Karkat's opinion of his own abilities vacillates wildly between overestimating and underestimating, but deep down he knows what things he is actually incapable of doing because he isn't smart enough and tends to avoid them, so I would say on the balance he actually underestimates it. Not that you would get that impression from listening to him talk, most of the time.
I think Emcee does? He's confident in all his strong points, but when it comes to things he's not familiar with, he defers to other people's expertise to the point of self-deprecation. He always displays interest or a willingness to learn, though, even if the subject matter goes over his head. Depending on the situation and the person (usually a potential john), he might even play up the dumb bimbo type and allow people to underestimate him (most people do, anyway).
My instinct was to say HAHAHA NO, which is... sort of true. He knows he's not a brilliant tactician or critical thinker, but also can't help but feel his skills in those areas have been underestimated, which... isn't really accurate.
Gene - yesssss. Sort of. I mean, he knows he's smarter than he lets on. He also knows - or is forced to see, by Sam and Alex - that there are massive gaps in his knowledge, stuff that he's never cared to learn. But he knows he can learn, and quite easily, he's just a stubborn bastard that doesn't like change.
Javert - is a tough one, because it's both yes and no. He knows he has virtually no schooling, and reads so that he won't be entirely illiterate. He will never be book-smart. On the other hand, he knows policing chapter and verse, so I think he's - and knows he has - just found his Thing with policing, and is very good at it (for a given value of good: what I mean is, he carries out the job exactly as the rules say it should be done). He doesn't consider himself intelligent in any other area, and he is correct.
Valjean - no. He's smarter than he gives himself credit for. He did dare to acknowledge that he was doing a good job as mayor of Montreuil, and then quickly believed in the folly of thinking anything good about himself when the opportunity presented itself. He didn't learn to read until he was forty, but educated himself from books thereafter - he certainly has the capacity to learn, and a desire for it, but he'll never push himself to find out how far he could go. It's too late now anyway. Intelligence is not what he values most in either himself, or anyone else.
The Bruce's - yep, both perfectly and realistically aware.
Courfeyrac - yeah, I think so. He's smart, he's sharp, and he knows it. He also fully accepts his limitations, with good cheer.
Aubrey - knows he is a very fine seaman on one hand, and struggles with words on the other. I think he gets a more realistic view of his talents as canon progresses, as he finds he has a natural affinity for maths and astronomy, becomes a decent landowner and politician, and is a skilled musician. At the start of canon he just thinks of himself as a sailor, and is a bit nervous (though he hides it) about the responsibility of being a captain. But he knows he can do it, and....does it. He's not much of a one for introspection, he just gets on with things whether he believes himself intelligent enough or not. He defers book-learning superiority entirely to those who deserve it, like Stephen.
Jim - yes. He's entirely aware of how intelligent he is, and it's all real. His game with Sherlock used pawns which included the British Security and Intelligence services, high-ranking officers of the Met, the national press and the highest criminal court in England, because that's just the stage he plays on. His intelligence has drowned everything else in life, and he knows it - the world just isn't geared towards people who think like him. There are other geniuses who don't destroy themeselves because of their minds, of course, but he's got a predisposition towards criminal behaviour and looks down on 'ordinary people', so the world is a terrible place for him. But yes, his opinion of his intelligence is realistic. As is his opinion of his insanity, because he knows about that too. :\
Hank is very aware that he is likely to be the smartest person in the room. I think this is why he likes Charles so much, since Charles is likely a peer and challenges Hank's intellect.
Izana is well aware of their talents and intelligence. They are also aware of their strengths and weak points in subject matter and comprehension.
Ahsoka doesn't give herself as much credit as she should I think. Although I wonder if intelligence is a crowning merit in the Jedi Order? Like does being really smart matter as much as being a proper jedi?
Sabine is well aware of her intelligence as well. She knows she's gifted and doesn't play it down.
Sam worries more about his emotional intelligence than his mental intelligence to be honest. That being said, he knows he no push over, but doesn't consider himself a big brain. I think he's smarter than he gives himself credit for.
Selina knows she has lots of street smarts, but doesn't consider herself too smart. I've worked in that she has a learning disabilities with handwriting, and so the public schools she went to likely would've called her lazy and dumb. She is not though, and I hope she figures this out.
Rollo doesn't bother considering his intelligence (at least at this point). He cares more for how great a warrior he is and how to win in battles.
Eliot is aware of his talents as a magician and that's all he really cares about to be honest. I'd imagine you'd need a fair bit of intelligence to understand spells though, so he is pretty smart.
