ControlsFreak
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User ID: 1422
ControlsFreak
1d ago
Why would the State care if Bob got his balls cut off years ago? Why would they make some special process to 'allow' this? It's extra work; it seems to serve little purpose on your account. They have a perfectly good default to revert to - you're cousins, so you don't get married. Why would they do this other mess?
ControlsFreak
1d ago
"By default any man/woman pair who ask for it can be legally married, but we will deny it to couples that could produce inbred children with defects in the hope that that'll make them give upon fucking one another at all"
What about the bit about letting them marry if they show that they're infertile?
ControlsFreak
1d ago
Specifically concerning the example of some people only being able to marry if they show that they are infertile. I thought I was speaking plainly about this, but apparently, it didn't come across. What do you think they were trying to do?
I am not treating this as a fight, but it's clear that you are. You call it such and your demeanor is indicative that you may have something like cortisol levels going on which correspond to you perceiving it as a fight. I just want you to think about a brute fact in the world and give some impression as to what you think is going on. If I was being a jerk, I'd say that your immediate reaction to lash out at your interlocutor rather than have a respectable conversation about the topic is, yes, why the wokies won so many political fights. Bullying and anger won a lot of political victories, but left a lot of people privately unconvinced and resentful that such tactics managed to ram through major societal changes, rather than reasoned discourse.
ControlsFreak
1d ago
Possibly. Possibly not. I'm not really viewing it as a "debate". I'm just encouraging you to think about things. It would be nice to get your perspective on how you think about it. Perhaps it's something you've never thought about before; it would then be useful to get your fresh perspective on the matter rather than simply treating it as a "debate" to be "won", because that often leads to people simply trying to shove things into a pre-canned bin where they think they can just draw from their pre-canned set of talking points. So far, I think it's apparent that you don't have a simple pre-canned talking point for this, specifically, so it's useful to get your first impressions concerning the brute fact of such laws.
ControlsFreak
1d ago
if the line between who should be allowed to marry
Again, the perspective change needs to be pretty deep. It is not about who is "allowed" to marry. It's about what the State is trying to encourage/discourage. Think about the example I gave; see if you can come up with an idea for what it is that they're trying to do.
ControlsFreak
1d ago
If you are saying the line between who can marry and who cannot, which puts gay couples on the "cannot" side, is drawn on the grounds of who can produce children and who cannot
This "if" is precisely what my example points out is not true. The entire premise of the argument is simply false. The entire frame of reference simply does not make sense. Basically the entire remainder of this comment is sort of pointless from the get-go because of this flaw.
ControlsFreak
1d ago
This sounds like needless complexity, and it would invite a whole host of additional complex questions. Is there an expiration on a provisional marriage? Suppose you want to get married early, but delay having children a bit, is that allowed? Why or why not? The outrageous news stories will kill you, too. "This couple has had two miscarriages and is now about to hit the deadline on their provisional marriage!" This kinda thing will never fly with the public.
ControlsFreak
1d ago
then where's the law banning infertile people from marrying? Because on the axis of "family formation," there's no difference between them and the gays, is there?
As mentioned below, there are actually laws saying that some people couldn't marry unless they could show that they were infertile. Your entire frame of reference simply does not make sense, and you need a pretty significant perspective change.
Further, rather than there being "no difference", there is actually quite a huge difference, particularly in terms of intrusiveness to privacy. The government can very very simply look at the government documents which state that they're the same sex. What kind of standards, and what kind of intrusive nightmare would it be to require something like proof of fertility? @WandererintheWilderness would call it "Chinese-style authoritarian social engineering". These examples are worlds apart rather than being "no different".
ControlsFreak
1d ago
What do you think the purpose of such laws is?
ControlsFreak
2d ago
entirely material, but do not support discrimination between same-gender couples and opposite-gender couples one or both members of which is entirely infertile
Interestingly, many states had laws on the books that some people couldn't marry unless they showed that they were infertile. Namely, close relatives.
This has been trod over time and time again, but people still draw on this silly argument.
Do not impose your religious beliefs on people who do not share them.
Do not impose your atheistic beliefs on people who do not share them.
