Today I noticed that Harry is dealing with a lot of strikingly rational people compared to canon and it feels wrong. We can understand this because we know that Eliezer’s subscribes to the first law of fan fiction (“You can’t make Frodo a Jedi without giving Sauron the Death Star”) but it seems that in this respect MoR is actually much less plausible than canon unless the “implicit demography” has been changed somehow. Its like the gold/silver exchange rate in canon… except this is brains.
Given a normally distributed trait (like intelligence?) the larger the population, the more spectacular you should expect the maximal outlier to be. And you shouldn’t expect lots of similar outliers unless their production was non-linearly explained (like a bunch of students taught by a singularly great teacher or something). The smartest person in a village of 1000 is going to be (literally) “1 in a 1000” compared to the smartest person in China who is going to be (again literally) “1 in a billion”. So those sorts of intuitions had me wondering about population sizes.
I googled it and came up with data and speculation. Roughly, it looks like Magical Britain (MB) has a population between 800 and 30,0000 with a median expectation somewhere around 5,000 depending on things like how many students are in Hogwarts (40/yr to 140/yr), whether Rowling’s numerically implausible media pronouncements are to be taken seriously, whether everyone in MB really goes to Hogwarts, what the life expectancy is, and what the age pyramid is like due to murder and tribal warfare and magical diseases and so on.
Once I’m calibrated this way, and I look for size-equivalent institutions, the “Ministry of Magic” starts sounding to me like like the “Small Town Chamber of Commerce of Magic” and the “Hogwarts School of Witchcraft and Wizardry” should be expected to work much more like an ordinary high school (tropes link tongue in cheek).
This contextual re-calibration makes it even more obvious that Rowling was (forgivably) pretending that the people at the top of a very tiny wizarding world would have anything like the political sophistication and infrastructure of the muggle world in order to say something meaningful about the muggle world by analogy.
A ministry with many departments makes me think of large buildings with complex hierarchies like in London or Washington DC or Beijing. In canon, the ministry can be similar to a modern government and enable the author to comment on non-fictional governments and the sociopolitical critique of reality can work symbolically and who cares about the sociology in a story for ten year olds :-)
But if the authorial physics changes (as per MoR) and analytical thinking is asserted to have some kind of mechanical reality in which to gain traction, then the wizarding world makes me think of, perhaps, a medium to large college campus. It could probably be run with a single office where anyone can stand in line for 30 minutes to see one of about 5 to 50 admins to personally get their stuff straightened out directly or to make an appointment to talk to the president of the school if something really unusual comes up. Obviously it wouldn’t be a fee-for-service arrangement the way a school is, but I wouldn’t expect the admin:student ratio to need to be that far off of the bureaucrat:citizen ratio of Magical Britain.
Following the re-calibrating further… Hogsmeade might contain 10% to 50% of the wizarding population… Why doesn’t Hogsmeade have one elected sheriff with a handful of deputies, with Diagon Alley similarly protected, and then just be done with it? And what are all these appointed “Aurors” running around for? Is Magical Britain some kind of “totalitarian police village” or something?
Rita Skeeter probably isn’t (or in MoR, wasn’t) truly similar to a professional journalist in a “large news organization” that was so big to create institutional anonymity and strategically deploy tabloid tactics and so on. People are generally more polite in small towns because reputation matters a lot more than in cities. The newspapers are more “yay for our pancake fundraiser and boo for littering” than malicious gossip rags. Its almost plausible (following the “small town” economic insight) that Rita may have been the only journalist in magical Britain (other than Luna’s farther, if you count him).
And politics wouldn’t need to work by mass-media-spread ideological PR in Magical Britain. You could just write 10 letters per day, five days a week, and wander around Hogsmeade or Diagon alley on the weekends, and after 25 weeks you’d probably have had direct personal contact with the bulk of the adult population who cared to involve themselves in group decision making. Simple, easy, done. We’re talking about a civilization way smaller than Athens, and look how big an impact Socrates appears to have had by wandering around talking to people!
