Mathematician, alignment researcher, doctor. Reach out to me on Discord and tell me you found my profile on LW if you’ve got something interesting to say; you have my explicit permission to try to guess my Discord handle if so. You can’t find my old abandoned LW account but it’s from 2011 and has 280 karma.
Lorxus
Karma: 105
I gave a short and unpolished response privately.
Dang. I wasn’t entirely sure whether you were firm on the definition of lottery-lottery dominance or if that was more speculative. I guess I wasn’t clear that MLLs were specifically meant to be “majoritarianism but better”? Given that you meant for it to be, this post sure doesn’t prove that they exist. You’re absolutely right that you can cook up electorates where the majority-favored candidate isn’t the Nash bargaining/Geometric MLL favored candidate.
The body uses up sodium and potassium as two major cations. You need them for neural firing to work, among many other things; it’s the body’s go-to for “I need a single-charge cation but sodium doesn’t work for whatever reason”. As such, you lose plenty in urine and sweat. Because modern table salt (i.e., neither rock salt nor better yet sea salt) contains basically no potassium, people can end up being slightly deficient because we do still get some from foods—lots of types of produce like tomatoes, root vegetables, and some fruits are rich in it, for instance.
To avoid confusion: this post and my reply to it were also on a past version of this post; that version lacked any investigation of dominance criterion desiderata for lottery-lotteries.
Yeah, I myself subvocalize absolutely everything and I am still horrified when I sometimes try any “fast” reading techniques—those drain all of the enjoyment our of reading for me, as if instead of characters in a story I would imagine them as p-zombies.
I speed-read fiction, too. When I do, though, I’ll stop for a bit whenever something or someone new is being described, to give myself a moment to picture it in a way that my mind can bring up again as set dressing.
Anyway, my prediction is that non-dyslectics do not subvocalize—it’s much too slow. You can’t read faster than you speak in that case.
Maybe I’m just weird, but I totally do sometimes subvocalize, but incredibly quickly. Almost clipped or overlapping to an extent, in a way that can only really work inside your head? And that way it can go faster than you can physically speak. Why should your mental voice be limited by the limits of physical lips, tongue, and glottis, anyway?
Excellent, thanks!
Your post makes me feel like I meaningfully contributed to the improvement of these sequences by merely asking a potentially dumb question in public, which is the internet at its very best.
IMO you did! Like I said in my comment, for reasons that are secret temporarily I care about those two sequences a lot, but I might not have thought to just ask whether they could be added to the library, nor did I know that the blocker was suitable imagery.
In college I was still reading out loud. Research papers have a voice. Mathematical equations especially. They take longer to say out loud than to read in your head, but you can never be sure what’s on the page if you don’t.
This is totally true. I am a professional mathematician, and I also have a strong “mental voice”. Whenever I read mathematical texts/research papers with equations inline, I totally read the equations aloud in my head. It makes me wonder to what extent being dyslexic for English (or other written natural languages) fails to co-occur with being dyslexic for math-tongue (as distinct from dyscalculia, with AIUI has to do mostly with disability at mental calculation and mental manipulation of quantitative facts).
Maybe that description was too minimal to help anyone recreate the effect. What you do is you pretend the roman alphabet is a foreign alphabet. E.g. Kanji. Whenever you write or read, trace every stroke of the letter like you are illuminating an ancient manuscript. Channel your inner Sumi-E brush artist. Imagine yourself a true artisan of calligraphy. It’s a bit of a semi-meditative process of noticing every single stroke of every single letter. Yes, this is excruciatingly slow at first. Yes, it will be only kind of slow eventually. But, even better, you can probably still drop this technique at will and then just switch back and forth before high and low error modes of processing languages. Also, you are likely to lower your error rate in fast mode over time cause mental skills are porous. Or maybe magic? Anyway, it does seem to cross-over a bit.
Also, I can read Korean and have had the distinct sensation of it being harder to make myself care about the differences between the characters, very early on; similarly, when practicing Chinese characters in class, I’ve seen a lot of classmates have a very hard time because they have to suddenly resort to having to treat the characters like they’re pictures without even having the mental technology of how to do that correctly, so I wonder how much of dyslexia transfers cross-linguistically! Are there people who can read Cyrillic and Greek, but not Latin script or Hebrew? Who knows!