ControlsFreak
2d ago
In general, how sure should we be that the stock market today is doing well because of Donald Trump and not in spite of/unrelated to him?
In general, I've found that the answer to whether the president causes the market to go up/down is an XNOR function with inputs "Is the market up?" and "Is the current president on my team?"
ControlsFreak
7d ago
For example, we know there was at least one decent Pharisee, Nicodemus. And yet, Jesus doesn’t say “Beware of the leaven of the Pharisees and Sadducees! Except Nicodemus, he’s one of the good ones.”
He just says, “Beware of the leaven of the Pharisees and Sadducees!”
I think plenty of people see daylight between treating people like a class and being able to speak with labels. Even going back to the Scholastics, this could probably be viewed as a component (lol) of mereology.
ControlsFreak
7d ago
lollipop example
Sure, there are ways to add actual gain of information that is relevant for X. I'd have to work through different precise formulations.
Anyway, this morning, after having written my last comment (and before reading yours, as it happens), I was feeling very confident in it. I figured (as I should figure) that I should actually check out the literature in the area a bit, and see what's there. Of course, I was also looking for whether anyone in the literature had proposed a similar solution... and if so, whether there was any responding literature saying that it was insufficient in some way.
I proceeded with a mix of Wikipedia cites and Google Scholar, but it turns out that Wikipedia actually sums up what I now think is a great representation of my view pretty well, with reference to Groisman's 2008 paper. It's in the Wiki section on Ambiguous-question position:
Imagine tossing a coin, if the coin comes up heads, a green ball is placed into a box; if, instead, the coin comes up tails, two red balls are placed into a box. We repeat this procedure a large number of times until the box is full of balls of both colours. A single ball is then drawn from the box. In this setting, the question from the original problem resolves to one of two different questions: "what is the probability that a green ball was placed in the box" and "what is the probability a green ball was drawn from the box". These questions ask for the probability of two different events, and thus can have different answers, even though both events are causally dependent on the coin landing heads.
I hadn't quite hit on the right language, but I was getting there with random variables X and Y. I was pretty sure, and I'm still pretty sure, that if one actually spells out, in detail, formal definitions of X and Y, one can see that they do not relate in the form of a simple conditional probability that can be used to 'update' X. What I hadn't yet specified was that the main way that they differ is that they're describing different sample spaces.
One can make this analogy even more explicit by saying that if heads is flipped, a green ball that has written on it, "Monday, heads" is placed in the box. If tails is flipped, one red ball labeled "Monday, tails" and one red ball labeled "Tuesday, tails" are placed in the box.
I think very clearly here, one can say that when you pull a ball from the box, there is a 1/3 chance that you see a green ball. That is exactly the same as saying that there's a 1/3 chance that you see "heads" written on the ball. Similarly, there is a 2/3 chance that you see "tails" written on a red ball. "Seeing heads/tails on a ball" is random variable Y.
...but you cannot say that there was a 2/3 chance of tails having been flipped (random variable X). That's just a different sample set. You don't "gain information" about what was flipped by knowing that a ball has been drawn from the box (waking up). You had all the information you needed at the first moment, because you knew the experimental setup and how the depositing/withdrawing mechanism worked.
Balls are deposited according to the sample set {One Green, Two Red}, where they have some stuff written on them, but they're withdrawn according to the sample set {Green/Monday, Red/Monday, Red/Tuesday}.
This is also, I believe, the key intellectual step that justifies the naive thirder position against the naive halfer position in the first place - that because you have no information about which situation you're waking up in, you have to realize that the set of possibilities has three elements (over which, you take a typical uniform distribution), only one which has you seeing heads (green) and two which have you seeing tails (red).
