SCP

Karma: 335

SCP 3 Oct 2024 13:09 UTC
1 point
0
in reply to: Jeremy Gillen’s comment on: Invulnerable Incomplete Preferences: A Formal Statement
My use of ‘next’ need not be read temporally, though it could be. You might simply want to define a transitive preference relation for the agent over {A,A+,B,B+} in order to predict what it would choose in an arbitrary static decision problem. Only the incomplete one I described works no matter what the decision problem ends up being.
As a general point, you can always look at a decision ex post and back out different ways to rationalise it. The nontrivial task is here prediction, using features of the agent.
If we want an example of sequential choice using decision trees (rather than repeated ‘de novo’ choice through e.g. unawareness), it’ll be a bit more cumbersome but here goes.
Intuitively, suppose the agent first picks from {A,B+} and then, in addition, from {A+,B}. It ends up with two elements from {A,A+,B,B+}. Stated within the framework:
- The set of possible prospects is X = {A,A+B,B+}×{A,A+B,B+}, where elements are pairs.
- There’s a tree where, at node 1, the agent picks among paths labeled A and B+.
- If A is picked, then at the next node, the agent picks from terminal prospects {(A,A+),(A,B)}. And analogously if path B+ is picked.
- The agent has appropriately separable preferences: (x,y) $≿$ (x’,y’) iff x $≿^{'}$ x″ and y $≿^{'}$ y″ for some permutation (x″,y″) of (x’y’), where $≿^{'}$ is a relation over components.
Then (A+,x) $≻$ (A,x) while (A,x) $⋈/$ (B,x) for any prospect component x, and so on for other comparisons. This is how separability makes it easy to say “A+ is preferred to A” even though preferences are defined over pairs in this case. I.e., we can construct $≿$ over pairs out of some $≿^{'}$ over components.
In this tree, the available prospects from the outset are (A,A+), (A,B), (B+,A+), (B+,B).
Using the same $≿^{'}$ as before, the (dynamically) maximal ones are (A,A+), (B+,A+), (B+,B).
But what if, instead of positing incomparability between A and B+ we instead said the agent was indifferent? By transitivity, we’d infer A $≻^{'}$ B and thus A+ $≻^{'}$ B. But then (B+,B) wouldn’t be maximal. We’d incorrectly rule out the possibility that the agent goes for (B+,B).

SCP 16 Sep 2024 11:21 UTC
3 points
0
in reply to: Jeremy Gillen’s comment on: Invulnerable Incomplete Preferences: A Formal Statement
Yes that’s right (regardless of whether it’s resolute or whether it’s using ‘strong’ maximality).
A sort of of a decision tree where the agent isn’t representable as having complete preferences is the one you provide here. We can even put the dynamic aspect aside to make the point. Suppose that the agent is fact inclined to pick A+ over A, but doesn’t favour or disfavour B to either one. Here’s my representation: maximal choice with A+ $≻$ A and B $⋈/$ A,A+. As a result, I will correctly predict its behaviour: it’ll choose something other than A.
Can I also do this with another representation, using a complete preference relation? Let’s try out indifference between A+ and B. I’d indeed make the same prediction in this particular case. But suppose the agent were next to face a choice between A+, B, and B+ (where the latter is a sweetening of B). By transitivity, we know B+ $≻$ A+, and so this representation would predict that B+ would be chosen for sure. But this is wrong, since in fact the agent is not inclined to favour B-type prospects over A-type prospects. In contrast, the incomplete representation doesn’t make this error.
Summing up: the incomplete representation works for {A+,A,B} and {A+,B,B+} while the only complete one that also works for the former fails for the latter.