That makes total sense. There are very cerebral jedi, Plo Koon comes to mind, but yeah, WIS and CHA is their priority. Which makes answering this question interesting since INT isn't seen as important for those raised in the Temple.
Yamato probably underestimates his own intelligence, since he has pretty low self-esteem even on a good day. He's pretty smart, even by the standards of the Chosen, who are all solidly above average, but I suspect he sees himself as either average or slightly below average.
Gabumon, meanwhile, is well aware of how smart he is, even if he quite often downplays it and plays the fool a bit. He has all of Yamato's perceptiveness, but he's able to apply it to himself just as well as he can apply it to other people.
Hawke, meanwhile, consistently overestimates his intelligence, or possibly just underestimates everyone else. Not by a lot - he is genuinely very sharp - but his insistence on solving everyone in Kirkwall's problems does stem at least partly from a feeling that he's the best qualified to do so, and that other people will just get it wrong. Not to mention, the fact that he underestimates Meredith (and Anders, to a lesser extent) plays at least a small part in what happens to Kirkwall.
Sherral takes measures to ensure that he can always get an objective view of his strengths and weaknesses, so his estimation of his own intelligence is pretty on-point.
Enjolras has a pretty realistic idea of his strengths and his limitations, and that includes intelligence, yes. He'd rather talk about how his friends are so smart and awesome!!! than about his own intellect, but he's aware that he's very intelligent in several arenas.
Cosette I think tends to underestimate a bit, but mostly she doesn't think about it a lot? She was pleased when she did well at things in school, or when she understands something, but I don't think she's ever really sat down and thought about whether she's more or less smart than most people. (She's no genius, but she's on the relatively smart side so far as book-learning intellect goes -- but that's not a thing she's ever really had nurtured beyond relative basics. She's quite good at emotional intelligence and reading people, though.)
Thor also tends to underestimate himself. He's pretty good at assessing whether he's up to dealing with a particular intelligence-requiring situation, though! (I mean, as long as he stops to think about it. He, uh, doesn't always stop to think.) But if you asked him how smart he is, he'd be comparing himself to Loki, who's got a formidably sharp mind and a scholarly bent. Thor has a lot of emotional intelligence, and no inclination towards scholarly analysis at alllll.
Kazul knows exactly how smart she is and that it's extremely, thank you. No, actually she's got a pretty realistic image of her own intelligence -- which is quite high -- but her level of patience and the accuracy of her assessment of someone else's intelligence are both a little variable.
Matt Murdock - Matt put a lot of work into his education and is aware of his intelligence and very proud of his accomplishments there. Being able to honor his father in at least that one aspect of his life by making something of himself is extremely important to Matt and he's proud of the fact, although he won't brag. And he'll certainly never accept any qualifiers to his achievements, ie; "He did well for a-- blind guy/Kitchen kid/orphan/etc."
Hellboy - Red is smarter than he realizes, but not prone to using that intelligence. He's totally a leap before you look kind of guy, but if and when he takes the time to use his noggin he's got some brains there. He's no scholar or genius, but he's also much more than a blunt instrument. Calling him dumb is a definite mistake.
Logan - Logan has a firm grasp on what he's capable of. With his attitude and aggression it's easy to assume he's like Hellboy, acting without thinking, but in truth Logan is much more calculating than most give him credit for. He's no slouch, but like most aspects of himself he keeps what he has guarded.
Charlie Kenton - Acts like he thinks he's smarter than he is, but in reality believes the opposite. He's a high school drop out who makes a lot of REALLY dumb decisions, but he's not actually an idiot. Well, actually he is an idiot, but not because he's not smart, he's just really stupid about how he's chosen to run his life.
Bill Pardy - At home Bill is very comfortable with his intelligence. He's got more smarts than most of the people around him, and generally uses them. In Milliways, though, and especially with Kate, Bill has some inadequacy issues. He joined the Academy straight out of high school and sometimes feels that lack of a college education. In reality it's a non-issue and in most cases he's definitely smarter than he gives himself credit for. That being said, he will always have a strong reaction to anyone openly questioning or putting down his intelligence.
Yes, the other problem is the people he's surrounded by. Between Abe and the highly educated and trained government agents around him Red is mostly fine with letting them do the planning, thinking and research while he just goes in and hits stuff.
Why use your noodle when it's much more satisfying to punch things in the face and ignore the people telling you important bits of info in your earpiece until you discover face-punching isn't working?
Case in point Sammael, when Red mostly ignores Abe up until the whole 'Hound of Resurrection' bit comes up. XD
Will underestimates his intelligence but part of that is he doesn't class his ability to figure out a situation or run things along the same lines as being a good fighter. This is a problem a number of mine class, they know what they can do but don't always think of that as meaning being smart.