I’m neither of these users, but for temporarily secret reasons I care a lot about having the Geometric Rationality and Maximal Lottery-Lottery sequences be slightly higher-quality. Warning: these are AI-generated, if that’s a problem. It’s that, an abstract pattern, or programmer art from me.
Two options for Maximal Lottery-Lotteries:
Two options for Geometric Rationality:
what are Smith lotteries?
Lotteries over the Smith set. That definitely wasn’t clear—I’ll fix that.
which result do you mean by “above result”?
Proposition: (Lottery-lotteries are strongly characterized by their selectivity of partitions of unity)
This one. “You can tell whether a lottery-lottery is maximal or not by how good the partitions of unity it admits are.” Sorry, didn’t really know a good way to link to myself internally and I forgot to number the various statements.
What does it mean for a lottery to be part of maximal lottery-lotteries?
Just that some maximal lottery-lottery gives it nonzero probability.
does “also subject to the partition-of-unity” refer to the smith lotteries or to the lotteries that are part of maximal lottery-lotteries? (it also feels like there is a word missing somewhere)
Oh no! I thought I caught all the typos! That should be “also subject to the partition-of-unity condition”, that is, you look at all the lotteries (which we know are over the Smith set, btw) that some arbitrary maximal lottery-lottery gives any nonzero probability to, and you should expect to be able to sort them into groups by what final probability over candidates they induce; those final probabilities over candidates should themselves result in identical geometric-expected utility for the voterbase.
Why would this suffice?
Consider: at this point we know that a maximal lottery-lottery would not just have to be comprised of lottery-Smith lotteries, i.e., lotteries that are in the lottery-Smith set - but also that they have to be comprised entirely of lotteries over the Smith set of the candidate set. Then on top of that, we know that you can tell which lottery-lotteries are maximal by which partitions of unity they admit (that’s the “above result”). Note that by “admit” we mean “some subset of the lotteries this lottery-lottery has support over corresponds to it” (this partition of unity).
This is the slightly complicated part. The game I described has a mixed strategy equilibrium; this will take the form of some probability distribution over . In fact it won’t just have one, it’ll likely have whole families of them. Much of the time, the lotteries randomized over won’t be disjoint—they’ll both assign positive probability to some candidate. The key is, the voter doesn’t care. As far as a voter’s expected utility is concerned, the only thing that matters is the final probability of each candidate.
That’s where your collapse of different possible maximal lottery-lotteries to the same partition of unity comes in. Because we know that equivalent candidate-lotteries give voters the same expected utility, the only two ways you get a voter who’s indifferent between two candidate-lotteries are 1) they’re the same lottery or 2) the voter’s utility function is just right to have two very different lotteries tie. Likewise, the only two ways you get a voterbase to be indifferent between two lottery-lotteries is 1) they reduce to the same lottery or 2) the geometric expectation of a voter’s utility over candidates sampled from the samples of the lottery-lottery Just Plain Ties.
So: if we can show that whatever equilibrium set of candidate-lotteries Alice and Bob pick always collapses to some convex combination of the Best partitions of unity...? Yeah, I don’t think that the second half of the proof holds up as is.
I think I’ve slightly messed up the definition of lottery-Smith, though not in a fatal way nor (thankfully) in a way that looks to threaten the existence result. The set condition is too strong, in requiring that a lottery-Smith lottery contain all lotteries which correspond to any of the admissible partitions. I’m just going to cut it; it’s not actually necessary.
Is this part also supposed to imply the existence of maximal lottery-lotteries? If so, why?
Yes.
Yes, and in particular, it implies the existence of maximal lottery-lotteries before it even tries to prove that they’re also lottery-Smith in the sense I define.
Scott’s proof doesn’t quite work (as he says there) - it almost works, except for the part where the reward functions for Alice and Bob can quite reasonably be discontinuous. My proof is intended as a patch—the reward functions for Alice and Bob should now be extremely continuous in a way that also corresponds well to “how much better did Alice do at picking a candidate-lottery that V will like than Bob did?”.