SCP 28 Jul 2024 23:19 UTC
4 points
1
in reply to: Closed Limelike Curves’s comment on: Closed Limelike Curves’s Shortform
Thanks. Let me end with three comments. First, I wrote a few brief notes here that I hope clarify how Independence and IIA differ. Second, I want to stress that the problem with the use of Dutch books in the articles is a substantial one, not just a verbal one, as I explained here and here. Finally, I’m happy to hash out any remaining issues via direct message if you’d like—whether it’s about these points, others I raised in my initial comment, or any related edits.

SCP 26 Jul 2024 10:19 UTC
6 points
5
in reply to: Closed Limelike Curves’s comment on: Closed Limelike Curves’s Shortform
I don’t apprecaite the hostility. I aimed to be helpful in spending time documenting and explaining these errors. This is something a heathy epistemic community is appreciative of, not annoyed by. If I had added mistaken passages to Wikipedia, I’d want to be told, and I’d react by reversing them myself. If any points I mentioned weren’t added by you, then as I wrote in my first comment:
...let me know that some of the issues I mention were already on Wikipedia beforehand. I’d be happy to try to edit those.
The point of writing about the mistakes here is to make clear why they indeed are mistakes, so that they aren’t repeated. That has value. And although I don’t think we should encourage a norm that those who observe and report a problem are responsible for fixing it, I will try to find and fix at least the pre-existing errors.

SCP 24 Jul 2024 9:34 UTC
8 points
7
in reply to: habryka’s comment on: Closed Limelike Curves’s Shortform
I agree that there exists the dutch book theorem, and that that one importantly relates to probabilism
I’m glad we could converge on this, because that’s what I really wanted to convey.^[1] I hope it’s clearer now why I included these as important errors:
- The statement that the vNM axioms “apart from continuity, are often justified using the Dutch book theorems” is false since these theorems only relate to belief norms like probabilism. Changing this to ‘money pump arguments’ would fix it.
- There’s a claim on the main Dutch book page that the arguments demonstrate that “rationality requires assigning probabilities to events [...] and having preferences that can be modeled using the von Neumann–Morgenstern axioms.” I wouldn’t have said it was false if this was about money pumps.^[2] I would’ve said there was a terminological issue if the page equated Dutch books and money pumps. But it didn’t.^[3] It defined a Dutch book as “a set of bets that ensures a guaranteed loss.” And the theorems and arguments relating to that do not support the vNM axioms.
Would you agree?
1. ^
  The issue of which terms to use isn’t that important to me in this case, but let me speculate about something. If you hear domain experts go back and forth between ‘Dutch books’ and ‘money pumps’, I think that is likely either because they are thinking of the former as a special case of the latter without saying so explicitly, or because they’re listing off various related ideas. If that’s not why, then they may just be mistaken. After all, a Dutch book is named that way because a bookie is involved!
2. ^
  Setting asside that “demonstrates” is too strong even then.
3. ^
  It looks like OP edited the page just today and added ‘or money pump’. But the text that follows still describes a Dutch book, i.e. a set of bets. (Other things were added too that I find problematic but this footnote isn’t the place to explain it.)

SCP 23 Jul 2024 23:32 UTC
13 points
5
in reply to: habryka’s comment on: Closed Limelike Curves’s Shortform
I think it’ll be helpful to look at the object level. One argument says: if your beliefs aren’t probabilistic but you bet in a way that resembles expected utility, then you’re succeptible to sure loss. This forms an argument for probabilism.^[1]
Another argument says: if your preferences don’t satisfy certain axioms but satisfy some other conditions, then there’s a sequence of choices that will leave you worse off than you started. This forms an agument for norms on preferences.
These are distinct.
These two different kinds of arguments have things in common. But they are not the same argument applied in different settings. They have different assumptions, and different conclusions. One is typically called a Dutch book argument; the other a money pump argument. The former is sometimes referred to as a special case of the latter.^[2] But whatever our naming convensions, it’s a special case that doesn’t support the vNM axioms.
Here’s why this matters. You might read assumptions of the Dutch book theorem, and find them compelling. Then you read a article telling you that this implies the vNM axioms (or constitutes an argument for them). If you believe it, you’ve been duped.
1. ^
  (More generally, Dutch books exist to support other Bayesian norms like conditionalisation.)
2. ^
  This distinction is standard and blurring the lines leads to confusions. It’s unfortunate when dictionaries, references, or people make mistakes. More reliable would be a key book on money pumps (Gustafsson 2022) referring to a key book on Dutch books (Pettigrew 2020):
  “There are also money-pump arguments for other requirements of rationality. Notably, there are money-pump arguments that rational credences satisfy the laws of probability. (See Ramsey 1931, p. 182.) These arguments are known as Dutch-book arguments. (See Lehman 1955, p. 251.) For an overview, see Pettigrew 2020.” [Footnote 9.]

