I was thinking a bit about Hogwarts Houses and about Dungeons and Dragons alignments, and now I'm going through the alignments to see if there are any Houses I think they would either disproportionately wind up in or not wind up in. [In case anyone is curious, I sort Gryffindor, and I seem to be Neutral Good, leaning more Chaotic Good than Lawful Good if I really had to go one way or the other.] Before I start, let me point out that while these kinds of alignments can be a useful tool, no, they're not going to tell you everything about a person or character. Also, all 36 combinations will exist and I'm just thinking about which ones I feel would be more common. [I like to Sort my original characters and I always know what their alignments are.]
So. Lawful Good: I feel like they'd wind up in Hufflepuff fairly often, because goodness and loyalty and friendship are big Hufflepuff things. I'd be really interested to write a Lawful Good Slytherin sometime, I feel like there wouldn't be a ton of them but yeah they'd exist. Major possitive correlation with Hufflepuff, minor negative correlation with Slytherin for Lawful Good.
Now Lawful Neutral: Lots of Ravenclaw, lots of Slytherin. I feel like there would be very few Gryffindors here, since their thing is being kind of foolhardy about what they believe in, not so much being “rules are rules” and following everything to a tee.
Lawful Evil: HUGELY NOT HUFFLEPUFFS. Seriously, this is not a Hufflepuff. Feels rather Slytherin, using the law to your own not so good ends. I think a lot of these folk would wind up in Slytherin. Umbridge, for example, I think is Lawful Evil Slytherin. (Did we ever find out where she was sorted?)
Neutral Good: Very Hufflepuff, very Gryffindor. Which one depends on how you show your goodness. Between Ravenclaw and Slytherin I don't think there'd be much difference in how often they go there, and it's not so much a negative relationship as “well there's a big positive relationship with someone who's not me.”
True Neutral: “I want to know about all the things, good and bad!” Sounds rather Ravenclaw, doesn't it? There would be a decent number of Ravenclaws here. I'm not convinced there would be any House that's specifically more likely to get folks of this alignment, really. Peter Pettigrew probably goes here- doesn't seem to care as much about what's good or bad, legal or illegal, just about protecting himself. Maybe a negative correlation with Hufflepuff? Not nessesarily though, since you can be true neutral by way of not caring what effects it has on anyone else or how it relates to the law- if it's what needs to be done to be loyal to friends/family, you'll do it. I think True Neutral is... kind of neutral.
Neutral Evil: No specific correlations, I don't think. It'd depend rather heavily on traits that are outside of their alignment. The Hufflepuffs here would have wound up here because Helga really was willing to teach everyone the same, and probably hate it. But canonically, Hufflepuff had the fewest Dark Wizards and Slytherin the most, so I guess they mostly went Slytherin in the books. I think that's more because people got kind of scared of Slytherin early on (the legend about the Chamber of Secrets, anyone?) and so people with choices didn't really want to go there, hence any evil alignment that didn't have any strong directionality towards another House would wind up in Slytherin because they'd be least worried about the reputation. That's different from saying they actually go there when the Hat doesn't need to worry about making the numbers about even, which it seems like it tries to do.
Chaotic Good: They tend to be Gryffindor or Slytherin. Gryffindor for the ones who blatantly go chaotic and openly break all the rules when breaking the rules is the only way to do the right thing, Slytherin for the ones who ignore laws sneakily, rely on connections to get away with it, maybe use the system to show how messed up the system is and therefore dismantle it, that sort of thing. Chaotic Good Gryffindors get caught. A lot. Chaotic Good Slytherins are a lot better at not getting caught. Fred and George totally strike me as Chaotic Good Gryffindors.
Chaotic Neutral: The first thing coming to my head is “I'd be unstoppable if it weren't for law enforcement and gravity.” Thanks to magic, gravity isn't much of a concern, so it's anti-law now. Negative correlation with Hufflepuff, but that's about it, I think.
Chaotic Evil: No traits specific to the alignment make me think of any specific House. In the world of Harry Potter, numbers and the image Slytherin has gotten means they'll overwhelmingly get Sorted Slytherin, but in terms of just the traits that make a person Chaotic Evil? Meh, I don't think they're actually any more likely to belong in Slytherin than anywhere else.