In particular, this theorem shows that players $i$ with very low $w_i$ (little capital/influence on $q$) will accurately predict $\hat{p}={\sum }_j{w}_j{p}_j$

You mean $f\left(\hat{p}\right)$?

Solution: Black box the whole setup and remove it from the simulation to avoid circularity.

Addendum: I now notice this amounts to brute-forcing a solution to certain particular counterfactuals.

Hi Vanessa! Thanks again for your previous answers. I've got one further concern.

        Are all mesa-optimizers really only acausal attackers?

I think mesa-optimizers don't need to be purely contained in a hypothesis (rendering them acausal attackers), but can be made up of a part of the hypotheses-updating procedures (maybe this is obvious and you already considered it).

Of course, since the only way to change the AGI's actions is by changing its hypotheses, even these mesa-optimizers will have to alter hypothesis selection. But their whole running program doesn't need to be captured inside any hypothesis (which would be easier for classifying acausal attackers away).

That is, if we don't think about how the AGI updates its hypotheses, and just consider them magically updating (without any intermediate computations), then of course, the only mesa-optimizers will be inside hypotheses. If we actually think about these computations and consider a brute-force search over all hypotheses, then again they will only be found inside hypotheses, since the search algorithm itself is too simple and provides no further room for storing a subagent (even if the mesa-optimizer somehow takes advantage of the details of the search). But if more realistically our AGI employs more complex heuristics to ever-better approximate optimal hypotheses update, mesa-optimizers can be partially or completely encoded in those (put another way, those non-optimal methods can fail / be exploited). This failure could be seen as a capabilities failure (in the trivial sense that it failed to correctly approximate perfect search), but I think it's better understood as an alignment failure.

The way I see PreDCA (and this might be where I'm wrong) is as an "outer top-level protocol" which we can fit around any superintelligence of arbitrary architecture. That is, the superintelligence will only have to carry out the hypotheses update (plus some trivial calculations over hypotheses to find the best action), and given it does that correctly, since the outer objective we've provided is clearly aligned, we're safe. That is, PreDCA is an outer objective that solves outer alignment. But we still need to ensure the hypotheses update is carried out correctly (and that's everything our AGI is really doing).

I don't think this realization rules out your Agreement solution, since if truly no hypothesis can steer the resulting actions in undesirable ways (maybe because every hypothesis with a user has the human as the user), then obviously not even optimizers in hypothesis update can find malign hypotheses (although they can still causally attack hacking the computer they're running on etc.). But I think your Agreement solution doesn't completely rule out any undesirable hypothesis, but only makes it harder for an acausal attacker to have the user not be the human. And in this situation, an optimizer in hypothesis update could still select for malign hypotheses in which the human is subtly incorrectly modelled in such a precise way that has relevant consequences for the actions chosen. This can again be seen as a capabilities failure (not modelling the human well enough), but it will always be present to some degree, and it could be exploited by mesa-optimizers.