Charles knows his limitations and his intelligence though he thinks of it in two different ways. He has his emotional intelligence that he works on alongside his telepathy and then his scientific knowledge and other stuff.
Quentin has a good sense of how smart he is as well as how much he still has to learn. He has his points of overestimating himself but that's usually do with entrenched cultural ideas.
Sameth completely underestimates himself and what he can do. He thinks of himself as capable and has been getting a better understanding of how rare the way he creates and understands the Charter actually is.
William doesn't see himself as smart, he's so aware of all he doesn't know and doesn't realize how much he actually does know.
Moist is confident in his intelligence and ability to think his way around anyone.
Jane knows how smart she is and it sometimes gets in trouble.
Ivan doesn't consider himself that intelligent, which is partly on him and also on everyone around him. He's spent his life comparing himself to Miles who is brilliant and knows he's not anywhere near Miles' level so misses that he actually is smart especially in social situations.
Demeter is a goddess who knows that she's not Athena but is well aware her intelligence doesn't work like human intelligence does.
Seimei is not in the business of estimating his own intelligence, because he observed the Dunning-Kruger Effect in action long before it had a name. There's really no way for a person to make an accurate assessment of their own intelligence.
Centuries ago, when Seimei was young, Seimei didn't consider himself to be exceptionally smart. He just wondered (with no small degree of frustration) why most other people were so dull. Take that how you will.
Okay, I had a long answer and it got eaten, so. In short:
Eriond: realistic Henry: doesn't really think about it, approximately realistic Evelyn: Realistic about academics, unrealistic--underestimating--competence and ability Deal With Stuff. Lois: Both underestimating and overestimating in very different ways. It might almost balance. R2-D2: Knows exactly what his circuits are capable of processing, always. Anakin: Is realistic when it comes to his military and mechanical intelligence. Does not realize this means exactly nothing about other forms of intelligence, and happens to be in many ways Dumb As Rocks and very easily manipulated--so very, very unrealistic overestimation there. (You're all shocked, I know.)
Tavi: Arrogant but not unrealistic. In Milliways, is painfully aware of the gaps in his knowledge based on scientific and technological progress--or lack thereof--but also very confident in his ability to catch up and learn things given enough time. Also knows there are actually people as smart as he is in Milliways. In Alera, used to being the smartest person in the room more often than not, and even when he isn't, differently smart. He does know he can be outsmarted, and uses that as a lesson to try to prevent it happening again. I think part of it is that his childhood drilled into him that if he wasn't the smartest person in the room, he had to become the smartest person in the room so he could get anything done ever.
So yeah. He usually doesn't overestimate himself, but that doesn't mean he's not arrogant about it. (Also he knows his emotional intelligence, except where manipulating people for the purposes of being a world leader, is close to nil.)
Joly tends to underestimate himself a little, but just a little. He knows technically he must be fairly bright, since no one gets into --or keeps up with-- medical school in Paris by being slow. But he's always been surrounded by people who are at least as smart as him, and often much more experienced, so he tends to think of himself as completely average. He doesn't feel bad about this in any way, it's just a slightly incorrect assessment.
Bahorel is sharp, and knows it, and has a pretty good idea of where his particular competencies fall through. The image he chooses to present about all that depends on...a lot of factors , but his self-assessment is solid underneath.
Gringoire, for mysterious reasons, thinks he's very clever and wise. All right,he's not entirely wrong-- if he couldn't think on his feet, he'd be very dead, and being someone who can do sums and read and write in multiple languages and who's had access to a considerable library (for his time) definitely puts him in the academic elite of his day. But if he were really using all that, he'd probably avoid at least a few of the catastrophes he stumbles into.
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X has a very precise and exact grasp of how smart she is and how good she is at integrating data.
Dean thinks he's dumber than he is by a lot.
Everyone else is pretty accurately aware of it, within reason.
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Javert - is a tough one, because it's both yes and no. He knows he has virtually no schooling, and reads so that he won't be entirely illiterate. He will never be book-smart. On the other hand, he knows policing chapter and verse, so I think he's - and knows he has - just found his Thing with policing, and is very good at it (for a given value of good: what I mean is, he carries out the job exactly as the rules say it should be done). He doesn't consider himself intelligent in any other area, and he is correct.
Valjean - no. He's smarter than he gives himself credit for. He did dare to acknowledge that he was doing a good job as mayor of Montreuil, and then quickly believed in the folly of thinking anything good about himself when the opportunity presented itself. He didn't learn to read until he was forty, but educated himself from books thereafter - he certainly has the capacity to learn, and a desire for it, but he'll never push himself to find out how far he could go. It's too late now anyway. Intelligence is not what he values most in either himself, or anyone else.
