just choosing B, except that you know one-boxing in general doesn’t work because of Newcomb’s paradox.

In other words, it’s just hard to come up with a general theory of rational decision that supports the intuitively pretty appealing notion of picking Box B. If we didn’t know about Newcomb’s Paradox itself, there would be no puzzle here—we’d take Box B and be happy.

By: Kenny Easwaran

Kenny Easwaran — Thu, 11 Dec 2008 09:40:55 +0000

A further problem with Answer 3 – it looks like it only depends on the differences between the amounts in the two boxes given a prediction, and not the comparison between the payoffs if the demon has made the correct prediction. For instance, if you added a million dollars to both payoffs if the demon predicted you would choose A, Answer 3 would still argue for choosing B. But it seems that this addition would at least give some more weight towards choosing A. (Though maybe I’m wrong – this might just be my one-boxer sympathies coming through here.)

Also, in your mention of Answer 1, I think you switched “700” and “100”.

By: wo

wo — Thu, 27 Nov 2008 23:17:46 +0000

I see. I always thought of ratifiability as an additional constraint: we should rule out unratifiable options on the grounds that they are unratifiable, no matter their expected utility; then we choose the best among the remaining options. It’s true that the mixed strategies never do better in terms of expected utility, but they always do better in terms of ratifiability.

By: Brian Weatherson

Brian Weatherson — Thu, 27 Nov 2008 16:55:22 +0000

I think a meta-mixed strategy like you describe just is a mixed strategy, and I think the demon would agree. (Since it’s my demon, I can specify that she would agree!)

I’m not convinced by the defence of a mixed strategy, but let me note that the argument against Jeffrey can be made with weaker assumptions than I have so far. On Jeffrey’s view, mixed strategies are uniquely rational. But there’s no credal state which, combined with either evidential or causal decision theory, that makes the mixed strategy do better than both pure strategies. So it seems very odd to say that it would be uniquely rational.

Thanks for the references – I’ll chase them up.

By: wo

wo — Thu, 27 Nov 2008 04:01:07 +0000

Maybe in this case the rational thing would be to toss a die to decide whether to choose A or B or a mixed strategy?

I’m also not sure that the mixed strategy would be “absolutely crazy”. If you opt for either of the pure strategies, you know that a mixed strategy would have higher expected payoff, while if you opt for a mixed strategy, you know that you’d fare no better if instead you had chosen a pure strategy. Yes, you can be certain that you’ll get nothing if you choose the mixed strategy. But you didn’t have a choice: the boxes were empty all along!

BTW, there has been a brief discussion of asymmetric Death in Damascus cases between Reed Richter and William Harper in the mid 1980s, starting (I think) with Richter’s “Rationality Revisited”.