Sure, but then why is it strange to do the same with duplication? You’re shifting your relative probability of seeing A, by creating extra versions of you that see A.
ike
Karma: 1,433
I don’t think the epsilon chance of observing now really helps. It makes the current probabilities meaningful but you still have no particular reason to insist that the current probabilities (“what happens if I were to observe this today”) matches the future probabilities (“what happens if I observe it in the future”), given that the observations are correlated.
Re death, it just doesn’t seem different to me. If I can magically increase my probability in outcome A by committing to suicide in not-A worlds, I can also increase my probability in A by duplicating myself in A worlds. You’ve set up a formalism that allows the former and not the latter, then you’re pointing to a contradiction. But they’re both about as mysterious and settled the same way. The first isn’t controversial and the second shouldn’t be either.
(The exact probabilities still depend on SSA vs SIA vs others. But the fact that they won’t match the objective probabilities seems fine.)
Note that the math isn’t showing up for me, might be a formatting issue.
There’s a fatal flaw in the logic here.
Note that the martingale is defined over observations and expected observations.
But then you talk about the prior probability of heads. This is not meaningful, since she does not observe the coin flip.
Here’s a consistent probability assignment that meets the martingale criteria.
On Sunday, she estimates probability ~1 of waking up tomorrow in a room. She doesn’t have a probability on a particular room or of a coin result as of Monday because she doesn’t observe that on Monday. She further estimates a probability of 2⁄3 for Tuesday room 1 and 1⁄3 for Tuesday room 2.
On Monday, she confirms that she woke up. She continues to have the same 2⁄3 and 1⁄3 probability assignment across the two rooms possibilities for Tuesday, since nothing has changed.
Alternatively, she can consistently maintain that each room is 1⁄2 likely.
I’ve got a different scenario with no duplicates. A fair coin is flipped today, if it’s heads, Roulette Rory gets killed with 75% probability before learning what the coin says. If it’s tails Rory survives. We ask Rory what her probability is. She says today her probability is 50⁄50, but if she learns about results she is 80% confident in tails.
Why is it ok for Rory to expect her future self to be 80% confident in something that she’s currently 50% confident in, but it’s not ok for Beauty to do the same? In both cases, the number of observers is varied in a way that’s correlated with the observation. That’s all that’s happening here.
SALP has blown up. Still unclear what happened, but CNBC reported they sold the entire public equities book to one buyer before the market opened today.
If you specify everything about the experiment, then you have added complexity on both sides. But note that things like “a fair coin will be flipped” is not actually possible to specify under SI, which works with deterministic Turing machines. It’s not clear how to specify something that works like that.
And we mostly care about these problems because of the relevance to more realistic versions like doomsday, where we do not have the specification and so you do have asymmetrical complexity. In any real world scenario, you have uncertainty over exactly what is going on, and some of the possibilities are simpler than others and get more weight. But you never really exclude possibilities like “Omega is lying to me about how this works” or “it’s all a simulation”, they just become improbable if you have significant evidence against.
Well a world with N people, with N large and not simple like a power of 2 or something, is going to be log2 N extra bits to specify over the same world with one person. Then an extra log2 N bits to locate a specific observer.
But since you might be any one of the N people, the second one cancels out and you’re left with the inherent complexity of the world. So log2 N, but if N is a simple number it can be much less. For N power of 2, it can be log log N. And you can have stuff that grows much faster than powers of 2, eg. N=Graham’s number doesn’t take many bits to specify.
In the standard SB question, not significantly, because the scenario is so contrived and the number of people under tails isn’t that high.
But in versions with thousands of people, yes.
There’s also the Solomonoff Induction location issue, where larger worlds get penalized if it takes many bits to locate observers within them.
I agree with Andrew Gelman that in many cases we should report probabilities with fewer significant digits.
Really, I think it would be just fine to specify win probabilities to the nearest 10%, which will register shifts of 0.4% in expected vote share. Probabilities to the nearest 10%: if it’s good enough for the National Weather Service, it’s good enough for me.
He quotes a comment that disagrees:
I disagree with Andrew that 65.7% is too precise. One reason is that intrade prices are quoted to 3 digit precision — viz., ranging from $0.00 to $10.00, with bid-ask spreads as low as 1 cent. So, for example, if I believed Nate’s formula was more accurate than Intrade, and the current quote was $6.56 bid, $6.57 ask, I would like Nate to provide more precision in order to determine whether or not to buy ‘Barack Obama to be re-elected on 2012′. Even with today’s low interest rates, I would still need Nate to forecast at least a 65.74% probability in order to believe purchasing ’Obama 2012′ at $6.57 would outperform a 0.90% money market rate over the next 18 days.
This is absurd to anyone who has traded election markets seriously. You do not trade a 0.1% edge on a market like this.
If Alice said “I need to provide a point estimate, so I think it’s 36.49284727693% likely”, we would all recognize it as absurd. So we’re just haggling over the price. In general, outside of areas where you have enough data to calibrate well, nearest 5% is all that’s meaningful.
This is separate from the probability range Bob offers, which should only be done when you specify what you mean.
You do better with leverage at the expense of increasing risk, including total loss in worlds that are only slightly off from what you expect.
You seem to be talking about what people with hundreds of billions collectively can do. Capacity is a real constraint at that point.
It’s also likely some of the best investments won’t want that much capital. Even if you’re right on the 60%, some of that can come from new private companies you can’t invest in or can only invest after they’ve grown a lot.
