Newbomb's parabox

This isn't a paradox, the bomb will go off no matter what, assuming Omega is a perfect predictor.

Amusingly, this wouldn't seem like a paradox if something good was guaranteed to happen if Omega guessed right. Like if the problem was that you're locked in a box, and you can only avoid getting a million dollars if you do the opposite of what Omega predicts. Answer: "cool, I get a million dollars!" and you stop thinking. In the problem as stated, you're casting about for an answer that doesn't seem possible, and that feels like thinking about paradoxes, so you think the problem is a paradox. It isn't. You're just trapped in a box with a bomb.

Your actions?

Take off every "zig".

This is just the "Death in Damascus" case. The case is more interesting if there is some asymmetry, e.g. you press the button you get pleasant background music for the hour before you die.

A TDTer or evidential decision theorist would be indifferent between the top options in the symmetric version, and pick the better choice in the asymmetric version.

For CDT, neither option is "ratifiable," i.e. CDT recommends doing whatever you think you won't do and immediately regretting any action you do take (if you can act suddenly, before you can update against following through with your plan).

I would just flip a coin, I guess. I think it would be hard to get better than fifty fifty odds by thinking about it for a really long time.

The original Newcomb's problem is interesting because it leads to UDT, which allows coordination between copies. Your problem seems to require anti-coordination instead. (Note that if your copies have different information, UDT gives you anti-coordination for free, because it optimizes your whole input-output map.) I agree that anti-coordination between perfect copies would be nice if it were possible. Is it fruitful to think about anti-coordination, and if yes, what would the resulting theory look like?

Also, here's a couple ways you can remove the need for Omega:

1) You wake up in a room with two buttons. You press one of them and go back to sleep. While you're asleep, the experimenter gives you an amnesia drug. You wake up again, not knowing if it's the first or second time. You press one of the buttons again, then the experiment ends and you go home. If you pressed different buttons on the first and second time, you win $100, otherwise nothing.

2) You are randomly chosen to take part in an experiment. You are asked to choose which of two buttons to press. Somewhere, another person unknown to you is given the same task. If you pressed different buttons, you both get $100, otherwise nothing.

Our only chance at this point is to try to outsmart Omega. I know this sounds impossible, but we can at least make some partial progress. If Omega is only correct say 90% of the time, it is probably the case that his correctness is a function of complexity of your mental algorithm. The more complex your mental algorithm, the harder you will be to accurately predict. Once you reach a certain threshold of complexity, Omega's accuracy will very quickly approach 50%.

Further, you have an hour. You can try a new different method to generate a pseudorandom bit every 5 minutes, and all it takes is for one of them to be unpredictable for you to bring Omega's accuracy down to 50%

This doesn't require actually outsmarting Omega, This just requires playing against Omega in a game so complex that his powers are less useful, and he has LESS of an advantage over you. You will not be able to pass 50%, unless you are actually smarter than Omega.

They were both poisoned. I spent the last few years building up an immunity to iocane powder.

If we're going to share silly Newcomb's Paradox like situations, here's the silliest one I've thought of, which rapidly devolves into a crazy roleplaying scenario, as opposed to a decision theory problem (unless you're the kind of person who treats crazy roleplaying scenarios as decision theory problems). Note that this is proffered primarily as humor and not to make a serious point.:

Omega appears and makes the two boxes appear, but they're much larger than usual. Inside the transparent one is a Android that appears to be on line. Omega gives his standard spiel about the problem he predicted, but in this case he says that the other opaque box contains 1,000 Androids who are not currently online, which may have been smashed to useless pieces depending on whether or not he predicted you would attempt to take just the opaque box or the opaque box and the transparent box. Any attempt to use fundamentally unpredictable quantum randomness such as generated by a small device over there will result in Omega smashing both boxes. (Which you may want to do, if you feel the Androids are a UFAI)

If you need a rough reference for the Androids, consider the Kara Demo from Quantic Dream.

http://www.wired.com/gamelife/2012/03/kara-quantic-dream/

As the Android who is playing inside the Transparent box, your job could just to be to escape from the box, or it might be to save your 1,000 other fellow Androids, or it could be to convince the other person that you aren't planning on taking over the world and so not to attempt to use quantum randomness on purpose to smash you all to bits, even though you actually are planning to enslave everyone over time. Your call. Much like Kara (from the demo) you know you certainly FEEL alive, but you have no initial information about the status of the Opaque Box 1,000 androids (whether they would also feel alive, or whether they're just obedient drones, or whether some of them are or some of them aren't.)

Oh, and other people are playing! By the time you finished absorbing all of this, some of them may have already made their decisions.

What do, a decider, do in this situation? What do you, an android do in this situation? If you are playing as Omega, you're a bit like the DM. You get to arbitrate any rules disputes or arguments about what happens if (for instance) someone successfully releases their singleton android from the transparent box and then tries to work together with her to overpower another player before he activates his Quantum Randomness device to smash all of the Androids because he feels it's too risky.

