This prediction seems flatly wrong: I wouldn’t bring about an outcome like that. Why do I believe that? Because I have reasonably high-fidelity access to my own policy, via imagining myself in the relevant situations.
This seems like you're confusing two things here, because the thing you would want is not knowable by introspection. What I think you're introspecting is that if you'd noticed that the-thing-you-pursued-so-far was different from what your brother actually wants, you'd do what he actually wants. But the-thing-you-pursued-so-far doesn't play the... (read more)
Why is the price of the un-actualized bet constant? My argument in the OP was to suppose that PCH is the dominant hypothesis, so, mostly controls market prices.
Thinking about this in detail, it seems like what influence traders have on the market price depends on a lot more of their inner workings than just their beliefs. I was thinking in a way where each trader only had one price for the bet, below which they bought and above which they sold, no matter how many units they traded (this might contradict "continuous trading strategies" because of finite wea... (read more)
So I don't see how we can be sure that PCH loses out overall. LCH has to exploit PCH -- but if LCH tries it, then we're seemingly in a situation where LCH has to sell for PCH's prices, in which case it suffers the loss I described in the OP.
So I've reread the logical induction paper for this, and I'm not sure I understand exploitation. Under 3.5, it says:
On each day, the reasoner receives 50¢ from T, but after day t, the reasoner must pay $1 every day thereafter.
So this sounds like before day t, T buys a share every day, and those shares never pay out - ot... (read more)
The payoff for 2-boxing is dependent on beliefs after 1-boxing because all share prices update every market day and the "payout" for a share is essentially what you can sell it for.
If a sentence is undecidable, then you could have two traders who disagree on its value indefinitely: one would have a highest price to buy, thats below the others lowest price to sell. But then anything between those two prices could be the "market price", in the classical supply and demand sense. If you say that the "payout" of a share is what you can sell it for... well, the ... (read more)
Because we have a “basic counterfactual” proposition for what would happen if we 1-box and what would happen if we 2-box, and both of those propositions stick around, LCH’s bets about what happens in either case both matter. This is unlike conditional bets, where if we 1-box, then bets conditional on 2-boxing disappear, refunded, as if they were never made in the first place.
I don't understand this part. Your explanation of PCDT at least didn't prepare me for it, it doesn't mention betting. And why is the payoff for the counterfactual-2-boxing determined b... (read more)
are the two players physically precisely the same (including environment), at least insofar as the players can tell?
In the examples I gave yes. Because thats the case where we have a guarantee of equal policy, from which people try to generalize. If we say players can see their number, then the twins in the prisoners dilemma needn't play the same way either.
But this is one reason why correlated equilibria are, usually, a better abstraction than Nash equilibria.
The "signals" players receive for correlated equilibria are already semantic. So I'm suspicious t... (read more)
Well, if I understand the post correctly, you're saying that these two problems are fundamentally the same problem
No. I think:
...the reasoning presented is correct in both cases, and the lesson here is for our expectations of rationality...
As outlined in the last paragraph of the post. I want to convince people that TDT-like decision theories won't give a "neat" game theory, by giving an example where they're even less neat than classical game theory.
Actually it could.
I think you're thinking about a realistic case (same algorithm, similar environment... (read more)
"The same" in what sense? Are you saying that what I described in the context of game theory is not surprising, or outlining a way to explain it in retrospect?
Communication won't make a difference if you're playing with a copy.
Another problem with this is that it isn't clear how to form the hypothesis "I have control over X".
You don't. I'm using talk about control sometimes to describe what the agent is doing from the outside, but the hypothesis it believes all have a form like "The variables such and such will be as if they were set by BDT given such and such inputs".
One problem with this is that it doesn't actually rank hypotheses by which is best (in expected utility terms), just how much control is implied.
For the first setup, where its trying to learn what it has control ov... (read more)
From my perspective, Radical Probabilism is a gateway drug.
This post seemed to be praising the virtue of returning to the lower-assumption state. So I argued that in the example given, it took more than knocking out assumptions to get the benefit.
So, while I agree, I really don't think it's cruxy.
It wasn't meant to be. I agree that logical inductors seem to de facto implement a Virtuous Epistemic Process, with attendent properties, whether or not they understand that. I just tend to bring up any interesting-seeming thoughts that are triggered during ... (read more)
Either way, we've made assumptions which tell us which Dutch Books are valid. We can then check what follows.
Ok. I suppose my point could then be made as "#2 type approaches aren't very useful, because they assume something thats no easier than what they provide".
I think this understates the importance of the Dutch-book idea to the actual construction of the logical induction algorithm.
Well, you certainly know more about that than me. Where did the criterion come from in your view?
This part seems entirely addressed by logical induction, to me.
Quite p... (read more)
I wanted to separate what work is done by radicalizing probabilism in general, vs logical induction specifically.
