This, again, seems plausible if the payoff is made sufficiently small.
How do you make the payoff small?
This is actually very similar to traditional Dutch-book arguments, which treat the bets as totally independent of everything.
Isn’t your Dutch-book argument more recursive than standard ones? Your contract only pays out if you act, so the value of the dutch book causally depends on the action you choose.
So the overall expectation is .
Wouldn’t it be P(Act=a|do(buy B)) rather than P(Act=a)? Like my thought would be that the logical thing for CDT would be to buy the contract and then as a result its expected utilities change, which leads to its probabilities changing, and as a result it doesn’t want to sell the contract. I’d think this argument only puts a bound on how much cdt and edt can differ, rather than on whether they can differ at all. Very possible I’m missing something though.
Directing a robot using motor actions and receiving camera data (translated into text I guess to not make it maximally unfair, but still) to make a cup of tea in a kitchen.
Did it memorize the way to beat the levels, or did it learn a generalized method of beating Helltaker?
Exciting stuff. One thing I suspect is that you’ll need some different account for abstractions in the presence of agency/optimization than abstractions that deal with unoptimized things, because agency implies “conspiracies” where many factors may all work together to achieve something.
Like your current point about “information at a distance” probably applies to both, but the reasons that you end up with information at a distance likely differ; with non-agency phenomena, there’s probably going to be some story based on things like thermodynamics, averages over large numbers of homogenous components, etc., while agency makes things more complex.
Suppose that the prosecutor has some random noise in their charges, such that they sometimes overcharge a bunch and sometimes undercharge a bunch. In that case it seems reasonable to suppose that things are more likely to go to court when the prosecutor is overcharging and the accused therefore thinks they can get more of the accusations dropped. But this would mean that the prosecutors are evaluated on a subset of the charges that are systematically too high, and therefore to compensate they end up lowering their assessed probabilities below what is actually counterfactually accurate if people just went to court about it always.
I don’t know how big a problem this would be, but it seems like something that would be good to evaluate in the proposal.
The ability of the prosecutor to accurately access the likelihood can be measured via the Briers score or a Log score.
Scoring predictions requires knowing the outcomes. But wouldn’t the outcome depend on whether the accused takes plea deals and such?
I’ve been thinking a lot about differences between people for… arguably most of my life, but especially the past few years. One thing I find interesting is that parts of your abstraction/chaos relationship don’t seem to transfer as neatly to people. More specifically, what I have in mind is to elements:
People carry genes around, and these genes can have almost arbitrary effects that aren’t wiped away by noise over time because the genes persist and are copied digitally in their bodies.
It seems to me that agency “wants” to resist chaos? Like if some sort of simple mechanical mechanism creates something, then the something easily gets moved away by external forces, but if a human creates something and wants to keep it, then they can place it in their home and lock their door and/or live in a society that respects private property. (This point doesn’t just apply to environmental stuff like property, but also to biological stuff.)
Individual differences often seem more “amorphous” and vague than you get elsewhere, and I bet elements like the above play a big role in this. The abstraction/chaos post helps throw this into sharp light.
If there is really both reverse causation and regular causation between Xr and Y, you have a cycle, and you have to explain what the semantics of that cycle are (not a deal breaker, but not so simple to do. For example if you think the cycle really represents mutual causation over time, what you really should do is unroll your causal diagram so it’s a DAG over time, and redo the problem there).
I agree, but I think this is much more dependent on the actual problem that one is trying to solve. There’s tons of assumptions and technical details that different approaches use, but I’m trying to sketch out some overview that abstracts over these and gets at the heart of the matter.
(There might also be cases where there is believed to be a unidirectional causal relationship, but the direction isn’t know.)
The real question is, why should Xc be unconfounded with Y? In an RCT you get lack of confounding by study design (but then we don’t need to split the treatment at all). But this is not really realistic in general—can you think of some practical examples where you would get lucky in this way?
Indeed that is the big difficulty. Considering how often people use these methods in social science, it seems like there is some general belief that one can have Xc be unconfounded with Y, but this is rarely proven and seems often barely even justified. It seems to me that the general approach is to appeal to parsimony and assume that if you can’t think of any major confounders, then they probably don’t exist.
This obviously doesn’t work well. I think people find it hard to get an intuition for how poorly it works, and I personally found that it made much more sense to me when I framed it in terms of the “Know your Xc!” point; the goal shouldn’t be to think of possible confounders, but instead to think of possible nonconfounded variance. I also have an additional blog post in the works arguing that parsimony is empirically testable and usually wrong, but it will be some time before I post this.
Counterpoint:
Why do people trade?
We often trade to express an opinion on whether a future event will drive value up or down.
You believe that a vaccine will be widely distributed, so you try investing in travel stocks. You believe emissions regulation is coming, so you try shorting auto companies.
But these trades don’t provide direct exposure to the event. There’s a lot of noise that gets in the way. Kalshi enables you to isolate trading on the event itself.
This makes me pessimistic about it, see Prediction Markets Fail To Mooch.
ὠ5 I think that is a very optimistic framing of the problem.