In this light, all the trappings of muggle government kinda start to look like a cargo cult. The politics around who runs Hogwarts starts to look kind of pitiful… like a sociopathically deranged PTA squabble. And what happens if Harry notices this stuff? And comments on it to Hermione and explore the implications? And then insert “some explanation” that shows why the ministry is actually necessary (rather than a cargo cult) and have “whatever the need is” become a vivid plot mechanism?
In Chapter 36 Harry compares the world of muggles to a third world country relative to the wizarding world. Magic appears to be so powerful that this is true in some sense… but its pretty weird if they appear to be the one’s with cargo cult versions of our political institutions...
And in the meantime, it really seems to make “Voldemort’s Deathstar” (that is, his general rational turbocharge and massive preparation for conquering several thousand people) look really silly to me, because it is such overkill. If Voldemort really wanted political power over Magical Britain, and was being simply rational about it, and MB is little more than a two or three small villages… then why not apply social psychology to winning the hearts and minds of a bunch of unsophisticated “magical rubes” in a local election and just be done with it?
Which gets me back around to Harry, boy genius, and all the people he’s interacting with in tiny little Magical Britain who have also somehow gotten rationality super powers. Maybe someone needs to plot wizard IQs and notice the weird bi-modal distribution caused by all the people just a bit less smart than Harry so he has people with whom to interact and thereby create a compelling story?
Maybe I’m overconfident in my ability to connect numerical population models with lived socio-political realities, but I’m thinking this is probably just me being more confused by fiction than by reality.
Wizards must inherently be much more intelligent than Muggles.
The Wizard government is insanely bureaucratic.
The first point is ignored in canon, but ought to be noticed by Harry in MoR. This makes it even more in need of explanation that Wizards never noticed the Enlightenment (or never had it themselves much earlier). The interesting possibility is that they did have it, and the Methods of Rationality have long been actively suppressed for some reason.
In contrast, the second point seems to be well recognised in canon. Besides all of the off-hand references to silly regulations (flying carpets, anybody?), the Ministry seems to account for around half of the adult employment, and well over half of the employment of intelligent people. All three of the main characters went to work for the Ministry in the epilogue, with Hermione having two Ministry careers in succession. Outside of Hogwarts (which is only somewhat independent of the government, like the BBC), the Ministry is the only source of high-class professional careers in Wizarding Britain. (I don’t count Gringott’s, because it is an international Goblin-run concern, although Bill Weasley worked there in canon. Now that I think of it, both Bill and Charlie Weasley left the country to find good careers, so maybe Britain suffers from this more than other countries do.)
Is Magical Britain some kind of “totalitarian police village” or something?
When Grindelwald was setting up his Muggle puppet states, he wasn’t trying to be evil; he was just doing what comes naturally to a Wizard.
It’s clear that magic must carry with it a fairly different psychology—not just (nonlinear, bimodal) changes to the level of general intelligence, but differences of personality as well.
The question is, can we coherently analyze what the Wizarding psychology looks like?
Yeah, I was thinking maybe the “world level” issue could be defense: perhaps witches spend 90% of their time on self defense in a state of nature and so a government that only uses 60% of the economy is a net good deal? It seems like this would necessitate magical mechanisms that make it easy to spread “generic safety” but hard to limit coverage to free riders. If such dynamics don’t “fall out” of magical physics, it should raise an additional flag.
I hadn’t thought of the Labour affiliation on the “author level”. I’d been thinking maybe it was just easy to ignore incompatibilities of this sort because of near/far dichotomies—its easy to pretend “famous people” are inhuman beings whose exalted struggles can not be truly influenced by “we mortals”.
I think the Labour insight is a better theory because it makes more concrete predictions about the symbolic level. If Rowling wants a story that teaches her kids to favor political wealth redistribution it predicts lots of specific details about what to expect in the “political realm” (many of which seem true of her story), rather than just to predict that the politics will be inconsistent with the near mode.