From my perspective, Radical Probabilism is a gateway drug. Explaining logical induction intuitively is hard. Radical Probabilism is easier to explain and motivate. It gives reason to believe that there's something interesting in the direction. But, as I've stated before, I have trouble comprehending how Jeffrey correctly predicted that there's something interesting here, without logical uncertainty as a motivation. In hindsight, I feel hi... (read more)
What is actually left of Bayesianism after Radical Probabilism? Your original post on it was partially explaining logical induction, and introduced assumptions from that in much the same way as you describe here. But without that, there doesn't seem to be a whole lot there. The idea is that all that matters is resistance to dutch books, and for a dutch book to be fair the bookie must not have an epistemic advantage over the agent. Said that way, it depends on some notion of "what the agent could have known at the time", and giving a coherent account of thi... (read more)
If you're reasoning using PA, you'll hold open the possibility that PA is inconsistent, but you won't hold open the possibility that A&¬A. You believe the world is consistent. You're just not so sure about PA.
Do you? This sounds like PA is not actually the logic you're using. Which is realistic for a human. But if PA is indeed inconsistent, and you don't have some further-out system to think in, then what is the difference to you between "PA is inconsistent" and "the world is inconsistent"? In both cases you just believe everything and its negatio... (read more)
If I'm using PA, I can prove that ¬(A&¬A).
Sure, thats always true. But sometimes its also true that A&¬A. So unless you believe PA is consistent, you need to hold open the possibility that the ball will both (stop and continue) and (do at most one of those). But of course you can also prove that it will do at most one of those. And so on. I'm not very confident whats right, ordinary imagination is probably just misleading here.
It seems particularly absurd that, in some sense, the reason you think that is just because you think that.
The fa... (read more)
Heres what I imagine the agent saying in its defense:
Yes, of course I can control the consistency of PA, just like everything else can. For example, imagine that you're using PA and you see a ball rolling. And then in the next moment, you see the ball stopping and you also see the ball continuing to roll. Then obviously PA is inconsistent.
Now you might think this is dumb, because its impossible to see that. But why do you think its impossible? Only because its inconsistent. But if you're using PA, you must believe PA really might be inconsistent, so you ca... (read more)
The first sentence of your first paragraph appears to appeal to experiment, while the first sentence of your second paragraph seems to boil down to "Classically, X causes Y if there is a significant statistical connection twixt X and Y."
No. "Dependence" in that second sentence does not mean causation. It just means statistical dependence. The definition of dependence is important because an intervention must be statistically independent from things "before" the intervention.
None of these appear to involve intervention.
These are methods of causal inf... (read more)
Pearl's answer, from IIRC Chapter 7 of Causality, which I find 80% satisfying, is about using external knowledge about repeatability to consider a system in isolation. The same principle gets applied whenever a researcher tries to shield an experiment from outside interference.
This is actually a good illustration of what I mean. You can't shield an experiment from outside influence entirely, not even in principle, because its you doing the shielding, and your activity is caused by the rest of the world. If you decide to only look at a part of the world, on... (read more)
What I had in mind was increasing precision of Y.
X and Y are variables for events. By complexity class I mean computational complexity, not sure what scaling parameter is supposed to be there?
we have an updating process which can change its mind about any particular thing; and that updating process itself is not the ground truth, but rather has beliefs (which can change) about what makes an updating process legitimate.This should still be a strong formal theory, but one which requires weaker assumptions than usual
we have an updating process which can change its mind about any particular thing; and that updating process itself is not the ground truth, but rather has beliefs (which can change) about what makes an updating process legitimate.
This should still be a strong formal theory, but one which requires weaker assumptions than usual
There seems to be a bit of a tension here. What you're outlining for most of the post still requires a formal system with assumptions within which to take the fixed point, but then that would mean that it can't change its mind about an... (read more)
But in a newly born child or blank AI system, how does it acquire causal models?
I see no problem assuming that you start out with a prior over causal models - we do the same for propabilistic models after all. The question is how the updating works, and if, assuming the world has a causal structure, this way of updating can identify it.
I myself think (but I haven't given it enough thought) that there might be a bridge from data to causal models though falsification. Take a list of possible causal models for a given problem and search through your d
If Markov models are simple explanations of our observations, then what's the problem with using them?
To be clear, by total propability distribution I mean a distribution over all possible conjunctions of events. A Markov model also creates a total propability distribution, but there are multiple Markov models with the same propability distribution. Believing in a Markov model is more specific, and so if we could do the same work with just propability distributions, then Occam would seem to demand we do.
The surface-level answer to your question would
One possibility is that it's able to find a useful outside view model such as "the Predict-O-Matic has a history of making negative self-fulfilling prophecies". This could lead to the Predict-O-Matic making a negative prophecy ("the Predict-O-Matic will continue to make negative prophecies which result in terrible outcomes"), but this prophecy wouldn't be selected for being self-fulfilling. And we might usefully ask the Predict-O-Matic whether the terrible self-fulfilling prophecies will continue conditional on us tak