SCP 23 Jul 2024 19:06 UTC
7 points
6
in reply to: habryka’s comment on: Closed Limelike Curves’s Shortform
check the edit history yourself by just clicking on the “View History” button and then pressing the “cur” button
Great, thanks!
I hate to single out OP but those three points were added by someone with the same username (see first and second points here; third here). Those might not be entirely new but I think my original note of caution stands.

SCP 23 Jul 2024 13:22 UTC
LW: 6 AF: 2
0
AF
on: Coalitional agency
Scott Garrabrant rejects the Independence of Irrelevant Alternatives axiom
*Independence, not IIA. Wikipedia is wrong (as of today).

SCP 23 Jul 2024 10:41 UTC
38 points
2
in reply to: Closed Limelike Curves’s comment on: Closed Limelike Curves’s Shortform
I appreciate the intention here but I think it would need to be done with considerable care, as I fear it may have already led to accidental vandalism of the epistemic commons. Just skimming a few of these Wikipedia pages, I’ve noticed several new errors. These can be easily spotted by domain experts but might not be obvious to casual readers.^[1] I can’t know exactly which of these are due to edits from this community, but some very clearly jump out.^[2]
I’ll list some examples below, but I want to stress that this list is not exhaustive. I didn’t read most parts of most related pages, and I omitted many small scattered issues. In any case, I’d like to ask whoever made any of these edits to please reverse them, and to triple check any I didn’t mention below.^[3] Please feel free to respond to this if any of my points are unclear!^[4]
False statements
- The page on Independence of Irrelevant Alternatives (IIA) claims that IIA is one of the vNM axioms, and that one of the vNM axioms “generalizes IIA to random events.”
  Both are false. The similar-sounding Independence axiom of vNM is neither equivalent to, nor does it entail, IIA (and so it can’t be a generalisation). You can satisfy Independence while violating IIA. This is a not a technicality; it’s a conflation of distinct and important concepts. This is repeated in several places.
- The mathematical statement of Independence there is wrong. In the section conflating IIA and Independence, it’s defined as the requirement that
  
