ControlsFreak
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User ID: 1422
ControlsFreak
1d 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
1d 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
2d 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
2d 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
2d 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
2d 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
3d 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
3d 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
4d 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
4d 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
5d 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.
ControlsFreak
6d ago
It says Idaho, so I looked up the Public Employee Retirement System of Idaho. They have a doc on Early Retirement. Looks like the fairly standard 'reductions depending on formula' business. One might quibble with the details, but it seems plausible. The base rate being 2% x [Years of Service] is pretty generous, but it looks like their rates are kinda steep. I don't have historical rates, but that particular awfulness has been a feature of essentially all public and private pension plans over the past century. At least it appears that when they're increasing contribution rates, they're doing it across the board, rather than something like, "You were hired thirty years ago, so you can still continue paying 1%, while everyone else has to pay 8%."
To a first approximation, it's not clear to me that they did better with the pension plan compared to just taking the cash and plowing it into the market. That seems to be pretty typical of most pension plans I've seen. A bit of a hit on return, but lower risk (the biggest risk being actually making it to retirement with them). Actually figuring out whether that tradeoff is a good deal for any particular individual/plan requires some details about the particular plan and, uh, assumptions.
I also did a few calculations concerning the $127k amount reported in the article. Given what's here about the Idaho pension, you again need some, uh, assumptions, but the ballpark numbers I get (including a discount for a woman's pay compared to a man's (not equal work) and a further discount for her having fewer years of working), the ballpark two-income high-3.5 household total seems at least plausible when you look at typical state salary public records. It doesn't appear to be likely that it's one of those situations where they scam out a half-mil of overtime right at the end to juice the pension.
I'm not particularly sad that I haven't done my entire career as an Idaho public employee. It doesn't seem like nearly as good of a scam as a whole host of other stuff. But then again, maybe he was a bad civil engineer and made terrible road designs that were no good for the people of Idaho; who knows?
ControlsFreak
8d ago
Everything in this comment is about the price of housing. The number. The aggregate number. So, we can kinda still discuss whether it should go up or down?
I agree that it can influence pay scales and such. I sort of fail to see how this matters? I don't see why this means that we can't just talk about the price of housing.
ControlsFreak
9d ago
Do you think it doesn't make sense to do this for any other product, either? Like, we can't talk about healthcare prices or education prices, or car prices, or apple prices, without discussing every other aspect of the economy? Or maybe it's that we must at least discuss wages to talk about apple prices? I'm really just not sure how I'm supposed to think about this.
ControlsFreak
9d ago
Best I can tell, this is just a less specific version of the response that @disk_interested gave, which was followed up by agreeing that if we hold wages constant for a conversation about the price of housing, then it just cashes out as saying that the aggregate number for the price of housing should go down. Should I be interpreting it differently?
ControlsFreak
10d ago
Deadlift is four plates, not yet five. At my size, that's not bad, but yeah, I'm not looking to set world records. In my current gym, at the time that I go, I'm definitely lifting more than everyone else, but that's more of a function of the current gym/time. I've certainly had prior gyms with legitimately huge dudes putting up ridiculous numbers.
It's not that I couldn't manage without them. It's just annoying, and it's not the main point of doing those things. If you're competing, then yeah, it's part of the deal to deal with the annoyance. Apparently, even for top competitors, there's a relatively definable "class" of "grip-limited deadlifters". I remember the Stronger By Science folks talking about this. It's apparently an annoyance to their sensibilities, too. They said that they would like to just have a category for deadlifts with straps; just take the grip out of it and see what people's major muscles can do. Nobody likes a hook grip.
Not sure on hand size. My current gym has one Rogue bar (I can't remember which exact model) that I swear feels noticeably thinner than the others (I haven't yet taken a micrometer to the gym). I prefer it for deadlifting, but anti-prefer it for bench/OHP.
ControlsFreak
10d ago
The thing is, though, I think if you simply reword what they're saying in this way: "So, uh, you want the aggregate number for the price of housing to go down?" you are unlikely to get a simple "yes". They also want other things, don't know how to process it, and likely do not have a coherent position.
ControlsFreak
10d ago
In this case, I think that if we hold wages constant for the conversation about the price of housing, what distinguishes this from what I think the summary of it is: the aggregate number for the price of housing should go down?
ControlsFreak
10d ago
I just use straps for deadlifts, and many other pulling motions, for that matter. Don't at me; I ain't competing. I set up my grip "in the fold", between the bottom pads of the fingers and the palm. The calluses never really get all that bad.
Much words have been said about how people bury incoherence in the phrase "affordable housing". What do you think it means?
ControlsFreak
11d ago
You may not like the latter, but fear of it is clearly part of the reason for the strategy. Note the very first words from him when he began his justification:
The government funds a good chunk to most of the residency spots
This is hiding that the industry is playing games here. I described the game here:
"We won't train doctors to the regulatory standard unless taxpayers give us bundles of money to do so," is an obvious confluence of terrible interests in the private sector and government, especially when the industry has achieved significant amounts of regulatory capture. Surely, there is a better way.
