SMK

Karma: 361

SMK Dec 3, 2023, 12:49 PM
1 point
0
AF
on: FixDT
Epistemic Constraint: The probability distribution $p$ which the agent settles on cannot be self-refuting according to the beliefs. It must be a fixed point of $b$ : a $p$ such that $b (p) = p$ .
Minor: there might be cases in which there is a fixed point $p$ , but where the agent doesn’t literally converge or deliberate their way to it, right? (Because you are only looking for $b$ 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 $p$ ”. EDIT: oh, maybe you are just using “settles on” in the colloquial way.

SMK Dec 3, 2023, 12:46 PM
LW: 10 AF: 7
2
AF
on: FixDT
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 $x$ between $0$ and $1$ , if Bob attempted to leap across the chasm while having degree of belief $x$ that he would succeed, his chance of success would then be $x$ . 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 $x$ is the colleague’s prediction for Charlie’s degree of belief that he’s guilty, then there is a chance $x$ 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 $n$ propositions $P_{1}, \dots, P_{n}$ . Charlie’s credence in each of the propositions $P_{i},$ conditional on the proposition that the files have been randomized, is $1 / 2$ ; her credence in each $P_{i}$ conditional on the proposition that the files have not been randomized is $1$ . What credence is it epistemically rational for Charlie to have in the proposition $G$ that her colleague is guilty and in the propositions $P_{i}$ 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.

SMK Nov 29, 2023, 10:56 AM
5 points
0
on: Self-Referential Probabilistic Logic Admits the Payor’s Lemma
We assume two rules of inference:
Necessitation: $⊢ x ⟹ ⊢ □ x$
Distributivity: $⊢ □ (x \to y) ⟹ ⊢ □ x \to □ y$
Is there a reason why this differs from the standard presentation of K? Normally you would say that K is generated by the following (coupled with substitution):
Axioms:
- All tautologies of propositional logic.
- Distribution: $□ (x \to y) \to (□ x \to □ y)$ .
Rules of inference:
- Necessitation: $⟨ x, □ x ⟩$ .
- Modus ponens: $⟨ x \to y, x, y ⟩$ .

SMK Sep 29, 2023, 8:40 PM
1 point
0
AF
on: Invulnerable Incomplete Preferences: A Formal Statement
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.)

SMK Sep 17, 2023, 6:33 PM
13 points
0
on: Reflexive decision theory is an unsolved problem
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.
What links here?

SMK Jul 25, 2023, 10:27 PM
6 points
0
in reply to: ben_levinstein’s comment on: Open-minded updatelessness
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.)

SMK Jul 14, 2023, 11:42 PM
2 points
0
in reply to: Daniel Kokotajlo’s comment on: Open-minded updatelessness
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?)

SMK Jul 14, 2023, 10:48 AM
1 point
0
in reply to: Charlie Steiner’s comment on: Betting on Logic
It’s fairly clear to me that the authors do not have any specific and precise method in mind, Bjerring or no Bjerring.
Of course they don’t have a specific proposal in the paper. I’m just saying that it seems like they would want to be more precise, or that a full specification requires more work on counterpossibles (which you seem to be arguing against). From the abstract:
While not necessary for considering classic decision theory problems, we note that a full specification of FDT will require a non-trivial theory of logical counterfactuals and algorithmic similarity.
...
What mathematical propositions get chosen to be “upstream” or “downstream” has to depend on what you’re thinking of as “doing the changing” or “doing the reacting” for the question at hand.
If this is in fact how we should think about FDT, the theory becomes very uninteresting since it seems like you can then just get whatever recommendations you want from it.

SMK Jul 13, 2023, 3:06 PM
1 point
1
in reply to: Charlie Steiner’s comment on: Betting on Logic
Right, but it’s fairly clear to me that this is not what the authors have in mind. For example, they cite Bjerring (2014), who proposes very specific and precise extensions of the Lewis-Stalnaker semantics.

SMK Jul 13, 2023, 3:04 PM
1 point
0
in reply to: Zane’s comment on: Betting on Logic
(See my response to gjm’s comment.)

SMK Jul 13, 2023, 3:03 PM
4 points
0
in reply to: gjm’s comment on: Betting on Logic
To be sure, switching to Bet 1 is great evidence that $\neg P$ is true (that’s the whole point), but that’s not the sort of reasoning FDT recommends. Rather, the question is if we take the Peano axioms to be downstream of the output of the algorithm in the relevant sense.

As the authors make clear, FDT is supposed to be “structurally similar” to CDT ^[1], and in the same way CDT regards the history and the laws to be out of their control in Ahmed’s problems, FDT should arguably regard the Peano axioms to be out of their control (i.e., “upstream” of the algorithm). What could be more upstream?
1. ^
  Levinstein and Soares write (page 2): “FDT is structurally similar to CDT, but it rectifies this mistake by recognizing that logical dependencies are decision-relevant as well.”.

Open-minded updatelessness

Nicolas Macé, JesseClifton and SMK

Jul 10, 2023, 11:08 AM

65 points

21 comments12 min readLW link

SMK Mar 22, 2023, 11:46 AM
4 points
0
on: Some Variants of Sleeping Beauty
Regarding Sleeping Counterfact: there seems to be two updates you could make, and thus there should be conceptual space for two interesting ways of being updatelessness in this problem; you could be ‘anthropically updateless’, i.e., not update on your existence in the standard Thirder way, and you could also be updateless with respect to the researchers asking for money (just as in counterfactual mugging). And it seems like these two variants will make different recommendations.

Suppose you make the first update, but not the second. Then the evidentialist value of paying up would plausibly be $(1 / 3) \cdot 250 - (2 / 3) \cdot 200 < 0$ .