  for any $p \in [0, 1]$ and any outcomes Bad, Good, and N satisfying Bad≺Good. This mistakes weak preference for strict preference. To see this, set p=1 and observe that the line now reads N≺N. (The rest of the explanation in this section is also problematic but the reasons for this are less easy to briefly spell out.)
- The Dutch book page states that the argument demonstrates that “rationality requires assigning probabilities to events [...] and having preferences that can be modeled using the von Neumann–Morgenstern axioms.” This is false. It is an argument for probabilistic beliefs; it implies nothing at all about preferences. And in fact, the standard proof of the Dutch book theorem assumes something like expected utility (Ramsey’s thesis).
  This is a substantial error, making a very strong claim about an important topic. And it’s repeated elsewhere, e.g. when stating that the vNM axioms “apart from continuity, are often justified using the Dutch book theorems.”
- The section ‘The theorem’ on the vNM page states the result using strict preference/inequality. This is a corollary of the theorem but does not entail it.
Misleading statements
- The decision theory page states that it’s “a branch of applied probability theory and analytic philosophy concerned with the theory of making decisions based on assigning probabilities to various factors and assigning numerical consequences to the outcome.” This is a poor description. Decision theorists don’t simply assume this, nor do they always conclude it—e.g. see work on ambiguity or lexicographic preferences. And besides this, decision theory is arguably more central in economics than the fields mentioned.
- The IIA article’s first sentence states that IIA is an “axiom of decision theory and economics” whereas it’s classically one of social choice theory, in particular voting. This is at least a strange omission for the context-setting sentence of the article.
- It’s stated that IIA describes “a necessary condition for rational behavior.” Maybe the individual-choice version of IIA is, but the intention here was presumably to refer to Independence. This would be a highly contentious claim though, and definitely not a formal result. It’s misleading to describe Independence as necessary for rationality.
- The vNM article states that obeying the vNM axioms implies that agents “behave as if they are maximizing the expected value of some function defined over the potential outcomes at some specified point in the future.” I’m not sure what ‘specified point in the future’ is doing there; that’s not within the framework.
- The vNM article states that “the theorem assumes nothing about the nature of the possible outcomes of the gambles.” That’s at least misleading. It assumes all possible outcomes are known, that they come with associated probabilities, and that these probabilities are fixed (e.g., ruling out the Newcomb paradox).
Besides these problems, various passages in these articles and others are unclear, lack crucial context, contain minor issues, or just look prone to leave readers with a confused impression of the topic. (This would take a while to unpack, so my many omissions should absolutely not be interpreted as green lights.) As OP wrote: these pages are a mess. But I fear the recent edits have contributed to some of this.
So, as of now, I’d strongly recommend against reading Wikipedia for these sorts of topics—even for a casual glance. A great alternative is the Stanford Encyclopedia of Philosophy, which covers most of these topics.
1. ^
  I checked this with others in economics and in philosophy.
2. ^
  E.g., the term ‘coherence theorems’ is unheard of outside of LessWrong, as is the frequency of italicisation present in some of these articles.
3. ^
  I would do it myself but I don’t know what the original articles said and I’d rather not have to learn the Wikipedia guidelines and re-write the various sections from scratch.
4. ^
  Or to let me know that some of the issues I mention were already on Wikipedia beforehand. I’d be happy to try to edit those.

SCP 16 Jul 2024 10:22 UTC
LW: 3 AF: 1
0
AF
on: A simple case for extreme inner misalignment
Two nitpicks and a reference:
an agent’s goals might not be linearly decomposable over possible worlds due to risk-aversion
Risk aversion doesn’t violate additive separability. E.g., for $u (x) = x^{a}$ we always get $E [u (x)] = \sum_{i} p_{i} x_{i}^{a}$ whether $a = 1$ (risk neutrality) or $a = 1 / 2$ (risk aversion). Though some alternatives to expected utility, like Buchak’s REU theory, can allow certain sources of risk aversion to violate separability.
when features have fixed marginal utility, rather than being substitutes
Perfect substitutes have fixed marginal utility. E.g., $v (x, y) = x + 2 y$ always has marginal utilities of 1 and 2.
I’ll focus on linearly decomposable goals which can be evaluated by adding together evaluations of many separate subcomponents. More decomposable goals are simpler
There’s an old literature on separability in consumer theory that’s since been tied to bounded rationality. One move that’s made is to grant weak separability accross goups of objects—features—to rationalise the behaviour of optimising accross groups first, and within groups second. Pretnar et al (2021) describe how this can arise from limited cognitive resources.

SCP 4 Mar 2024 12:37 UTC
11 points
4
in reply to: SMK’s comment on: Wei Dai’s Shortform
It may be worth thinking about why proponents of a very popular idea in this community don’t know of its academic analogues, despite them having existed since the early 90s^[1] and appearing on the introductory SEP page for dynamic choice.
Academics may in turn ask: clearly LessWrong has some blind spots, but how big?
1. ^
  And it’s not like these have been forgotton; e.g., McClennen’s (1990) work still gets cited regularly.