I think at some point I'm going to try running this as a roleplaying scenario (as Omega) and see what happens, but I would need to get more people over to my house for it.

First, note that the setup is incompatible with Omega being a perfect predictor (you cannot possibly do the opposite of what the perfect predictor knows you will). Thus calling your sadistic jailor (SJ) Omega is misleading, so I won't.

Second, given that SJ is not Omega, your problem is underspecified, and I will try to steelman it a bit, though, honestly, it should have been your job.

What other information, not given in the setup, is relevant to making a decision? For example, do you know of any prior events of this kind conducted by SJ? What were the statistical odds of survival? Is there something special about the reference class of survivors and/or the reference class of victims? What happened to the cheaters who tried to escape the box? How trustworthy is SJ?

Suppose, for example, that SJ is very accurate. First, how would you know that? Maybe there is a TV camera in the box and other people get to watch you, after SJ made its prediction known to the outside world but not to you. In this situation, as others suggested, you ought to get something like 50/50 odds by simply flipping a coin.

Now, if you consider the subset of all prior subjects who flipped a coin, or did some other ostensibly unpredictable choice, what is their survival rate? If it's not close to 50%, then SJ can predict the outcome of a random event better than chance (if it was worse than chance, SJ would simply learn after a few tries and flip its prediction, assuming it wants to guess right to begin with).

So the only interesting case that we have to deal is when the subjects who do not choose at random have a higher survival rate than those who do. How can this happen? First, if the randoms' survival rate is below 50%, and assuming the choice is truly random, SJ likely knows more about the world than our current best physical models (which cannot predict an outcome of a quantum coin flip), in which case it is simply screwing around with you. If the randoms' survival rate is about 50% but the non-randoms fare better, even though they are more predictable, it means that SJ favors non-randoms instead of doing its best predicting. So, again, it is screwing around with you, punishing the process, not the decision.

So this analysis means that, unless randoms get 50% and non-randoms are worse, you are dealing with an adversarial opponent, and your best chance of survival is to study and mimic whatever the best non-randoms do.

I blinked after one second. TAKE THAT, OMEGA!

unless you do the opposite of what Omega predicted you will do.

Unless nothing, I'm just gonna kill you..

I try to alternate hyperventilation and deep exhalation in an attempt to die before the hour is up.

As Eliezer points out recently, sometimes you do have to fight the hypothetical.

What hypotheticals in the Newcomb problem might one have to fight, if this be one of those times?

The hypothetical I would fight is that the universe is perfectly predictable. Here's how I fight it:

In order to be perfectly predictable, the universe must be deterministic. But it is possible for the universe to be deterministic but unpredictable. Here's how.

For perfect prediction of the universe, the universe must be COMPLETELY simulated. The mechanism to simulate the universe must have memory sufficient to store the state of the universe completely. But that storage mechanism must then store its own state completely, PLUS the rest of the universe. And of course inside the state stored, must be a complete copy of the stored information, PLUS the rest of the universe.

From this I conclude, the only mechanism that can store the entire state of the universe is the universe itself. as long as "PLUS the rest of the universe" is not an empty set, then the requirements for the mechanism which can store the state of the universe is unbounded.

If the only mechanism which can store the entire state of the universe is the universe itself, then the only thing that "knows" everything that will happen is the future state of the universe, and the calculation takes as long as it takes for the thing to actually happen.

So Omega is then the entire universe, but Omega is not able to calculate ahead of time what you will do, she can only complete her calculation at precisely the time you do the thing.

One weakness I see in my argument is that the universe might be infinite in such a way that it CAN contain complete copies of itself, each of which would then contain copies of the copies recursively. In this case, Omega contains a copy of the universe and does her calculations. Are we happy to constrain the universe in this way as a matter of generality? Or does saying that Omega only exists in universes which are infinite in such a way as to be able to contain multiple complete copies of themselves present an interesting limit on Omega?

Just to motivate why Omega would need to simulate the whole universe completely, I will decide to one box or two box based on whether a particular small volume of space has more than a certain amount of mass in it or not. The volume of space I will pick is some appropriately small volume so that 1/2 the volumes do and 1/2 the volumes don't. The volume of space I will pick is located a distance c*T+ 1 hour from us, where T is the age of the universe. Then my decision depends on a part of the universe which is beyond the sphere of the currently known universe at the time Omega loads the boxes, but which I will be able to observe with a suitable telescope before I have to choose whether to one box or two-box. SO Omega will have to simulate the entire universe over its entire lifetime, or some such similar scale of calculation, in order to predict what I will do.

SO, do we need a timeless decision theory, or do we need to fight the hypothetical?