The society’s stance towards crime- preventing it via the threat of punishment- is not what would work on smarter people
This is one of two claims here that I'm not convinced by. Informal disproof: If you are a smart individual in todays society, you shouldn't ignore threats of punishment, because it is in the states interest to follow through anyway, pour encourager les autres. If crime prevention is in peoples interest, intelligence monotonicity implies that a smart population should be able to make punishment work at least this well. Now I don't trust intelligence monotonicity, but I don't trust it's negation either.
The second one is:
You can already foresee the part where you're going to be asked to play this game for longer, until fewer offers get rejected, as people learn to converge on a shared idea of what is fair.
Should you update your idea of fairness if you get rejected often? It's not clear to me that that doesn't make you exploitable again. And I think this is very important to your claim about not burning utility: In the case of the ultimatum game, Eliezers strategy burns very little over a reasonable-seeming range of fairness ideals, but in the complex, high-dimensional action spaces of the real world, it could easily be almost as bad as never giving in, if there's no updating.
Maybe I'm missing something, but it seems to me that all of this is straightforwardly justified through simple selfish pareto-improvements.
Take a look at Critchs cake-splitting example in section 3.5. Now imagine varying the utility of splitting. How high does it need to get, before [red->Alice;green->Bob] is no longer a pareto improvement over [(split)] from both player's selfish perspective before the observation? It's 27, and thats also exactly where the decision flips when weighing Alice 0.9 and Bob 0.1 in red, and Alice 0.1 and Bob 0.9 in green.
Intuitively, I would say that the reason you don't bet influence all-or-nothing, or with some other strategy, is precisely because influence is not money. Influence can already be all-or-nothing all by itself, if one player never cares that much more than the other. The influence the "losing" bettor retains in the world where he lost is not some kind of direct benefit to him, the way money would be: it functions instead as a reminder of how bad a treatment he was willing to risk in the unlikely world, and that is of course proportional to how unlikely he thought it is.
So I think all this complicated strategizing you envision in influence betting, actually just comes out exactly to Critches results. Its true that there are many situations where this leads to influence bets that don't matter to the outcome, but they also don't hurt. The theorem only says that actions must be describable as following a certain policy, it doesn't exclude that they can be described by other policies as well.
The timescale for improvement is dreadfully long and the day-to-day changes are imperceptible.
This sounded wrong, but I guess is technically true? I had great in-session improvements as I'm warming up the area and getting into it, and the difference between a session where I missed the previous day, and one where I didn't, is absolutely preceptible. Now after that initial boost, it's true that I couldn't tell if the "high point" was improving day to day, but that was never a concern - the above was enough to give me confidence. Plus with your external rotations, was there not perceptible strength improvement week to week?
So I've reread your section on this, and I think I follow that, but its arguing a different claim. In the post, you argue that a trader that correctly identifies a fixed point, but doesn't have enough weight to get it played, might not profit from this knowledge. That I agree with.
But now you're saying that even if you do play the new fixed point, that trader still won't gain?
I'm not really calling this a proof because it's so basic that something else must have gone wrong, but:
has a fixed point at , and doesn't. Then . So if you decide to play , then predicts , which is wrong, and gets punished. By continuity, this is also true in some neighborhood around p. So if you've explored your way close enough, you win.
On reflection, I didn't quite understand this exploration business, but I think I can save a lot of it.
>You can do exploration, but the problem is that (unless you explore into non-fixed-point regions, violating epistemic constraints) your exploration can never confirm the existence of a fixed point which you didn't previously believe in.
I think the key here is in the word "confirm". Its true that unless you believe p is a fixed point, you can't just try out p and see the result. However, you can change your beliefs about p based on your results from exploring things other than p. (This is why I call the thing I'm objecting to humean trolling.) And there is good reason to think that the available fixed points are usually pretty dense in the space. For example, outside of the rule that binarizes our actions, there should usually be at least one fixed point for every possible action. Plus, as you explore, your beliefs change, creating new believed-fixed-points for you to explore.