Imagine this in other industries. Grocery stores get the government to set up a licencing requirement to stock shelves, with some boilerplate reasoning about food safety or something. The thing is, the only way to get licensed is to get a grocery store to give you the mandatory years of experience. And, of course, they refuse to have such positions unless the government pays them for it. I would predict that there would be fewer grocery store employees, their pay would be higher, industry profits would be higher, government outlays would be higher, prices to the consumer would be higher, and service quality would decrease.
The kicker is that the industry gets to choose the regulatory standards to boot. I completely agree that there are going to be some standards. In my follow-up comment, I make comparisons to how we see similar problem when universities control their own accreditation standards and leave a related thought experiment for grocery stores:
Let's put it this way - perhaps there is a "right" level of training for doctors, and perhaps there is a "right" level of training for grocery stores. Maybe the latter is much smaller than the former. Now, imagine we set up the system I described in my last comment for grocery store training. Do you think their incentives would lead to them selecting the "right" level of training?
If they successfully restricted supply, you'd see the same sort of situation where there are desirable/undesirable locales for grocery store workers, and you could imagine the same sort of ignorant-acting pleading that oh it's just not their fault that everyone wants to work in the fancy grocery stores in the cities; I guess your only choice is to raise salaries (please ignore the licensing regime).
You see the exact same self-dealing that you see in other industries that get this sort of sweetheart deal over their own regulatory apparatus, as I described here. In that comment, I was discussing Alex Tabarrock reviewing Rebecca Haw Allensworth's book "The Licensing Racket". I later saw an interview with her and discussed it here. All these industries that control their own regulatory apparatus display the same phenomenon. When it comes to actually enforcing standards on their own, the people who are part of their club, it's, "Meh. Maybe we'll get around to it." (There are horror stories.) But when it comes to shutting out competition, the tone changes entirely, and it's alllll about their supposed standards. (There are horror stories here, too.) Alex describes the phenomenon in the medical industry thus:
No system is perfect, but Ms. Allensworth’s point is that the board system is not designed to protect patients or consumers. She has a lot of circumstantial evidence that signals the same conclusion. The National Practitioner Data Bank (NPDB), for example, collects data on physician misconduct and potential misconduct as evidenced by medical-malpractice lawsuits. But “when Congress tried to open the database to the public, the [American Medical Association] ‘crushed it like a bug.’”
One of the most infuriating aspects of the system is that the AMA and the boards limit the number of physicians with occupational licensing, artificially scarce residency slots and barriers preventing foreign physicians from practicing in the U.S. Yet when a physician is brought before a board for egregious misconduct, the AMA cites physician shortage as a reason for leniency. When it comes to disciplining bad actors, the mantra seems to be that “any physician is better than no physician,” but when it comes to allowing foreign-trained doctors to practice in the U.S., the claim suddenly becomes something like “patient safety requires American training.”
I'm generally not super high on game-playing with residency slots - or even shutting out foreign doctors - being a huge factor in overall medical costs; they're probably factors, but probably not big ones. I just get annoyed at the games being played and the fractal bad justifications offered. He once offered this data to claim that there is a "surplus" of residency slots. I didn't think the data presented supported the claim, and I think he's refrained from making that exact claim anymore, instead just still demanding (while thinking nothing of it, like it's totally normal) government-funding for all training slots (that they control) and repeating that there are still some unmatched slots. I think the alternate explanation that there will always be frictions and that an increase in slots will probably still result in about the same amount of unfilled slots within some range is probably still at least as plausible.
You do very well to notice that doctors are not special in that economics still holds for them. Don't let him convince you that the same incentive problems we see in every other industry that has similar control over their own regulatory apparatus somehow don't apply to doctors as well. I argue very similar phenomena in other industries, universities, realtors, etc. Each domain does have some unique twists, but many of the basics are similar if you understand economics and incentives.
ControlsFreak
12d ago
It sounds like you're also interested in context long before the modern era. For that, probably the most important thing to check out is the debate over the Apportionment Act of 1842. Before then, plenty of states used "general tickets". I can't describe it any better than here:
Under this system, voters could cast as many votes as there were seats to be filled in each state, while voting for each candidate only once. In practice, this typically led to voters selecting each candidate on a slate provided by a political party. Proponents argued this method led to more cohesive party delegations, and states that used general tickets almost uniformly sent single-party delegations to Congress.
In 1842, Congress mandated that the states create districts for federal congressional representatives sent to the House. Thus almost inherently requiring some form of redistricting. If you don't make adjustments over time, you almost surely end up with "rotten boroughs" over time, not unlike what was described by the Reynolds v. Sims wiki article @Lewis2 linked:
for example, in the Nevada Senate, the smallest district had 568 people, while the largest had approximately 127,000 people.
That's unlikely to be politically tenable really long-term, so the main questions become who does it, how often do they do it, and what rules do they have to follow when doing it. Even if you want to say, "We're just not going to do it and keep the same districts forever," you're likely to still do it eventually, just when it becomes so politically untenable that you end up with a crisis, as in the Historia Civilis video concerning Britain. And of course, since it's so hard to find durable political compromises that extend well over time concerning those three main questions, we also ended up with judicial meddling in the process.
Districting in general is A Hard Problem.
ControlsFreak
12d ago
The vast majority of normies (and probably still a majority of non-normies) lack a coherent answer to the simple question, "Should housing be more expensive or cheaper?" They want too many different competing things from one aggregate number.
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.
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