Suppose, on the other hand, that you are updateless with respect to both variables. Then the evidentialist value of paying up would be $(1 / 2) \cdot 250 - (1 / 2) \cdot 200 > 0$ .

SMK Mar 7, 2023, 11:21 AM
2 points
0
in reply to: Jim Buhler’s comment on: Some Variants of Sleeping Beauty
Interesting! Did thinking about those variants make you update your credences in SIA/SSA (or else)?
No, not really! This was mostly just for fun.

SMK Mar 3, 2023, 8:11 PM
5 points
2
in reply to: JBlack’s comment on: Some Variants of Sleeping Beauty
My follow-up question for almost all of them though, is based on use of the word “should” in the question. Since it presumably is not any moral version of “should”, it’s presumably a meaning in the direction of “best achieves a desired outcome”.
The ‘should’ only designates what you think epistemic rationality requires of you in the situation. That might be something consequentialist (which is what I think you mean by “best achieves a desired outcome”), like maximizing accuracy^[1], but it need not be; you could think there are other norms^[2].
To see why epistemic consequentialism might not be the whole story, consider the following case from Greaves (2013) where the agent seemingly maximises accuracy by ignoring evidence and believing an obviously false thing.
Imps. Emily is taking a walk through the Garden of Epistemic Imps. A child plays on the grass in front of her. In a nearby summerhouse are n further children, each of whom may or may not come out to play in a minute. They are able to read Emily ’s mind, and their algorithm for deciding whether to play outdoors is as follows. If she forms degree of belief 0 that there is now a child before her, they will come out to play. If she forms degree of belief 1 that there is a child before her, they will roll a fair die, and come out to play iff the outcome is an even number. More generally, the summerhouse children will play with chance $(1 - \frac{1}{2} q (C_{0}))$ , where $q (C_{0})$ is the degree of belief Emily adopts in the proposition $C_{0}$ that there is now a child before her. Emily ’s epistemic decision is the choice of credences in the proposition $C_{0}$ that there is now a child before her, and, for each $j = 1, \dots, n$ , the proposition $C_{j}$ that the $j$ th summerhouse child will be outdoors in a few minutes’ time.
See Konek and Levinstein (2019) for a good discussion, though.
If I give the same answer twice based on the same information, is that scored differently from giving that answer once?
Once again, this depends on your preferred view of epistemic rationality, and specifically how you want to formulate the accuracy-first perspective. Whether you want to maximize individual, average or total accuracy is up to you! The problems formulated here are supposed to be agnostic with regard to such things; indeed, these are the types of discussions one wants to motivate by formulating philosophical dilemmas.
1. ^
  This is plausibly cashed out by tying your epistemic utility function to a proper scoring rule, e.g. the Brier score.
2. ^
  See e.g. Sylvan (2020) for a discussion of what non-consequentialism might look like in the general, non-anthropic, case.

Some Variants of Sleeping Beauty

SMK and EOC

Mar 1, 2023, 4:51 PM

34 points

10 comments8 min readLW link

SMK Dec 26, 2022, 9:49 AM
2 points
0
in reply to: paulfchristiano’s comment on: Three reasons to cooperate
Ah, okay, got it. Sorry about the confusion. That description seems right to me, fwiw.

SMK Dec 25, 2022, 9:52 AM
2 points
0
in reply to: paulfchristiano’s comment on: Three reasons to cooperate
Thanks for clarifying. I still don’t think this is exactly what people usually mean by ECL, but perhaps it’s not super important what words we use. (I think the issue is that your model of the acausal interaction—i.e. a PD with survival on the line—is different to the toy model of ECL I have in my head where cooperation consists in benefitting the values of the other player [without regard for their life per se]. As I understand it, this is essentially the principal model used in the original ECL paper as well.)

SMK Dec 24, 2022, 11:04 PM
10 points
2
on: Three reasons to cooperate
The effective correlation is likely to be (much) larger for someone using UDT.
Could you say more about why you think this? (Or, have you written about this somewhere else?) I think I agree if by “UDT” you mean something like “EDT + updatelessness”^[1]; but if you are essentially equating UDT with FDT, I would expect the “correlation”/”logi-causal effect” to be pretty minor in practice due to the apparent brittleness of “logical causation”.
Correlation and kindness also have an important nonlinear interaction, which is often discussed under the heading of “evidential cooperation in large worlds” or ECL.
This is not how I would characterize ECL. Rather, ECL is about correlation + caring about what happens in your opponent’s universe, i.e. not specifically about the welfare/life of your opponent.
1. ^
  Because updatelessness can arguably increase the game-theoretic symmetry of many kinds of interactions, which is exactly what is needed to get EDT to cooperate.

SMK Nov 29, 2022, 10:40 PM
7 points
0
on: Respecting your Local Preferences
Related: A bargaining-theoretic approach to moral uncertainty by Greaves and Cotton-Barratt. Section 6 is especially interesting where they highlight a problem with the Nash approach; namely that the NBS is variant to whether (sub-)agents are bargaining over all decision problems (which they are currently facing and think they will face with nonzero probability) simultaneously, or whether all bargaining problems are treated separately and you find the solution for each individual problem—one at a time.

In the ‘grand-world’ model, (sub-)agents can bargain across situations with differing stakes and prima facie reach mutually beneficial compromises, but it’s not very practical (as the authors note) and would perhaps depend too much on the priors in question (just as with updatelessness). In the ‘small-world’ model, on the other hand, you don’t have problems of impracticality and so on, but you will miss out on a lot of compromises.

SMK

Open-minded updatelessness

Some Var­i­ants of Sleep­ing Beauty

Some Variants of Sleeping Beauty