To reiterate, yes, the correct betting strategy for what you observe will be 2/3 red/tails, but I don't believe that any property of conditional probability implies that your estimate should be that tails was flipped with probability 2/3. I think it would actually directly violate the laws of probability, for if you apply the laws of probability to the actual mechanics of the experiment and say that tails is flipped with probability 2/3, then you should observe tails with probability 4/5. This is actually a pretty straightforward calculation.
p = probability of flipping tails/depositing 2red
Un-normalized probability of observing tails/observing red: 2p
Un-normalized probability of observing heads/observing green: (1-p)
2p + (1-p) = p+1 is our normalization constant over the three possible balls
Normalized probability of observing tails/observing red: 2p/(p+1)
Normalized probability of observing heads/observing green: (1-p)/(p+1)
This is just the mechanics of the game. For p=1/2, we get 2/3 and 1/3. For p=2/3, we get 4/5 and 1/5.
This math should work for the extended versions of the game, too. If you wake up once (have one green ball) on heads, but wake up n times (have n green balls) on tails, then
p = probability of flipping tails/depositing n red
Un-normalized probability of observing tails/observing red: np
Un-normalized probability of observing heads/observing green: (1-p)
np + (1-p) = (n-1)p+1 is our normalization constant over the n+1 possible balls
Normalized probability of observing tails/observing red: np/((n-1)p+1)
Normalized probability of observing heads/observing green: (1-p)/((n-1)p+1)
I also took a little time on Google Scholar to check some of the papers that cited this Groisman paper. Many of them did the typical thing of just citing a paper because it came up in their own GS search, clearly not having read it (this has happened to my own work plenty, much to my chagrin). I already can't remember whether there was one or two papers that actually said something about what Groisman did and complained about it, but their complaint wasn't really comprehensible to me (maybe if I spent more than a morning on it, I could figure out whether I think it's valid or not). Perhaps you'll still disagree along some lines like that and be able to explain it better.
Maybe I could still imagine a critique, perhaps in terms of moving sums around (I.e., there are cases of multiple summation where you can/can't moving an inner sum out to an outer sum), but sums are often not that hard to move around. I'd definitely need to see a pretty detailed formal argument of where exactly a problem occurs. Otherwise, I'm pretty doubtful that any more informal argument is going to move me much.
It also comports with my casino game example. A static, non-feedback policy is just queried a different number of times, so it observes tails more often. I know that it'll observe tails more often (2p/(p+1) of the time), so that's how I should bet on what it observes. Perhaps to reach your preference for saying that whether you bet right matters the most, let's say this casino has you play two games simultaneously. In the first game, you're just betting on the outcome of a coin flip with probability p (maybe we even remove p=1/2 to remove possible degeneracies). In the second game, at the same time, you're betting on this modified game where your policy is queried twice if it's tails. They use the same coin and then evaluate both games, with your separate bets. If someone is not betting according to p and 2p/(p+1) in the two respective games, then I think you would declare that they are wrong. The difference between these two bets is simply that these two static policies have different observation/evaluation functions. The second policy doesn't somehow update mid-game and think that the properties of the coin flip have changed. If it did, your two policies would have weird and conflicting estimates for the properties of the coin flip. How would you even make your second set of bets?
...I guess finally, since I can't shut up, go back to computing policies for parallel Sleeping Beauty games. One is betting on a normal coin flip, while the other has this weird observation function. They use the same coin. Should those policies (people) have different estimates for the coin flip when they wake up... or just different estimates for what they will observe in their appropriately-blinded state?
ControlsFreak
7d ago
Let me be clear: nothing in my comment implies that you have ever said or implied that you are God. It is purely a matter of a tool for biblical interpretation. AFAICT, the Bible says that there is a difference between you and God. (Nothing to do with anything you have or haven't said.) Ergo, presumably, the Bible may think that there are things that God does which may not necessarily be things that you should do. One possible thing that might be in that category could be "treating people as a class". But of course, it could be complicated; maybe it's not in that category! But I don't think one can generally reason from, "Here is an example of God doing X," to, "Therefore, I should do X."
ControlsFreak
8d ago
SMBC does the philosophy of mathematics joke. As a bonus, throwing shade on the "unreasonable effectiveness of mathematics" line.
There are tons of culture war topics where this could be applicable, and I'm sure I'll link it many times in the future in those conversations, but I won't bring up any specific topics for a Friday thread. Just enjoying the funny today. It nails the sort of Internet Brashness that you get from various folks on a whole variety of topics when mathematics/philosophy of mathematics may be relevant.