The hard part isn’t really weighing the costs of different known observables to find efficient ways to study things, the hard part is in figuring out what observables that there are and how to use them correctly.
I don’t think this is particularly viable algorithmically; it seems like an AI-complete problem. (Though of course one should be careful about claiming that, as often AI-complete things turn out to not be so AI-complete anyway.)
The core motivation for the series of blog posts I’m writing is, I’ve been trying to study various things that require empirical causal inference, and so I need to apply theory to figure out how to do this. But I find existing theory to be somewhat ad-hoc, providing a lot of tools with a lot of assumptions, but lacking an overall picture. This is fine if you just want to apply some specific tool, as you can then learn lots of details about that tool. But if you want to study a phenomenon, you instead need some way to map what you already know about the phenomenon to an appropriate tool, which requires a broader overview.
This post is just one post in a series. (Hopefully, at least—I do tend to get distracted.) It points out a key requirement for a broad range of methods—having some cause of interest where you know something about how the cause varies. I’m hoping to create a checklist with a broad range of causal inference methods and their key requirements. (Currently I have 3 other methods in mind that I consider to be completely distinct from this method, as well as 2 important points of critique on this method that I think usually get lost in the noise of obscure technical requirements for the statistics to be 100% justified.)
Regarding “theorizing with flowcharts”, I tend to find it pretty easy. Perhaps it’s something that one needs to get used to, but graphs are a practical way to summarize causal assumptions. Generating data may of course be helpful too, and I intend to do this in a later blog post, but it quickly gets unwieldy in that e.g. there are many parameters that can vary in the generated data, and which need to be explored to ensure adequate coverage of the possibilities.
Also, a sidenote—I tend to think of Pearl-style conditional independence methods as being related to instrumental variables and thus being a multivariate generalization of these sorts of methods. But I’m not entirely sure. Any thoughts on that?
You need enough of my trust in advance for me to be willing to quote you my cheerful price.
plus I barely know you
Are cheerful prices a good idea among near-strangers? The original idea was to address the issue of spending social capital among friends. Here you’d presumably have some trust and knowledge to make these things less of a problem.
The framing of Europe flip-flopping for no reason on the safety of AstraZeneca’s vaccine seems inaccurate. As you point out, Scandinavia still has it suspended, but it was also Scandinavia that kicked off the decision to suspend, with other European countries following. (It’s still bad ofc, but y’know, less self-contradictory.)
It’s funny that you should mention this, because I’ve considered working on a machine learning system for image recognition using this principle. However, I don’t think this is necessarily all of it. I bet we come pre-baked with a lot of rules for what sorts of features to “look for”. To give an analogy to machine learning, there’s an algorithm called pi-GAN, which comes pre-baked with the assumption that pictures originate from 3D scenes, and which then manages to learn 3D scenes from the 2D images it is trained with. (Admittedly only when the images are particularly nice.)
Your model uses correlational notions like “conditional independence” to make sense of it. But I think one could perhaps come with an alternate model using causal notions?
Specifically: If two variables X and Y are correlated, then they usually are so due to confounding, because there are a lot more ways that things can be confounded than that they can be causally related. So it makes sense to assume that they are confounded.
You could approximate all of the confounders of a suitably chosen set of observable variables by postulating a new variable, which affects all of the observables. This confounder then turns into your feature axis (if continuous) or cluster (if discrete).
Maybe this applies in most cases? I don’t know, I’ve worked on making communities for puppy-cuddlers where I’ve thought they ended too psychotic-monkey-Czarist in the end. At the very least, it seems unfair to ignore the fact that a Blue coalition does exist, even if Bob is also overreacting in his accusations.
We can also use our new framework for understanding the No True Scotsman fallacy. Alice isn’t equivocating between two definitions of Blue. She is consistently using “Blue” to mean “supporting cuddling puppies”. It is, in fact, Bob who is equivocating between “Blue” meaning “supporting giving psychotic monkeys control over the economy” and “Blue” meaning “supporting cuddling puppies”.
This seems to be assuming that coalitions don’t exist. Suppose Alice starts a puppy-cuddling club. How likely is this to get filled with Blues? And how likely are those Blues to start strategizing about how to give psychotic monkeys control over the economy? My expectation would be that it’s a lot higher than the base rate, but how much probably depends a lot on many factors, such as how Blue-coded puppy-cuddling is and how many Blues support psychotic monkey economy Czars.
I disagree, I don’t think it’s a simple binary thing. I don’t think Dutch book arguments in general never apply to recursive things, but it’s more just that the recursion needs to be modelled in some way, and since your OP didn’t do that, I ended up finding the argument confusing.
I don’t think your argument goes through for the imp, since it never needs to decide its action, and therefore the second part of selling the contract back never comes up?
Hmm, on further reflection, I had an effect in mind which doesn’t necessarily break your argument, but which increases the degree to which other counterarguments such as AlexMennen’s break your argument. This effect isn’t necessarily solved by multiplying the contract payoff (since decisions aren’t necessarily continuous as a function of utilities), but it may under many circumstances be approximately solved by it. So maybe it doesn’t matter so much, at least until AlexMennen’s points are addressed so I can see where it fits in with that.