If your model obeys “independence of causal mechanisms” (basically: you can decompose your model into a collection of stochastic functions defining conditional probabilities, and these functions themselves aren’t strongly dependent on one another)
And you assume “precedent”, meaning something like “what I can do has been done before and its consequences observed, though I can’t tell exactly when it was done”
And you observe the right conditional independence
Then you can treat actions that affect certain variables like interventions on that variable
NOW, here is an interesting point. In Newcomb’s problem, a naive model would include two separate functions and , but these two functions are strongly dependent—they always (or almost always) give the same output. We can restore ICM: we introduce a “disposition” such that and , and now the entanglement between the two is “explained” by and ICM is restored. Now, if is such that its value depends on our choice, we also have a conditional independence of the right type: the consequences (1 box/2 box, plus payoff) are independent of context given . However, we cannot change only “our” 1 box or 2 box decision without violating precedent (if they are perfectly correlated in our observations, then driving them apart with our actions yields a measure 0 event, exactly what precedent rules out*) - if we want to satisfy the requirements, we are required to have depend upon our choice as well. But all the conditions are satisfied to treat our actions as an intervention on .
Now my justification for interventions is clearly far from broadly accepted, and in fact I myself think it’s quite half baked. Furthermore, this is an argument from convenience: introducing is a means by which we can make decisions according to a model under which interventional semantics are (according to my work) valid. You may not consider this to be particularly compelling. But still, isn’t it interesting that Yudkowsky’s original TDT solution ends up being the most obvious convenient solution to the problem of building a model of Newcomb that satisfies ICM + precedent?
*With an imperfect predictor, the situation is more complicated, and it seems to come down to: my theory can license you to conclude that consequences given -plus-my-box-number is invariant, but is silent on how to handle the distribution of , if we suppose that my choice ends up with a particular box number.
I have one more contribution. I have myself attempted to justify causal interventional semantics from more fundamental principle. The justification I landed on was (abridged):
If your model obeys “independence of causal mechanisms” (basically: you can decompose your model into a collection of stochastic functions defining conditional probabilities, and these functions themselves aren’t strongly dependent on one another)
And you assume “precedent”, meaning something like “what I can do has been done before and its consequences observed, though I can’t tell exactly when it was done”
And you observe the right conditional independence
Then you can treat actions that affect certain variables like interventions on that variable
NOW, here is an interesting point. In Newcomb’s problem, a naive model would include two separate functions
Now my justification for interventions is clearly far from broadly accepted, and in fact I myself think it’s quite half baked. Furthermore, this is an argument from convenience: introducing
*With an imperfect predictor, the situation is more complicated, and it seems to come down to: my theory can license you to conclude that consequences given