>I think your idea for how to find repulsive fixed-points could work if there's a trader who can guess the location of the repulsive point exactly rather than approximately
I don't think thats needed. If my net beliefs have a closed surface in propability space on which they push outward, then necessarily those beliefs have a repulsive fixed point somewhere in that surface. I can then explore that believed fixed point. Then if its not a true fixed point, and I still believe in the closed surface, theres a new fixed point in that surface that I can again explore (generally more in the direction I just got pushed away from). This should converge on a true fixed point. The only thing that can go wrong is that I stop believing in the closed surface, and it seems like I should leave open that possibility - and even then, I might believe in it again after I do some checking along the outside.
>However, the wealth of that trader will act like a martingale; there's no reliable profit to be made (even on average) by enforcing this fixed point.
This I don't understand at all. If you're in a certain fixed point, shouldn't the traders that believe in it profit from the ones that don't?
I don't think the learnability issues are really a problem. I mean, if doing a handstand with a burning 100 riyal bill between your toes under the full moon is an exception to all physical laws and actually creates utopia immediately, I'll never find out either. Assuming you agree that that's not a problem, why is the scenario you illustrate? In both cases, it's not like you can't find out, you just don't, because you stick to what you believe is the optimal action.
I don't think this would be a significant problem in practice any more than other kinds of humean trolling are. It always seems much more scary in these extremely barebones toy problems, where the connection between the causes and effects we create really are kind of arbitrary. I especially don't think it will be possible to learn the couterfactuals of FDTish cooperation and such in these small settings, no matter the method.
Plus you can still do value-of-information exploration. The repulsive fixed points are not that hard to find if you're looking for them. If you've encircled one and found repulsion all around the edge, you know there must be one in there, and can get there with a procedure that just reverses your usual steps. Combining this with simplicity priors over a larger setting into which the problem is integrated, I don't think its any more worrying than the handstand thing.
That prediction may be true. My argument is that "I know this by introspection" (or, introspection-and-generalization-to-others) is insufficient. For a concrete example, consider your 5-year-old self. I remember some pretty definite beliefs I had about my future self that turned out wrong, and if I ask myself how aligned I am with it I don't even know how to answer, he just seems way too confused and incoherent.
I think it's also not absurd that you do have perfect caring in the sense relevant to the argument. This does not require that you don't make mistakes currently. If you can, with increasing intelligence/information, correct yourself, then the pointer is perfect in the relevant sense. "Caring about the values of person X" is relatively simple and may come out of evolution whereas "those values directly" may not.
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 role of "your utility function" in the goodhart argument. All of you plays into that. If the goodharting were to play out, your detector for differences between the-thing-you-pursued-so-far and what-your-brother-actually-wants would simply fail to warn you that it was happening, because it too can only use a proxy measure for the real thing.
The idea is that we can break any decision problem down by cases (like "insofar as the predictor is accurate, ..." and "insofar as the predictor is inaccurate, ...") and that all the competing decision theories (CDT, EDT, LDT) agree about how to aggregate cases.
Doesn't this also require that all the decision theories agree that the conditioning fact is independent of your decision?
Otherwise you could break down the normal prisoners dilemma into "insofar as the opponent makes the same move as me" and "insofar as the opponent makes the opposite move" and conclude that defect isn't the dominant strategy even there, not even under CDT.
And I imagine the within-CDT perspective would reject an independent probability for the predictors accuracy. After all, theres an independent probability it guessed 1-box, and if I 1-box it's right with that probability, and if I 2-box it's right with 1 minus that probability.
What are real numbers then? On the standard account, real numbers are equivalence classes of sequences of rationals, the finite diagonals being one such sequence. I mean, "Real numbers don't exist" is one way to avoid the diagonal argument, but I don't thinks that's what cubefox is going for.