Sylvester Kollin

You might also find the following cases interesting (with self-locating uncertainty as an additional dimension), from this post.

Sleeping Newcomb-1. Some researchers, led by the infamous superintelligence Omega, are going to put you to sleep. During the two days that your sleep will last, they will briefly wake you up either once or twice, depending on the toss of abiasedcoin (Heads: once; Tails: twice). After each waking, they will put you back to sleep with a drug that makes you forget that waking. The weight of the coin is determined by what the superintelligence predicts that you would say when you are awakened and asked to what degree ought you believe that the outcome of the coin toss is Heads. Specifically, if the superintelligence predicted that you would have a degree of beliefin Heads, then they will have weighted the coin such that the 'objective chance' of Heads is . So, when you are awakened, to what degree ought you believe that the outcome of the coin toss is Heads?

Sleeping Newcomb-2. Some researchers, led by the superintelligence Omega, are going to put you to sleep. During the two days that your sleep will last, they will briefly wake you up either once or twice, depending on the toss of abiasedcoin (Heads: once; Tails: twice). After each waking, they will put you back to sleep with a drug that makes you forget that waking. The weight of the coin is determined by what the superintelligence predicts your response would be when you are awakened and asked to what degree you ought to believe that the outcome of the coin toss is Heads. Specifically, if Omega predicted that you would have a degree of beliefin Heads, then they will have weighted the coin such that the 'objective chance' of Heads is.Then: when you are in fact awakened, to what degree ought you believe that the outcome of the coin toss is Heads?

3moΩ010

Epistemic Constraint:The probability distribution which the agent settles on cannot be self-refuting according to the beliefs. It must be aof : a such that .fixed point

Minor: there might be cases in which there is a fixed point , but where the agent doesn't literally converge or deliberate their way to it, right? (Because you are only looking for to satisfy the conditions of Brouwer/Kakutani, and not, say, Banach, right?) In other words, it might not always be accurate to say that the agent "settles on ". EDIT: oh, maybe you are just using "settles on" in the colloquial way.

3moΩ7102

A common trope is for magic to work only when you believe in it. For example, in Harry Potter, you can only get to the magical train platform 9 3/4 if you believe that you can pass through the wall to get there.

Are you familiar with Greaves' (2013) epistemic decision theory? These types of cases are precisely the ones she considers, although she is entirely focused on the epistemic side of things. For example (p. 916):

Leap. Bob stands on the brink of a chasm, summoning up the courage to try and leap across it. Confidence helps him in such situations: specifically, for any value of between and , if Bob attempted to leap across the chasm while having degree of belief that he would succeed, his chance of success would then be . What credence in success is it epistemically rational for Bob to have?

And even more interesting cases (p. 917):

Embezzlement. One of Charlie’s colleagues is accused of embezzling funds. Charlie happens to have conclusive evidence that her colleague is guilty. She is to be interviewed by the disciplinary tribunal. But Charlie’s colleague has had an opportunity to randomize the content of several otherwise informative files (files, let us say, that the tribunal will want to examine if Charlie gives a damning testimony). Further, in so far as the colleague thinks that Charlie believes him guilty, he will have done so. Specifically, if is the colleague’s prediction for Charlie’s degree of belief that he’s guilty, then there is a chance that he has set in motion a process by which each proposition originally in the files is replaced by its own negation if a fair coin lands Heads, and is left unaltered if the coin lands Tails. The colleague is a very reliable predictor of Charlie’s doxastic states. After such randomization (if any occurred), Charlie has now read the files; they (now) purport to testify to the truth of propositions . Charlie’s credence in each of the propositions conditional on the proposition that the files have been randomized, is ; her credence in each conditional on the proposition that the files have not been randomized is . What credence is it epistemically rational for Charlie to have in the proposition that her colleague is guilty and in the propositions that the files purport to testify to the truth of?

In particular, Greaves' (2013, §8, pp. 43-49) epistemic version of Arntzenius' (2008) deliberational (causal) decision theory might be seen as a way of making sense of the first part of your theory. The idea, inspired by Skyrms (1990), is that deciding on a credence involves a cycle of calculating epistemic expected utility (measured by a proper scoring rule), adjusting credences, and recalculating utilities until an equilibrium is

obtained. For example, in *Leap* above, epistemic D(C)DT would find any credence permissible. And I guess that the second part of your theory serves as a way of breaking ties.

3mo50

We assume two rules of inference:

Necessitation:

Distributivity:

Is there a reason why this differs from the standard presentation of **K**? Normally, I think you would say that **K** is generated by the following (coupled with substitution):

Axioms:

- All tautologies of propositional logic.

- Distribution: .

Rules of inference:

- Necessitation: .

- Modus ponens: .

5moΩ010

And, second, the agent will continually implement that plan, even if this makes it locally choose counter-preferentially at some future node.

Nitpick: IIRC, McClennen never talks about counter-preferential choice. Rather, that's Gauthier's (1997) approach to resoluteness.

as devised by Bryan Skyrms and Gerald Rothfus (cf Rothfus 2020b).

Found a typo: it is supposed to be *Gerard*. (It is also misspelt in the reference list.)

5mo130

Some people know that they do not have a solution. Andy Egan, in "Some Counterexamples to Causal Decision Theory" (1999, Philosophical Review)

This should say *2007.*

These people all defect in PD and two-box in Newcomb.

Spohn argues for one-boxing in *Reversing 30 years of discussion: why causal decision theorists should one-box**.*

Thanks.

Roughly, you don't actually get to commit your future-self to things. Instead, you just do what you (in expectation) would have committed yourself to given some reconstructed prior.

Agreed.

Just as a literature pointer: If I recall correctly, Chris Meacham's approach in "Binding and Its Consequences" is ultimately to estimate your initial credence function and perform the action from the plan with the highest EU according to that function.

Yes, that's a great paper! (I think we might have had a footnote on cohesive decision theory in a draft of this post.) Specifically, I think the third version of cohesive decision theory which Meacham formulates (in footnote 34), and variants thereof, are especially relevant to dynamic choice with changing awareness. The general idea (as I see it) would be that you optimize relative to your *ur-priors,* and we may understand the ur-prior function as the prior you would or should have had if you had been more aware. So when you experience awareness growth, the ur-priors change (and thus the evaluation of a given plan will often change as well).

He doesn't talk about awareness growth, but open-mindedness seems to fit in nicely within his framework (or at least the framework I recall him having).

(Meacham actually applies the ur-prior concept and ur-prior conditionalization to awareness growth in this paper.)

What do you mean by "the Bayesian Conditionalization thing" in this context? (Just epistemically speaking, standard Conditionalization is inadequate for dealing with cases of awareness growth. Suppose, for example, that one was aware of propositions {X, Y}, and that this set later expands to {X, Y, Z}. Before this expansion, one had a credence P(X ∨ Y) = 1, meaning Conditionalization recommends remaining certain in X ∨ Y; i.e., one is only permitted to place a credence P(Z) = 0. Maybe you are referring to something like Reverse Bayesianism?)

Thanks.

Do you have a reference for this? Or perhaps there is a quick proof that could convince me?