Ooh! Idea! Applying this insight to Eliezer himself (because it was his characters acting funny that got me on the track of the population size in the first place) …
Earlier, I didn’t think time travel prime factorization would work because Eliezer is writing about rationality rather than time travel. If time travel was too easy the rationality would lose center stage. But since then I haven’t been using the supported theory to predict other things…
The didactic function of MoR means that Eli has to tie up the lose end of Voldemort at some point, and it should be really dramatic and cool ending because otherwise the story loses its aura of awesome and the rationality lessons suffer by proximity. In the meantime, it seems like awareness that one is living in a story explains magical physics and other discrepancies like those related to the population size...
So my over-specific prediction is that evidence is going to build up for a while until Eliezer has room to impart all the lessons to the readers that he thinks are sufficient to make his political case (utilitarian ethics, scope insensitivity, simplified humanism, politics is the mindkiller, maybe “insight cascades” since they are critical to his theory about the singularity?). Then Harry figures out that he’s in a story, necessarily immediately , but the end means “no more lessons” so the end and the amount of teaching have to be synced and genre-awareness could help the ending be awesome.
The “I’m in a story” insight and a super amazing trick or two that grow out of it (unknown at this point, but Eliezer is clever), are being saved up for the fight against Voldemort at the end, with the insight coming after Harry and Voldemort have a falling out (unless Harry’s true task is to redeem Voldemort, rather than defeat him).
Its quite possible that the falling out could actually precipitate the insight, because in point of fact, Voldemort’s Deathstar almost certainly exists to make the story interesting, rather than because it’s necessary to conquer Magical Britain. When Harry finds out his enemy is also his favorite teacher who has even more super powers than he thought, this is more evidence that Harry is in a story.
So it would be good timing all around to have Voldemort be revealed and reality fall apart when all the lessons are done or in sight of being done.
The “I’m in a story” insight and a super amazing trick or two that grow out of it (unknown at this point, but Eliezer is clever)
I was hoping Eliezer wouldn’t go there since it would seem rather trite. But thinking about how it would relate to the subject matter it does have some potential. A suitable lesson would come if it was actually Voldemort who figured out where he was. He would then solve the “Dark Lord in a Box” problem, break out by hacking a reader, leveraging the intellectual capacity of the author to give the hacked reader the ability to create an AI capable of extracting Voldemort’s volition. By that mechanism Voldemort would then take control of the cosmic commons of the “1 level up” reality.
Obviously the “1 level up” reality couldn’t be this one. Because that requires that Eliezer (or a combination of Eliezer and the hacked reader) solve both the Friendliness and General Artificial Intelligence problems. (Where ‘Friendly’ is ′ to Voldemort’.)
, are being saved up for the fight against Voldemort at the end, with the insight coming after Harry and Voldemort have a falling out (unless Harry’s true task is to redeem Voldemort, rather than defeat him).
Better yet would be if Harry continues to defy the usual form of fiction and not define himself in terms of an enemy. He has his own goal of universe optimisation and Voldemort doesn’t actually need to be a big part in that for good or ill.
Oh man, I hadn’t thought of Quirellmort as a sentient being running under a layer of emulation with a goal to escapes from its emulation layer. I’m imagining some kind of crazy moral principle here like “Though shalt not emulate sentient beings capable of becoming metaphysically meta-aware.”
If Quirellmort found out that we were all muggles, would he even want to escape if he couldn’t be a dark wizard up here? Maybe he wouldn’t see us as muggles if he remained focused on the way we have “god level access” to his “plot physics” by virtue of our ability to communicate with Eliezer?
I don’t know if it would be horrifying or amusing if he managed to escaped into our world… and then turned around and started writing novels about civilizations with 10^50 slaves in thrall to an obvious author insert :-P
I don’t think Hogwarts is supposed to be the only wizarding school in Magical Britain. It’s referred to on a number of occasions as the “best”, never the “only”.
