SuddenlyParanoid

I would use the one with the higher quantitative. The scores on that section are so compressed that a 780 is an 89th percentile and a 720 is 75th, which is a huge drop and I would think that would hurt more for engineering. As long as you have something that shows you can speak and read English (SOP, writing sample, high TOEFL, American BA) I would emphasize your math ability.

I'm a current senior at a large public "Ivy." 3.7 overall, 3.97 poli sci. 730 Verbal, 790 Quant, 5.5 AW. I'm interested in American institutions and elections. Solid letters from well-known, full profs. I'm applying to: Michigan, Stanford, OSU, Harvard, WUSTL, Duke, Rochester, UCSD, Berkeley, UCLA, Yale, Columbia, Princeton. I don't really have a safety right, which is part of the reason I applied to so many. Maybe I should add one?

A good safety might be Notre Dame. They're top ten in political theory but 30-50 overall, so you should be able to get in, but the subfield is still very well respected. You might want to try UCLA but their funding isn't the best. Notre Dame is very Catholic unlike most "Catholic" universities which could be good or bad for you. I would say if you're gay, a committed feminist, a Protestant who thinks the Church is the Whore of Babylon, or a New Atheist, you probably should not go there. Otherwise, it's a great school!

It seems really solid, especially the academic background and why it's a good fit. I would change the first paragraph a tiny bit, though. I would not refer to another country as "peculiar." I'm sure I would find Korea pretty strange but to call it peculiar just seems a little bit condescending and ethnocentric. Maybe mention something specific about Korea that grabbed you rather than just alluding to its exoticism. You mention specific interests later in your SOP so I think you could probably just move them up a bit.

Perhaps you could pretend to answer it with something like "Although I plan to focus on further research on yada yada yada in my career, I would like like to be able to combine it with teaching at multiple levels from introductory undergraduate courses to graduate research seminars." And then maybe throw in some policymaking thing you could do with your degree.

I finished applying today but just realized that means many of my schools got my transcripts a week before they got my actual applications. That's not a problem is it? Or did I just screw myself over because they had nothing to file it with?

So i took on too heavy of a course load this semester and it's going to knock my cumulative gpa down a bit. I'm submitting all of my applications in the next week with my current transcript. Schools aren't going to unaccept me when they look at senior year grades, are they?

I'm applying to basically the top ten. I have a 3.7, 3 great letters from tenured professors, and a decent GRE, 730 verbal, 790 quant. I'm an Americanist. I really want to go to grad school next year and not have to reapply. This cycle is supposed to be really tough since so many people are trying to go to grad school since it's so hard to get a normal job. What's the best American place I should almost definitely be able to get into?

Chicago is great and theory but only good at American and quant, while Harvard, Princeton, and Stanford are strong across the board. So at the top schools, a lot more people apply because they know it will put them in a good position whatever they decide to do, so they have higher GREs than Chicago. Chicago lists its median as 638 verbal, 698 quant so that is significantly below.

For methods a high quant is super-important, below 750 would be terrible and even an 800 isn't impressive. I'm not into theory, not my thing, but from what I've picked up the quant is much less important. A 680 isn't stellar but it shows that you're definitely not stupid so I think it shouldn't be a problem. And a 710 is definitely strong. What is that 98th percentile? If you're interested in subfields other than political theory, the 680 might be a problem. In American definitely, maybe in some IR programs. But if theory is what you're all about, you should be fine. Are you applying to Chicago?