SCP 11 Jan 2024 19:04 UTC
LW: 6 AF: 3
0
AF
on: Meaning & Agency
I argued that the signal-theoretic^[1] analysis of meaning (which is the most common Bayesian analysis of communication) fails to adequately define lying, and fails to offer any distinction between denotation and connotation or literal content vs conversational implicature.
In case you haven’t come accross this, here are two papers on lying by the founders of the modern economics literature on communication. I’ve only skimmed your discussion but if this is relevant, here’s a great non-technical discussion of lying in that framework. A common thread in these discussions is that the apparent “no-lying” implication of the analysis of language in the Lewis-Skyrms/Crawford-Sobel signalling tradition relies importantly on common knowledge of rationality and, implicitly, on common knowledge of the game being played, i.e. of the available actions and all the players’ preferences.

SCP 31 Oct 2023 11:28 UTC
LW: 1 AF: 1
0
AF
in reply to: dxu’s comment on: Invulnerable Incomplete Preferences: A Formal Statement
In your example, DSM permits the agent to end up with either A+ or B. Neither is strictly dominated, and neither has become mandatory for the agent to choose over the other. The agent won’t have reason to push probability mass from one towards the other.
You can think of me as trying to run an obvious-to-me assertion test on code which I haven’t carefully inspected, to see if the result of the test looks sane.
This is reasonable but I think my response to your comment will mainly involve re-stating what I wrote in the post, so maybe it’ll be easier to point to the relevant sections: 3.1. for what DSM mandates when the agent has beliefs about its decision tree, 3.2.2 for what DSM mandates when the agent hadn’t considered an actualised continuation of its decision tree, and 3.3. for discussion of these results. In particular, the following paragraphs are meant to illustrate what DSM mandates in the least favourable epistemic state that the agent could be in (unawareness with new options appearing):
It seems we can’t guarantee non-trammelling in general and between all prospects. But we don’t need to guarantee this for all prospects to guarantee it for some, even under awareness growth. Indeed, as we’ve now shown, there are always prospects with respect to which the agent never gets trammelled, no matter how many choices it faces. In fact, whenever the tree expansion does not bring about new prospects, trammelling will never occur (Proposition 7). And even when it does, trammelling is bounded above by the number of comparability classes (Proposition 10).
And it’s intuitive why this would be: we’re simply picking out the best prospects in each class. For instance, suppose prospects were representable as pairs $⟨ s, c ⟩$ that are comparable iff the $s$ -values are the same, and then preferred to the extent that $c$ is large. Then here’s the process: for each value of $s$ , identify the options that maximise $c$ . Put all of these in a set. Then choice between any options in that set will always remain arbitrary; never trammelled.

SCP 23 Oct 2023 23:51 UTC
3 points
−3
on: What’s Hard About The Shutdown Problem
The key question is whether the revealed preferences are immune to trammelling. This was a major point of confusion for me in discussion with Sami—his proposal involves a set of preferences passed into a decision rule, but those “preferences” are (potentially) different from the revealed preferences. (I’m still unsure whether Sami’s proposal solves the problem.)
I claim that, yes, the revealed preferences in this sense are immune to trammeling. I’m happy to continue the existing discussion thread but here’s a short motivation: what my results about trammelling show is that there will always be multiple (relevant) options between which the agent lacks a preference and the DSM choice rule does not mandate picking one over another. The agent will not try to push probability mass toward one of those options over another.

SCP 23 Oct 2023 23:39 UTC
11 points
4
on: What’s Hard About The Shutdown Problem
(I learned from Sami’s post that this is called “trammelling” of incomplete preferences.)
Just for reference: this isn’t a standard term of art; I made it up. Though I do think it’s fitting.