Hogwarts does seem to have some fairly incompetent students, but HP canon makes it pretty clear that the wizarding population has plenty of incompetent adults, so there’s plenty of room at the bottom. Less capable students (such as Crabbe and Neville) probably get in due to family connections, while muggle born students may have some sort of affirmative action initiative going on for them (think how disadvantaged they already are, having no family at all in the world they’re going to inhabit, on top of discrimination from the higher classes.)
Since Hogwarts is the premier school of Magical Britain, it’s not surprising if the most important and/or successful individuals in Magical Britain were mostly educated there, but we do not know that more than a small fraction of all the various wizarding adults who appear in the series outside the school were educated there. It also makes sense if the administration of Hogwarts is taken particularly seriously by the government, since field and government leaders disproportionately graduate there.
I’ve always figured canon Magical Britain to have a population of perhaps 3-600,000 (although I believe Harry speculates a smaller number in HPMoR.) I also figured that they have a disproportionate amount of the population in government positions because governing the wizarding world is much more complicated than governing a similar population of muggles. Magic provides each trained wizard with far more varied and creative ways to cause trouble than an ordinary muggle (imagine if every person in a First World country had access to a set of fully equipped and funded university laboratories, with at least basic understanding of how to use them. Even the least dangerously creative individuals would have access to poison and explosives. Wizards are more troublesome than that.) They also have to manage all sorts of magical creatures (dragons, manticores, etc.,) which as Hagrid proves can even be cross bred in danerous and unpredictable ways. And they’re sitting on top of a bunch of weird and potentially dangerous mysteries which the regular population can’t be trusted with (the Death Portal, research of time magic, prophesies, and so on.) And to top it all off, they have to keep all of this secret from the muggle population. A governing body in the same relative proportion to the population as we have in the muggle world couldn’t possibly manage all of that.
Quirrel and Harry are clearly both outliers in the Wizarding World with respect to intelligence, but considering the outlets that every individual in the wizarding world has at their disposal, it wouldn’t be surprising if their culture and education tended to develop more creative and original thinkers.
I also only just noticed that the comment I’m replying to was posted two years ago yesterday, not yesterday.
Today I noticed that Harry is dealing with a lot of strikingly rational people compared to canon and it feels wrong. We can understand this because we know that Eliezer’s subscribes to the first law of fan fiction (“You can’t make Frodo a Jedi without giving Sauron the Death Star”) but it seems that in this respect MoR is actually much less plausible than canon unless the “implicit demography” has been changed somehow. Its like the gold/silver exchange rate in canon… except this is brains.
Given a normally distributed trait (like intelligence?) the larger the population, the more spectacular you should expect the maximal outlier to be. And you shouldn’t expect lots of similar outliers unless their production was non-linearly explained (like a bunch of students taught by a singularly great teacher or something). The smartest person in a village of 1000 is going to be (literally) “1 in a 1000” compared to the smartest person in China who is going to be (again literally) “1 in a billion”. So those sorts of intuitions had me wondering about population sizes.
I googled it and came up with data and speculation. Roughly, it looks like Magical Britain (MB) has a population between 800 and 30,0000 with a median expectation somewhere around 5,000 depending on things like how many students are in Hogwarts (40/yr to 140/yr), whether Rowling’s numerically implausible media pronouncements are to be taken seriously, whether everyone in MB really goes to Hogwarts, what the life expectancy is, and what the age pyramid is like due to murder and tribal warfare and magical diseases and so on.
Once I’m calibrated this way, and I look for size-equivalent institutions, the “Ministry of Magic” starts sounding to me like like the “Small Town Chamber of Commerce of Magic” and the “Hogwarts School of Witchcraft and Wizardry” should be expected to work much more like an ordinary high school (tropes link tongue in cheek).
This contextual re-calibration makes it even more obvious that Rowling was (forgivably) pretending that the people at the top of a very tiny wizarding world would have anything like the political sophistication and infrastructure of the muggle world in order to say something meaningful about the muggle world by analogy.