Vara doesn’t seem close to 5x. Both of these seem highly unlikely to produce those kinds of returns going forward because of capacity, let alone a 400x compounded return.
I’d be interested in reading a longer defense of this.
the hedge funds have recently been appreciating at ~5x per year (after fees, before taxes) (for some value of “recently”), which is crazy.
Can you provide more details? This seems more than an order of magnitude off.
To the extent FDT is picking its decision based on the way the decision influences your beliefs about the decision, that seems dangerous. In this case the belief is self-confirming, but would FDT lead you to form false beliefs if you get rewarded for doing so?
FDT will pay $50 to temporarily implant a false belief that it will pay $100 to the driver. Something seems unfair about this whole setup.
The goodness of their prediction doesn’t matter to FDT. What matters is if they’re running the same algorithm, which they aren’t, regardless of what you do. They’re observing things like facial expressions that are correlated with your decision in ways you can’t control but which have nothing to do with the algorithm you use.
The human is reading your own beliefs about what you’ll do in the future. It’s not simulating any algorithm you’re using.
CDT and FDT both want to self modify to be the type of person who pays, but they don’t pay. Or really, they want to self modify to believe they will pay and then don’t pay.
Edit: I’m not sure about this, maybe FDT can pay based on the beliefs being a consequence of its output? It wouldn’t be because of the human predictor then.
FDT doesn’t pay in Parfit Hitchhiker against a human. There being some correlation between your decision and their prediction is far less than required by FDT. It’s nowhere close to being the same algorithm.
Many of the interesting problems need some kind of “spirit of FDT.” It’s fair to complain that this is not formalized well.
Third, I’ve realized that my gut endorses some vague argument like this: Insects just don’t matter. But if they were sentient, they would. So, they must not be sentient.
That, of course, is a bad line of reasoning. We don’t learn facts by consulting our ethical intuitions. And it’s helpful — for me, anyway — to call that out explicitly. When I detach the idea of insect sentience from its moral significance — that is, when I consider the possibility completely isolated from any level of concern for nonhuman pain — it seems much more plausible to me that insects can hurt. And if so, I shouldn’t shy away from that conclusion just because of its possible moral consequences.
I disagree with this, and strongly disagree with your claim that it is obvious.
You are assuming that sentience/ability to suffer is a factual question, when it’s actually a moral question and it’s perfectly fine to apply moral evidence to moral questions.
The exact argument depends on definition. If you define suffering as only applicable to moral patients, then the question if something is suffering requires a determination of whether it is a moral patient , which is there a moral question. If you define suffering more broadly, then whether it is bad depends on whether it’s happening to a moral patient, which again is a moral question.
Step 8 is problematic. (I would also quibble with wording on others, including 2, but those are less critical.)
What exactly does “real” mean there?
11 is also problematic. At best you can get that a model which assumes other people are conscious similar to you will help your predictions be more accurate. This says nothing about whether other people actually are conscious.
You can’t actually bootstrap a refutation of solipsism.
I would claim that ultimately anti solipsism is a moral position, not a factual one. I.e. it is a moral good to treat others as conscious. I can’t write up a full argument for that though.
If “I” “exist” in multiple universes, I don’t view there being a fact of the matter as to which one I’m “really” in. I think at least some realists agree, and it is to that subset of realists that my argument is directed. Their worldview is internally inconsistent.
Any statement about external reality is true in some worlds and false in others. Almost all such statements will be false if you’re located in a Boltzmann brain world, for example.
I’m not using the multiverse as an axiom. It’s the possibility of a multiverse that undermines meaning of realism.
To be a realist, you need one of the following claims:
There is only one universe containing entities subjectively indistinguishable from us, or there are so few universes that we can effectively ignore them (MWI, or any other Big world theory implies otherwise)
There is a fact of the matter as to where we are under self locating uncertainty
I think e.g EY rejects both of these but is still a realist. You seem to be hinting that you believe in 2?
Note that you can further build on my QM example. Scott Aaronson has suggested that you can affect the past via your decisions in the present. I haven’t read his arguments recently but I think this is related to the self locating uncertainty point—there could be no fact of the matter as to what the initial conditions were that led to your decision until after it’s made.
>I don’t think that you can argue to anti realism by assuming a theory of the universe as a starting point. Even a very maximal large world theory allows sentences to correspond to local laws and conditions. A quantum multiverse, which is comparatively smaller, has QM true everywhere
Well again, this is not meant to be the actual argument. But if you have self-locating uncertainty as to where you are in a large world, you might say there’s no fact of the matter as to where you are, which is close enough for my purposes.
I gave a specific Sequences quote earlier, and you suggested you don’t disagree.
>What does that even mean? You observe what’s around you, and that characterises which branch your in. It’s the branch where Hitler lost
I meant no fact of the matter prior to observation. If you think you simultaneously exist in every branch, and then your consciousness splits, prior to the split there’s no fact of the matter as to which one you’ll end up in. You end up in both, and each side of the split has a different observation.
Then I’m saying something similar is going on if you believe in a large world where some universes have different ontologies. Stuff like “you live in a simulation” will be true in some, false in others, so there’s no fact of the matter as to whether that’s true. Same applies to any statement about external reality.
This isn’t quite what I think, because on my worldview it’s not even meaningful to talk about what large worlds “exist”.
I don’t buy this distinction.
Every thread going on from you will observe something in Roulette too. (The threads that die don’t go on from you, then.)
When predicting your future experiences, you automatically condition on the fact that there will be future experiences, so they won’t always match objective probabilities. And you can also adjust for some versions of you having more experiences than others.