The Bruce's - yep, both perfectly and realistically aware.
Courfeyrac - yeah, I think so. He's smart, he's sharp, and he knows it. He also fully accepts his limitations, with good cheer.
Aubrey - knows he is a very fine seaman on one hand, and struggles with words on the other. I think he gets a more realistic view of his talents as canon progresses, as he finds he has a natural affinity for maths and astronomy, becomes a decent landowner and politician, and is a skilled musician. At the start of canon he just thinks of himself as a sailor, and is a bit nervous (though he hides it) about the responsibility of being a captain. But he knows he can do it, and....does it. He's not much of a one for introspection, he just gets on with things whether he believes himself intelligent enough or not. He defers book-learning superiority entirely to those who deserve it, like Stephen.
Jim - yes. He's entirely aware of how intelligent he is, and it's all real. His game with Sherlock used pawns which included the British Security and Intelligence services, high-ranking officers of the Met, the national press and the highest criminal court in England, because that's just the stage he plays on. His intelligence has drowned everything else in life, and he knows it - the world just isn't geared towards people who think like him. There are other geniuses who don't destroy themeselves because of their minds, of course, but he's got a predisposition towards criminal behaviour and looks down on 'ordinary people', so the world is a terrible place for him. But yes, his opinion of his intelligence is realistic. As is his opinion of his insanity, because he knows about that too. :\
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Izana is well aware of their talents and intelligence. They are also aware of their strengths and weak points in subject matter and comprehension.
Ahsoka doesn't give herself as much credit as she should I think. Although I wonder if intelligence is a crowning merit in the Jedi Order? Like does being really smart matter as much as being a proper jedi?
Sabine is well aware of her intelligence as well. She knows she's gifted and doesn't play it down.
Sam worries more about his emotional intelligence than his mental intelligence to be honest. That being said, he knows he no push over, but doesn't consider himself a big brain. I think he's smarter than he gives himself credit for.
Selina knows she has lots of street smarts, but doesn't consider herself too smart. I've worked in that she has a learning disabilities with handwriting, and so the public schools she went to likely would've called her lazy and dumb. She is not though, and I hope she figures this out.
Rollo doesn't bother considering his intelligence (at least at this point). He cares more for how great a warrior he is and how to win in battles.
Eliot is aware of his talents as a magician and that's all he really cares about to be honest. I'd imagine you'd need a fair bit of intelligence to understand spells though, so he is pretty smart.
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Gabumon, meanwhile, is well aware of how smart he is, even if he quite often downplays it and plays the fool a bit. He has all of Yamato's perceptiveness, but he's able to apply it to himself just as well as he can apply it to other people.
Hawke, meanwhile, consistently overestimates his intelligence, or possibly just underestimates everyone else. Not by a lot - he is genuinely very sharp - but his insistence on solving everyone in Kirkwall's problems does stem at least partly from a feeling that he's the best qualified to do so, and that other people will just get it wrong. Not to mention, the fact that he underestimates Meredith (and Anders, to a lesser extent) plays at least a small part in what happens to Kirkwall.
Sherral takes measures to ensure that he can always get an objective view of his strengths and weaknesses, so his estimation of his own intelligence is pretty on-point.
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Cosette I think tends to underestimate a bit, but mostly she doesn't think about it a lot? She was pleased when she did well at things in school, or when she understands something, but I don't think she's ever really sat down and thought about whether she's more or less smart than most people. (She's no genius, but she's on the relatively smart side so far as book-learning intellect goes -- but that's not a thing she's ever really had nurtured beyond relative basics. She's quite good at emotional intelligence and reading people, though.)
Thor also tends to underestimate himself. He's pretty good at assessing whether he's up to dealing with a particular intelligence-requiring situation, though! (I mean, as long as he stops to think about it. He, uh, doesn't always stop to think.) But if you asked him how smart he is, he'd be comparing himself to Loki, who's got a formidably sharp mind and a scholarly bent. Thor has a lot of emotional intelligence, and no inclination towards scholarly analysis at alllll.
Kazul knows exactly how smart she is and that it's extremely, thank you. No, actually she's got a pretty realistic image of her own intelligence -- which is quite high -- but her level of patience and the accuracy of her assessment of someone else's intelligence are both a little variable.
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Hellboy - Red is smarter than he realizes, but not prone to using that intelligence. He's totally a leap before you look kind of guy, but if and when he takes the time to use his noggin he's got some brains there. He's no scholar or genius, but he's also much more than a blunt instrument. Calling him dumb is a definite mistake.