A ministry with many departments makes me think of large buildings with complex hierarchies like in London or Washington DC or Beijing. In canon, the ministry can be similar to a modern government and enable the author to comment on non-fictional governments and the sociopolitical critique of reality can work symbolically and who cares about the sociology in a story for ten year olds :-)
But if the authorial physics changes (as per MoR) and analytical thinking is asserted to have some kind of mechanical reality in which to gain traction, then the wizarding world makes me think of, perhaps, a medium to large college campus. It could probably be run with a single office where anyone can stand in line for 30 minutes to see one of about 5 to 50 admins to personally get their stuff straightened out directly or to make an appointment to talk to the president of the school if something really unusual comes up. Obviously it wouldn’t be a fee-for-service arrangement the way a school is, but I wouldn’t expect the admin:student ratio to need to be that far off of the bureaucrat:citizen ratio of Magical Britain.
Following the re-calibrating further… Hogsmeade might contain 10% to 50% of the wizarding population… Why doesn’t Hogsmeade have one elected sheriff with a handful of deputies, with Diagon Alley similarly protected, and then just be done with it? And what are all these appointed “Aurors” running around for? Is Magical Britain some kind of “totalitarian police village” or something?
Rita Skeeter probably isn’t (or in MoR, wasn’t) truly similar to a professional journalist in a “large news organization” that was so big to create institutional anonymity and strategically deploy tabloid tactics and so on. People are generally more polite in small towns because reputation matters a lot more than in cities. The newspapers are more “yay for our pancake fundraiser and boo for littering” than malicious gossip rags. Its almost plausible (following the “small town” economic insight) that Rita may have been the only journalist in magical Britain (other than Luna’s farther, if you count him).
And politics wouldn’t need to work by mass-media-spread ideological PR in Magical Britain. You could just write 10 letters per day, five days a week, and wander around Hogsmeade or Diagon alley on the weekends, and after 25 weeks you’d probably have had direct personal contact with the bulk of the adult population who cared to involve themselves in group decision making. Simple, easy, done. We’re talking about a civilization way smaller than Athens, and look how big an impact Socrates appears to have had by wandering around talking to people!
In this light, all the trappings of muggle government kinda start to look like a cargo cult. The politics around who runs Hogwarts starts to look kind of pitiful… like a sociopathically deranged PTA squabble. And what happens if Harry notices this stuff? And comments on it to Hermione and explore the implications? And then insert “some explanation” that shows why the ministry is actually necessary (rather than a cargo cult) and have “whatever the need is” become a vivid plot mechanism?
In Chapter 36 Harry compares the world of muggles to a third world country relative to the wizarding world. Magic appears to be so powerful that this is true in some sense… but its pretty weird if they appear to be the one’s with cargo cult versions of our political institutions...
And in the meantime, it really seems to make “Voldemort’s Deathstar” (that is, his general rational turbocharge and massive preparation for conquering several thousand people) look really silly to me, because it is such overkill. If Voldemort really wanted political power over Magical Britain, and was being simply rational about it, and MB is little more than a two or three small villages… then why not apply social psychology to winning the hearts and minds of a bunch of unsophisticated “magical rubes” in a local election and just be done with it?
Which gets me back around to Harry, boy genius, and all the people he’s interacting with in tiny little Magical Britain who have also somehow gotten rationality super powers. Maybe someone needs to plot wizard IQs and notice the weird bi-modal distribution caused by all the people just a bit less smart than Harry so he has people with whom to interact and thereby create a compelling story?
Maybe I’m overconfident in my ability to connect numerical population models with lived socio-political realities, but I’m thinking this is probably just me being more confused by fiction than by reality.
I’m drawing two conclusions from your analysis:
Wizards must inherently be much more intelligent than Muggles.
The Wizard government is insanely bureaucratic.
The first point is ignored in canon, but ought to be noticed by Harry in MoR. This makes it even more in need of explanation that Wizards never noticed the Enlightenment (or never had it themselves much earlier). The interesting possibility is that they did have it, and the Methods of Rationality have long been actively suppressed for some reason.