SCP 21 Oct 2023 14:04 UTC
LW: 4 AF: 4
1
AF
in reply to: johnswentworth’s comment on: Invulnerable Incomplete Preferences: A Formal Statement
Great, I think bits of this comment help me understand what you’re pointing to.
the desired behavior implies a revealed preference gap
I think this is roughly right, together with all the caveats about the exact statements of Thornley’s impossibility theorems. Speaking precisely here will be cumbersome so for the sake of clarity I’ll try to restate what you wrote like this:
1. Useful agents satisfying completeness and other properties X won’t be shutdownable.
2. Properties X are necessary for an agent to be useful.
3. So, useful agents satisfying completeness won’t be shutdownable.
4. So, if a useful agent is shutdownable, its preferences are incomplete.
This argument would let us say that observing usefulness and shutdownability reveals a preferential gap.
I think the question I’m interested in is: “do trammelling-style issues imply that DSM agents will not have a revealed preference gap (under reasonable assumptions about their environment and capabilities)?”
A quick distinction: an agent can (i) reveal p, (ii) reveal ¬p, or (iii) neither reveal p nor ¬p. The problem of underdetermination of preference is of the third form.
We can think of some of the properties we’ve discussed as ‘tests’ of incomparability, which might or might not reveal preferential gaps. The test in the argument just above is whether the agent is useful and shutdownable. The test I use for my results above (roughly) is ‘arbitrary choice’. The reason I use that test is that my results are self-contained; I don’t make use of Thornley’s various requirements for shutdownability. Of course, arbitrary choice isn’t what we want for shutdownability. It’s just a test for incomparability that I used for an agent that isn’t yet endowed with Thornley’s other requirements.
The trammelling results, though, don’t give me any reason to think that DSM is problematic for shutdownability. I haven’t formally characterised an agent satisfying DSM as well as TND, Stochastic Near-Dominance, and so on, so I can’t yet give a definitive or exact answer to how DSM affects the behaviour of a Thornley-style agent. (This is something I’ll be working on.) But regarding trammelling, I think my results are reasons for optimism if anything. Even in the least convenient case that I looked at—awareness growth—I wrote this in section 3.3. as an intuition pump:
we’re simply picking out the best prospects in each class. For instance, suppose prospects were representable as pairs $⟨ s, c ⟩$ that are comparable iff the $s$ -values are the same, and then preferred to the extent that $c$ is large. Then here’s the process: for each value of $s$ , identify the options that maximise $c$ . Put all of these in a set. Then choice between any options in that set will always remain arbitrary; never trammelled.
That is, we retain the preferential gap between the options we want a preferential gap between.
[As an aside, the description in your first paragraph of what we want from a shutdownable agent doesn’t quite match Thornley’s setup; the relevant part to see this is section 10.1. here.]

SCP 20 Oct 2023 9:09 UTC
LW: 1 AF: 1
0
AF
in reply to: dxu’s comment on: Invulnerable Incomplete Preferences: A Formal Statement
On my understanding, the argument isn’t that your DSM agent can be made better off, but that the reason it can’t be made better off is because it is engaging in trammeling/“collusion”, and that the form of “trammeling” you’ve ruled out isn’t the useful kind.
I don’t see how this could be right. Consider the bounding results on trammelling under unawareness (e.g. Proposition 10). They show that there will always be a set of options between which DSM does not require choosing one over the other. Suppose these are X and Y. The agent will always be able to choose either one. They might end up always choosing X, always Y, switching back and forth, whatever. This doesn’t look like the outcome of two subagents, one preferring X and the other Y, negotiating to get some portion of the picks.
As far as an example goes, consider a sequence of actions which, starting from an unpressed world state, routes through a pressed world state (or series of pressed world states), before eventually returning to an unpressed world state with higher utility than the initial state.
Forgive me; I’m still not seeing it. For coming up with examples, I think for now it’s unhelpful to use the shutdown problem, because the actual proposal from Thornley includes several more requirements. I think it’s perfectly fine to construct examples about trammelling and subagents using something like this: A is a set of options with typical member $a_{i}$ . These are all comparable and ranked according to their subscripts. That is, $a_{1}$ is preferred to $a_{2}$ , and so on. Likewise with set B. And all options in A are incomparable to all options in B.
If your proposed DSM agent passes up this action sequence on the grounds that some of the intermediate steps need to bridge between “incomparable” pressed/unpressed trajectories, then it does in fact pass up the certain gain. Conversely, if it doesn’t pass up such a sequence, then its behavior is the same as that of a set of negotiating subagents cooperating in order to form a larger macroagent.
This looks to me like a misunderstanding that I tried to explain in section 3.1. Let me know if not, though, ideally with a worked-out example of the form: “here’s the decision tree(s), here’s what DSM mandates, here’s why it’s untrammelled according to the OP definition, and here’s why it’s problematic.”