Logan - Logan has a firm grasp on what he's capable of. With his attitude and aggression it's easy to assume he's like Hellboy, acting without thinking, but in truth Logan is much more calculating than most give him credit for. He's no slouch, but like most aspects of himself he keeps what he has guarded.
Charlie Kenton - Acts like he thinks he's smarter than he is, but in reality believes the opposite. He's a high school drop out who makes a lot of REALLY dumb decisions, but he's not actually an idiot. Well, actually he is an idiot, but not because he's not smart, he's just really stupid about how he's chosen to run his life.
Bill Pardy - At home Bill is very comfortable with his intelligence. He's got more smarts than most of the people around him, and generally uses them. In Milliways, though, and especially with Kate, Bill has some inadequacy issues. He joined the Academy straight out of high school and sometimes feels that lack of a college education. In reality it's a non-issue and in most cases he's definitely smarter than he gives himself credit for. That being said, he will always have a strong reaction to anyone openly questioning or putting down his intelligence.
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Why use your noodle when it's much more satisfying to punch things in the face and ignore the people telling you important bits of info in your earpiece until you discover face-punching isn't working?
Case in point Sammael, when Red mostly ignores Abe up until the whole 'Hound of Resurrection' bit comes up. XD
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Charles knows his limitations and his intelligence though he thinks of it in two different ways. He has his emotional intelligence that he works on alongside his telepathy and then his scientific knowledge and other stuff.
Quentin has a good sense of how smart he is as well as how much he still has to learn. He has his points of overestimating himself but that's usually do with entrenched cultural ideas.
Sameth completely underestimates himself and what he can do. He thinks of himself as capable and has been getting a better understanding of how rare the way he creates and understands the Charter actually is.
William doesn't see himself as smart, he's so aware of all he doesn't know and doesn't realize how much he actually does know.
Moist is confident in his intelligence and ability to think his way around anyone.
Jane knows how smart she is and it sometimes gets in trouble.
Ivan doesn't consider himself that intelligent, which is partly on him and also on everyone around him. He's spent his life comparing himself to Miles who is brilliant and knows he's not anywhere near Miles' level so misses that he actually is smart especially in social situations.
Demeter is a goddess who knows that she's not Athena but is well aware her intelligence doesn't work like human intelligence does.
Tumnus doesn't consider himself terribly smart.
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Kylo I think is pretty aware of his limitations. It's admitting them that's the problem.
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Centuries ago, when Seimei was young, Seimei didn't consider himself to be exceptionally smart. He just wondered (with no small degree of frustration) why most other people were so dull. Take that how you will.
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Eriond: realistic
Henry: doesn't really think about it, approximately realistic
Evelyn: Realistic about academics, unrealistic--underestimating--competence and ability Deal With Stuff.
Lois: Both underestimating and overestimating in very different ways. It might almost balance.
R2-D2: Knows exactly what his circuits are capable of processing, always.
Anakin: Is realistic when it comes to his military and mechanical intelligence. Does not realize this means exactly nothing about other forms of intelligence, and happens to be in many ways Dumb As Rocks and very easily manipulated--so very, very unrealistic overestimation there. (You're all shocked, I know.)
Tavi: Arrogant but not unrealistic. In Milliways, is painfully aware of the gaps in his knowledge based on scientific and technological progress--or lack thereof--but also very confident in his ability to catch up and learn things given enough time. Also knows there are actually people as smart as he is in Milliways. In Alera, used to being the smartest person in the room more often than not, and even when he isn't, differently smart. He does know he can be outsmarted, and uses that as a lesson to try to prevent it happening again. I think part of it is that his childhood drilled into him that if he wasn't the smartest person in the room, he had to become the smartest person in the room so he could get anything done ever.
So yeah. He usually doesn't overestimate himself, but that doesn't mean he's not arrogant about it. (Also he knows his emotional intelligence, except where manipulating people for the purposes of being a world leader, is close to nil.)
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Bahorel is sharp, and knows it, and has a pretty good idea of where his particular competencies fall through. The image he chooses to present about all that depends on...a lot of factors , but his self-assessment is solid underneath.
Gringoire, for mysterious reasons, thinks he's very clever and wise. All right,he's not entirely wrong-- if he couldn't think on his feet, he'd be very dead, and being someone who can do sums and read and write in multiple languages and who's had access to a considerable library (for his time) definitely puts him in the academic elite of his day. But if he were really using all that, he'd probably avoid at least a few of the catastrophes he stumbles into.