In contrast, the second point seems to be well recognised in canon. Besides all of the off-hand references to silly regulations (flying carpets, anybody?), the Ministry seems to account for around half of the adult employment, and well over half of the employment of intelligent people. All three of the main characters went to work for the Ministry in the epilogue, with Hermione having two Ministry careers in succession. Outside of Hogwarts (which is only somewhat independent of the government, like the BBC), the Ministry is the only source of high-class professional careers in Wizarding Britain. (I don’t count Gringott’s, because it is an international Goblin-run concern, although Bill Weasley worked there in canon. Now that I think of it, both Bill and Charlie Weasley left the country to find good careers, so maybe Britain suffers from this more than other countries do.)
When Grindelwald was setting up his Muggle puppet states, he wasn’t trying to be evil; he was just doing what comes naturally to a Wizard.
It’s clear that magic must carry with it a fairly different psychology—not just (nonlinear, bimodal) changes to the level of general intelligence, but differences of personality as well.
The question is, can we coherently analyze what the Wizarding psychology looks like?
Maybe with magic giving each wizzard much more destructive power, a higher degree of regulation is required.
Or maybe it was just JK Rowling’s Labour affiliations showing through.
Yeah, I was thinking maybe the “world level” issue could be defense: perhaps witches spend 90% of their time on self defense in a state of nature and so a government that only uses 60% of the economy is a net good deal? It seems like this would necessitate magical mechanisms that make it easy to spread “generic safety” but hard to limit coverage to free riders. If such dynamics don’t “fall out” of magical physics, it should raise an additional flag.
I hadn’t thought of the Labour affiliation on the “author level”. I’d been thinking maybe it was just easy to ignore incompatibilities of this sort because of near/far dichotomies—its easy to pretend “famous people” are inhuman beings whose exalted struggles can not be truly influenced by “we mortals”.
I think the Labour insight is a better theory because it makes more concrete predictions about the symbolic level. If Rowling wants a story that teaches her kids to favor political wealth redistribution it predicts lots of specific details about what to expect in the “political realm” (many of which seem true of her story), rather than just to predict that the politics will be inconsistent with the near mode.
Ooh! Idea! Applying this insight to Eliezer himself (because it was his characters acting funny that got me on the track of the population size in the first place) …
Earlier, I didn’t think time travel prime factorization would work because Eliezer is writing about rationality rather than time travel. If time travel was too easy the rationality would lose center stage. But since then I haven’t been using the supported theory to predict other things…
The didactic function of MoR means that Eli has to tie up the lose end of Voldemort at some point, and it should be really dramatic and cool ending because otherwise the story loses its aura of awesome and the rationality lessons suffer by proximity. In the meantime, it seems like awareness that one is living in a story explains magical physics and other discrepancies like those related to the population size...
So my over-specific prediction is that evidence is going to build up for a while until Eliezer has room to impart all the lessons to the readers that he thinks are sufficient to make his political case (utilitarian ethics, scope insensitivity, simplified humanism, politics is the mindkiller, maybe “insight cascades” since they are critical to his theory about the singularity?). Then Harry figures out that he’s in a story, necessarily immediately , but the end means “no more lessons” so the end and the amount of teaching have to be synced and genre-awareness could help the ending be awesome.
The “I’m in a story” insight and a super amazing trick or two that grow out of it (unknown at this point, but Eliezer is clever), are being saved up for the fight against Voldemort at the end, with the insight coming after Harry and Voldemort have a falling out (unless Harry’s true task is to redeem Voldemort, rather than defeat him).
Its quite possible that the falling out could actually precipitate the insight, because in point of fact, Voldemort’s Deathstar almost certainly exists to make the story interesting, rather than because it’s necessary to conquer Magical Britain. When Harry finds out his enemy is also his favorite teacher who has even more super powers than he thought, this is more evidence that Harry is in a story.
So it would be good timing all around to have Voldemort be revealed and reality fall apart when all the lessons are done or in sight of being done.