Hopefully this helped? Reading this is confusing even for me sometimes—the word “lottery/lotteries”, which appears 59 times in this comment alone, no longer looks like a real word to me and hasn’t since late Wednesday. Your comment was really helpful—I have some editing to do! (update—editing is done.)
Firstly, your utility is not logarithmic in dollars. Utilities are bounded.
Ehn, the universe is finite and there’s no way we can get anywhere near a dollar per atom of value out of the universe. There’s well less than particles in the universe and , so if you were wrong about utility not being O(log(money)) because it has to be bounded, how could you ever tell even in principle? (That said I do think you’re right, but that’s because economium is likely as edible as dollar bills are.)
If that’s the case, that seems like a huge hole in your argument/concern. But from statistics taken for the US, it looks like AAPIs get oropharynx cancers at a significantly lower rate than both non-Hispanic Whites and general population both, despite a possibly-higher rate of smoking (for cultural reasons) and a definitely-much-higher rate of defective ALDH polymorphisms.
To make no choice is to make a choice, and to take no action is to take an action. I’d ask the flip side of Lao Mein here—how confident are you, exactly, that your current state of affairs is all that great in an absolute sense, and what are you willing to risk a small chance of in exchange for clear benefits now and in future?
Nuke might miss the moon
and fall back to earth, where it would detonate, because of the planned design which would explode upon impact
in the USSR
in the non-USSR (causing international incident)
and circle sadly around the sun forever
• and circle gleefully about the Earth-Moon Langrange points, wandering around the Earth’s Hill sphere, causing consternation for years
UPDATE: Two boxed vials of the Lumina treatment arrived in the mail for me last week. I’ve put them in the fridge for best shelf life and plan to bring one to my next cleaning. I got my wisdom tooth surgery over a decade ago, and to the best of my knowledge I have no active caries.
I am an Asian ~30yo man (ethnically Korean, specifically) who has suffered from bad cavities all his life and who also suffers from Asian glow to the point of it being uncomfortable to drink; I am also planning to get the Lumina treatment. I do not think that the amount of alcohol produced is particularly relevant; I drink occasionally and eat a ton of fruit, and thus I think that my marginal risk is basically negligible.I don’t smoke, and to the best of my knowledge, I have no particular family history of cancer, let alone oral/esophageal cancer, despite high rates of smoking in my family history.
As such, I’m pretty sure that the expected value calculation is overdetermined towards “get the Lumina”, given how unpleasant caries and carie treatment are for me and the (weak but maybe real?) connection between caries and Alzheimer’s. Given a choice of damnations, I think I’d prefer oral cancer to Alzheimer’s even with ~identical proportional changes in likelihood; given how dubious I am on the marginal risk of oral cancers to start with, I’m only that much more set on fixing my oral microbiome.
If anyone wants me to take measurements or keep data or logs of observations, please let me know.
Adam:
You could argue a similar thing about lawyers, that prosecutors and defense lawyers speak the same jargon and have more of a repeated game going than citizens they represent. And yet we have a system that mostly works.
Yud:
Lawyers combined cannot casually exterminate nonlawyers.
Adam:
…
Uh… what? If we stretch the definition of “lawyer” a bit to mean “anyone who carries out, enforces, or whose livelihood primarily depends on the law”—that is, we include government agents, cops, soldiers, and so on… yes they absolutely totally can? (In the same sense that anyone can drench their own house with gasoline and burn it down.) But maybe that’s only a weird tangent—although I’d argue that some of the power dynamics that fall out of that are likely disquietingly similar.
Gonna put a few more recommendations here, given that I seem to have broadly overlapping puzzle taste (especially Stephen’s Sausage Roll, which I even got to beta test!):
Clearly in the same vein: Antichamber, English Country Tune
Less clearly in the same vein for various reasons but still very very good: Return of the Obra Dinn (ish), Contradiction (the FMV game, less good), Gorogoa (very weird, not quite complete information, stylistically gorgeous)
On the object level I agree. On the meta level, though, making the seemingly-dumb object-level move (~here specifically) of announcing that you think that all minds are the same in some specific way means that people will come out of the woodwork to correct you, which results in everyone getting better models about what minds are like.