ControlsFreak
8d ago
Sorry to belabor this, because I think we've made progress and are maybe not on the same page, perhaps somewhere in the same chapter... but...
My only issue is that I really, honestly cannot wrap my mind around a mindset that doesn't treat Y as the obvious thing the question's about.
I think it's because people... sorry to say, like yourself... say things like...
You can learn things about past events that change your probability estimates!
and present it as though someone told you that they rolled an even number, which would be a case in which you are genuinely gaining information about the past event.
And I think that's probably the core of the philosophical debate and why people try to connect this problem to anthropics. Many people genuinely think that there is something here that "updates" (or "changes" or something) their belief about a past event. This is a genuinely tricky question, and I'm not completely confident of my own perspective. I clearly lean toward just saying that they're separate mathematical objects, and you're not saying anything about changing your estimate of X when you make an estimate of Y. But tons of people want it to say something about changing their estimate of X and they present it with language that clearly indicates that they're trying to say something about changing their estimate of X.
I think that if you mostly agree with my presentation that you can simply cleave them apart and say something separate about X and Y, and that your estimate for Y doesn't necessarily have some temporally-bound back-implications for beliefs about X, then you're actually taking a particular philosophical position... one that I think a lot of thirders would disagree with. One that many of them (like yourself, frankly) would start off vehemently denying and claiming that it's just obvious mathematics that you're saying something about X.
ControlsFreak
8d ago
There are multiple examples of God, in the Bible, treating people as a class.
You are not God. God is not you.
But in any event, the biblical account of God also has multiple examples of God engaging differently with some individuals out of a class. These things are not trivial to just take one way or another.
ControlsFreak
8d ago
Yup. That's why I pair it with straps. I don't care to have to deal with bad calluses or hook grips or anything. Not competing; don't care. Like everything, it comes down to what your purpose is.
Observable Y. Satisfied?
Yes, thanks.
It should be obvious that, when you're asking Sleeping Beauty for a probability estimate, it's about her current state of knowledge.
...about observable Y, yes.
"number of answers" was @kky's language, not mine.
One which you embraced, saying that this was core to the field of probability:
Do you count getting a correct answer twice "more valuable" than getting it once?
Um, yes? The field of probability arose because Pascal was trying to analyze gambling, where you want to be correct more often in an unpredictable situation. If you're in a situation where you will observe heads 1/3 of the time, either you say the probability is 1/3, or you're wrong.
This was a significant component of why I entered this conversation in the first place.
Stated without any justification.
Uh... I need to spell out the obvious? There's nobody in your scenario that has 2/3 confidence that the coin flip was tails
This is simply asserting your conclusion. There is no justification here. There is absolutely someone who has a bet that has 2/3 confidence concerning the stated evaluation criteria. This is a pre-computed single decision and potentially queried multiple times, given all of the information prior to the event happening.
Let's make this simple. You say here:
there IS a mathematically correct theory of probability, if you just stick with axioms and theorems.
Then just do this. You claimed that this was as simple as P(X|I), as though someone told you that they rolled an even number. Now, you're telling me that you're estimating P(Y). Use the axioms and theorems to get from one to the other. Hopefully your next comment will "stick with" them.
If you're throwing out terms like "random variable" but you need me to walk you through this, then I'm sadly starting to suspect you're just trolling me.
I'm confident from my background and career that I will be able to evaluate your formal proof. Just start from, "There is a binary random variable X," and proceed formally.
EDIT: Consolidating this other bit here:
When people bring up the Monty Hall problem, do you go around telling THEM that probability is philosophically complex and gosh, how can they really know they should switch with 2/3 confidence? No? Then why is Sleeping Beauty different?
Monty Hall has zero problem showing how exactly information changes over time. Your policy is clearly closed-loop feedback, rather than pre-computed static (done so in a way solely for the purpose of a stated utility criterion, as in the casino example). There is no ambiguity concerning what quantity you are providing an estimator for.