I was hoping Eliezer wouldn’t go there since it would seem rather trite. But thinking about how it would relate to the subject matter it does have some potential. A suitable lesson would come if it was actually Voldemort who figured out where he was. He would then solve the “Dark Lord in a Box” problem, break out by hacking a reader, leveraging the intellectual capacity of the author to give the hacked reader the ability to create an AI capable of extracting Voldemort’s volition. By that mechanism Voldemort would then take control of the cosmic commons of the “1 level up” reality.
Obviously the “1 level up” reality couldn’t be this one. Because that requires that Eliezer (or a combination of Eliezer and the hacked reader) solve both the Friendliness and General Artificial Intelligence problems. (Where ‘Friendly’ is ′ to Voldemort’.)
Better yet would be if Harry continues to defy the usual form of fiction and not define himself in terms of an enemy. He has his own goal of universe optimisation and Voldemort doesn’t actually need to be a big part in that for good or ill.
Oh man, I hadn’t thought of Quirellmort as a sentient being running under a layer of emulation with a goal to escapes from its emulation layer. I’m imagining some kind of crazy moral principle here like “Though shalt not emulate sentient beings capable of becoming metaphysically meta-aware.”
If Quirellmort found out that we were all muggles, would he even want to escape if he couldn’t be a dark wizard up here? Maybe he wouldn’t see us as muggles if he remained focused on the way we have “god level access” to his “plot physics” by virtue of our ability to communicate with Eliezer?
I don’t know if it would be horrifying or amusing if he managed to escaped into our world… and then turned around and started writing novels about civilizations with 10^50 slaves in thrall to an obvious author insert :-P
I don’t think Hogwarts is supposed to be the only wizarding school in Magical Britain. It’s referred to on a number of occasions as the “best”, never the “only”.
Hogwarts does seem to have some fairly incompetent students, but HP canon makes it pretty clear that the wizarding population has plenty of incompetent adults, so there’s plenty of room at the bottom. Less capable students (such as Crabbe and Neville) probably get in due to family connections, while muggle born students may have some sort of affirmative action initiative going on for them (think how disadvantaged they already are, having no family at all in the world they’re going to inhabit, on top of discrimination from the higher classes.)
Since Hogwarts is the premier school of Magical Britain, it’s not surprising if the most important and/or successful individuals in Magical Britain were mostly educated there, but we do not know that more than a small fraction of all the various wizarding adults who appear in the series outside the school were educated there. It also makes sense if the administration of Hogwarts is taken particularly seriously by the government, since field and government leaders disproportionately graduate there.
I’ve always figured canon Magical Britain to have a population of perhaps 3-600,000 (although I believe Harry speculates a smaller number in HPMoR.) I also figured that they have a disproportionate amount of the population in government positions because governing the wizarding world is much more complicated than governing a similar population of muggles. Magic provides each trained wizard with far more varied and creative ways to cause trouble than an ordinary muggle (imagine if every person in a First World country had access to a set of fully equipped and funded university laboratories, with at least basic understanding of how to use them. Even the least dangerously creative individuals would have access to poison and explosives. Wizards are more troublesome than that.) They also have to manage all sorts of magical creatures (dragons, manticores, etc.,) which as Hagrid proves can even be cross bred in danerous and unpredictable ways. And they’re sitting on top of a bunch of weird and potentially dangerous mysteries which the regular population can’t be trusted with (the Death Portal, research of time magic, prophesies, and so on.) And to top it all off, they have to keep all of this secret from the muggle population. A governing body in the same relative proportion to the population as we have in the muggle world couldn’t possibly manage all of that.
Quirrel and Harry are clearly both outliers in the Wizarding World with respect to intelligence, but considering the outlets that every individual in the wizarding world has at their disposal, it wouldn’t be surprising if their culture and education tended to develop more creative and original thinkers.
I also only just noticed that the comment I’m replying to was posted two years ago yesterday, not yesterday.
Were you maybe looking for this?
I linkhopped from there, and then left the computer and forgot that what I had open was a past discussion.