SCP 19 Oct 2023 19:13 UTC
LW: 4 AF: 4
3
AF
in reply to: johnswentworth’s comment on: Invulnerable Incomplete Preferences: A Formal Statement
That makes sense, yeah.
Let me first make some comments about revealed preferences that might clarify how I’m seeing this. Preferences are famously underdetermined by limited choice behaviour. If A and B are available and I pick A, you can’t infer that I like A more than B — I might be indifferent or unable to compare them. Worse, under uncertainty, you can’t tell why I chose some lottery over another even if you assume I have strict preferences between all options — the lottery I choose depends on my beliefs too. In expected utility theory, beliefs and preferences together induce choice, so if we only observe a choice, we have one equation in two unknowns.^[1] Given my choice, you’d need to read my mind’s probabilities to be able to infer my preferences (and vice versa).^[2]
In that sense, preferences (mostly) aren’t actually revealed. Economists often assume various things to apply revealed preference theory, e.g. setting beliefs equal to ‘objective chances’, or assuming a certain functional form for the utility function.
But why do we care about preferences per se, rather than what’s revealed? Because we want to predict future behaviour. If you can’t infer my preferences from my choices, you can’t predict my future choices. In the example above, if my ‘revealed preference’ between A and B is that I prefer A, then you might make false predictions about my future behaviour (because I might well choose B next time).
Let me know if I’m on the right track for clarifying things. If I am, could you say how you see trammelling/shutdown connecting to revealed preferences as described here, and I’ll respond to that?
1. ^
  $L^{*} \in arg {max}_{L} \sum_{i} u (x_{i}) p (x_{i} [L])$
2. ^
  The situation is even worse when you can’t tell what I’m choosing between, or what my preference relation is defined over.

SCP 19 Oct 2023 8:25 UTC
LW: 1 AF: 1
0
AF
in reply to: dxu’s comment on: Invulnerable Incomplete Preferences: A Formal Statement
I disagree; see my reply to John above.

SCP 19 Oct 2023 8:16 UTC
LW: 3 AF: 3
0
AF
in reply to: johnswentworth’s comment on: Invulnerable Incomplete Preferences: A Formal Statement
if the subagents representing a set of incomplete preferences would trade with each other to emulate more complete preferences, then an agent with the plain set of incomplete preferences would precommit to act in the same way
My results above on invulnerability preclude the possibility that the agent can predictably be made better off by its own lights through an alternative sequence of actions. So I don’t think that’s possible, though I may be misreading you. Could you give an example of a precommitment that the agent would take? In my mind, an example of this would have to show that the agent (not the negotiating subagents) strictly prefers the commitment to what it otherwise would’ve done according to DSM etc.
Yeah, I wasn’t using Bradley. The full set of coherent completions is overkill, we just need to nail down the partial order.
I agree the full set won’t always be needed, at least when we’re just after ordinal preferences, though I personally don’t have a clear picture of when exactly that holds.

SCP

False statements

Misleading statements