EDIT EDIT: Let me put it another way. I think a person is completely justified in saying, "My credence that the coin originally came up (X) tails is 1/2, and because of that and my knowledge of the experimental setup, my probability estimate for what I will see if you show me the coin now (Y) is 2/3. In fact, if my credence that the coin originally came up (X) tails was 2/3, then because I know the experimental setup, my probability estimate for what I will see if you show me the coin now (Y) would be 4/5 (I believe)."
ControlsFreak
9d ago
Are you estimating observable X or observable Y? Just state this outright.
You can learn things about past events that change your probability estimates!
Are you learning something about observable X? Or are you simply providing a proper estimator for observable Y? I notice that you have now dropped any talk of "number of answers", which would have had, uh, implications here.
If I roll a die and then tell you it was even
Obviously, there are ways to gain information about an observable. In this case, we can clearly state that we are talking about P(X|I), where I is the information from you telling me. Be serious. Tell me if you think we're saying something about X or Y.
No one has told you anything, no information has been acquired, when your pre-computed policy is queried. Where are you getting the information from? It's coming entirely from the pre-defined problem set-up, which went into your pre-computation, just like in my casino example.
Your casino example is correct, but there's no analogue there to the scenario Sleeping Beauty finds herself in.
Stated without any justification.
If you'd like to fix it, imagine that you're one of two possible bettors (who can't see each other), and if the coin flip is heads then only one bettor (chosen at random) will be asked to bet. If it's tails, both will be. Now, when you're asked to bet, you're in Sleeping Beauty's situation, with the same partial knowledge of a past event.
I will say that this is not analogous with the same justification you gave for mine.
ControlsFreak
9d ago
Do you count getting a correct answer twice "more valuable" than getting it once?
Um, yes? The field of probability arose because Pascal was trying to analyze gambling, where you want to be correct more often in an unpredictable situation. If you're in a situation where you will observe heads 1/3 of the time, either you say the probability is 1/3, or you're wrong.
This is asking a subtly different question. Here, you're asking, "When woken, you will be told, I am going to create an observable by showing you the result of the coin flip. What do you think an appropriate probability for that observable is?"
That is, you have taken one random variable, X, describing the nature of the coin flip, itself, and applied a transformation to get a different observable, Y, describing the random variable that you may see when awoken. This Y has X in it, but it also has the day and whether you're awake in it.
It is not clear to me that the original problem statement clearly identifies which observable we're asking about or betting on.
If the problem statement unambiguously stated, "What is your probability for Y, the coin I am about to show you?" then indeed, you should be a thirder. Forms of the question like what are listed in the Wiki presentation of the 'canonical form', "What is your credence now for the proposition that the coin landed heads?" are far more linguistically ambiguous as to whether we are asking about X or Y. "Landed" is past-tense, which to me indicates that it's simply asking about the thing that happened in the past, which is observable X, rather than the thing that is about to happen in the future, which is observable Y. There's nothing meaningful in there about payoffs or number of answers or anything.
Next, I'd like to join criticism of both the "number of answers" explanation and:
you waking up gives you information that restricts you to three of them.
I think these are both flawed explanations, and I'll use one example alternative to explain.
Suppose you go to a casino. They say that either they have already flipped a coin or will flip a coin after you place a bet (I don't think it matters; you can't see it either way until after you bet). If the coin is heads, your bet will be simply resolved, but if the coin is tails, your bet will be taken as two identical bets. One can obviously compute the probabilities, the utilities, and calculate a correct wager, which would be the thirder wager. But in this case, everyone understands that they are not actually wagering directly on X, the direct probability of the coin flip. Nor are they making multiple separate "answers"; they are giving one answer, pre-computed at the beginning and simply queried in a static fashion. Likewise in the Sleeping Beauty problem; one is giving a single pre-computed answer that is just queried a different number of times depending.
It is also clear from this that there is no additional information from waking up or anything happening in the casino. You had all of the information needed at the initial time, about the Sleeping Beauty experimental set-up or about the structure of the casino's wager, when you pre-computed your one answer that would later be queried.
You just have to be very clear as to whether you're asking about X or Y, or what the actual structure of the casino game is for you to compute a utility. One you have that, it is, indeed, obvious. But I think your current explanations about number of answers or additional information from waking are flawed and that the 'canonical' language is more ambiguous.
ControlsFreak
10d ago
Nobody is trying to change the basic principles under which US military operates
I think this is the main and best claim. It is likely true, in my view. That said, the context of this thread is that @MadMonzer presented an opposite view. Your response was, expressly, a "side note" on the general topic of whether it matters where/how money comes to gov't purposes. I was responding to that. It's not really responsive to my comments to just go all the way back, pre-side-note, and have your claim really be that the whole original premise is just false, anyway, as a contingent factual matter.
I'm here to talk about why people would, in general and in theory, care about the topic of your side note. Notice that your side note was not in any way connected to any contingent, on-the-ground, facts about what Trump or his political opponents are currently doing or trying to do.
ControlsFreak
10d ago
I understand your perspective, but I don't see how this responded at all to my comment. You may think that the system is "broken" because your political opponents are leveraging their role in it against your preferred politician. Sure. I never contested that. I said something different, which I believe remains unaddressed.
ControlsFreak
11d ago
For a variety of government purposes, I probably wouldn't care all that much. For things like paying the military, it touches bad historical examples. At least part of the mess in Rome is attributable to individual generals slash political figures paying their armies effectively out of their own pocket. This not only breeds loyalty to an individual over the legitimacy of a system, but it also produced plenty of situations where the leader they were loyal to was making promises to pay them, only once they conquered some stuff and extracted loot (and political victory for the leader). It thus ties the military's individual remuneration directly to an individual political figure's political success.
IF one is not a total abolish-the-government libertarian/anarchist type and instead thinks that there is at least some value in having a democratic Constitutional system with civilian control of the military (yes, an extractive gang, but with some structure to try to align it), and CIVMIL relations that try to breed military loyalty primarily to said democratic Constitutional system rather than to the political success of individual political figures, then yeah, it's probably a good thing to have the foot soldiers be paid more by the abstract system and a formal process of the extractive gang as a whole rather than directly by particular extractive gang leaders.
I don't know that I agree. This is sort of a weird and arbitrary thing to try to maximize. I think plenty of effort has gone into messaging that marriage is a big, serious thing, shouldn't be entered into lightly, and really annoying for the State to unwind if it goes poorly. Plenty of States have processes that take some time and effort, in part so that they're not just maximally implementing all marriage requests, when they could be really rash and hastily/carelessly requested.
I don't buy this one, because I don't think many citizens want to care about some cousins getting married. It's a tiny portion of the population. I think plenty of citizens are perfectly fine just not letting them get married. That's a perfectly fine default. Most citizens think they probably shouldn't even be having sex in the first place! There's basically no point in even thinking about them getting married. There's almost certainly not a ton of folks clamoring to create some special process for this for apparently no reason other than some vague quantity maximization. In fact, I think most citizens don't even know that this sort of case exists! On first impression, I imagine plenty would be perfectly happy with just reverting to the default of 'you're cousins, so you don't get married'.
I don't see how that's the case, either. It doesn't make administration much easier to have such a tiny percentage of people having sex marginally getting married, especially not for some weird special case that most people disapprove of anyway. This would be a tiny tiny change in the numbers and almost certainly not worth the effort.
Yeah, I just don't see how there's "value" in them just getting married. Even if there was, then there seems to be little reason for the rigmarole of proving infertility. The biggest issue with your account is that there's just no reason for the rigmarole if they're just maximizing requested marriages implemented.
Instead, what I think is far more parsimonious is that the State is using marriage as an incentive. They know that there will be some cousins out there who want to be having sex and such. They can't just ban this. But they certainly don't want irresponsible, inbred procreation. So hey, Bob and Alice; you'd like to get married, right? Ya know what, Bob, if you just cut off your balls (or take some less drastic measure to ensure infertility), we'll let you get married. I think this is much more parsimonious than some vague quantity maximization, especially if they're going to go to the trouble to set up a whole process for this, with what are likely to be some necessarily complex rules (how exactly do you verify infertility, what is sufficient verification, etc.).
Would you disagree?
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