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@CherylMinn,I just wanted to add two points about Duke. Thirst, even though you will be an MA student, you will likely take most of your classes together with PhD students. I think this is a big advantage, also because your future letter writers will be able to compare you to them. Second of all, being an MA student, I think you should look at the faculty more broadly. You are not searching for a dissertation advisor, who does what research should be much less relevant. There are other faculty members who can give you the guidance you may need. Even for PhD students who research authoritarian politics, just look at their dissertation committees. 

To me, a statement that's double what is allowed just sends a terrible signal - that you're a person who thinks s/he entitled to special treatment and who thinks s/he's not bound by any rules (I'm not saying this about you personally, just in general). You can hope nobody will notice, but honestly, why take such a risk? 

I think mentioning particular faculty members you want to work with shows that you have done your homework on the department and chose to apply to it based on some degree of fit. The downside of course is that you don't know a lot of things - you may mention somebody who is about to retire or move or be denied tenure, or simply not taking new doctoral students for whatever reason. Because of this, if you do list faculty members, make sure it will be three or four professors. 

I think mentioning particular faculty members you want to work with shows that you have done your homework on the department and chose to apply to it based on some degree of fit. The downside of course is that you don't know a lot of things - you may mention somebody who is about to retire or move or be denied tenure, or simply not taking new doctoral students for whatever reason. Because of this, if you do list faculty members, make sure it will be three or four professors. 

"departments" are in the end people. It's really up to the individuals and how important they think the GRE is. Nobody will be able to give you a definitive answer. I think @munch22 has a correct take - if you have taken GRE and your score is great, send it. 

It certainly is true that the academic job market in the US is a tough as never before and most people do not appreciate the extent this is true until they near the end of their PhD programs and are on the job market. I think YOU SHOULD think about this carefully when applying. But there are a few 'buts':
1. There still are academic jobs in the US, just less (and more PhDs competing for them). While this means that competition is higher and so are expectations, you can still get hired. You just need to have realistic expectations - not everyone will get an R1 job (not that everyone wants one!) and you may need to first do a postdoc or two after you graduate.
2. Check out the latest APSA Graduate Placement Report. 26% get TT jobs straight out of PhD. 85% get jobs. 15% are unplaced. These numbers are for all PhD granting institutions. They vary between universities. With some exceptions, your best bet on getting a job is to go to the best department possible. The jobs prospects of somebody from a top 10 department are vastly different than for somebody from much lower ranked schools. It's not just the number of jobs but also the type of jobs that will be available to you that differs.  
3. There are still jobs in Europe and an increasing number of good jobs in Asia. Many are willing to take these! In fact, this may sometimes be the preferred option for non-US citizens. 
4. Be prepared from the start that you may need to consider non-academic jobs. Many upper year PhD students will actually prefer those, even if they came into their program with academic aspirations. Make sure you invest in skills that are useful both in the academic and non-academic paths. This will be both helpful in actually getting a good non-academic job and also will help reduce the stress and pressure of the academic job market, knowing that you do have an outside option. 
 
 

I'm not exactly sure what other than GRE can you improve given that, as I understand, you are applying this Fall. Is your question: should I retake the GRE? Well, my suggestion then is: yes, if you can, do retake the GRE. The Q score seems on the low end for top 10 IR. 

The feeling you have is very common among PhD students. Do keep in mind that past your second year, the life of a graduate student is very different - you will be very much focused on research and take few if any classes, depending on your program. Having said that, it will not necessarily be less stressful. I would suggest you talk about your feelings with your director of graduate studies or/and with any faculty member who you feel comfortable talking to. But also do try and consult a mental health professional; possibly your university will have a place where you can go and talk to specialists. Depression is common these days but it should be taken seriously. Your health is most important!!!
I personally found it beneficial to also talk to other people in my cohort - the chance is, they are going through a similar struggle. Also, remember, in grad school, there is always more work than there is time to complete it. This means you will have to prioritize and draw a line - you need to set aside time for yourself, even if the work is pilling up. Physical exercise is a great way to relieve stress and combat mild depression, and it helps with the consequences of all the sitting. A tip: buy/construct a standing table, don't just sit all day long.
Regarding job prospects with an MA degree for international students, well, that depends on what country you are in, what's your citizenship and visa status, do you speak the local language, and a bunch of other things. I don't think anybody here will be able to advise you on that without having much more information. The short answer is: it depends.

I think you have minimal/zero chances of getting admission into a polisci PhD program, let alone getting funding, with your GRE scores. I do not know anything else about your profile, but even if the relevant department would want you (because of whatever factors), I don't think any graduate school will sign on it.
Basically, you only answered 9 out of 40 high school math questions correctly. This will be a huge red flag and I don't think anything else will matter much.
That is, of course, just my opinion.

I think you have minimal/zero chances of getting admission into a polisci PhD program, let alone getting funding, with your GRE scores. I do not know anything else about your profile, but even if the relevant department would want you (because of whatever factors), I don't think any graduate school will sign on it.
Basically, you only answered 9 out of 40 high school math questions correctly. This will be a huge red flag and I don't think anything else will matter much.
That is, of course, just my opinion.

I think you have minimal/zero chances of getting admission into a polisci PhD program, let alone getting funding, with your GRE scores. I do not know anything else about your profile, but even if the relevant department would want you (because of whatever factors), I don't think any graduate school will sign on it.
Basically, you only answered 9 out of 40 high school math questions correctly. This will be a huge red flag and I don't think anything else will matter much.
That is, of course, just my opinion.

As Dwar said, this is not because of economic problems but rather a recognition that resources are constrained. Admitting more students when you have larger cohorts already means less resources available to existing students, which is something Duke is trying to avoid.

Most of the top programs allow you to do quant-heavy stuff these days. You can easily add Stanford, Duke, Princeton to the list, and I'm sure other some other ones as well. In many programs, you will be able to take classes outside of your department too, so taking stats or econ classes shouldn't be a problem.

The feeling you have is very common among PhD students. Do keep in mind that past your second year, the life of a graduate student is very different - you will be very much focused on research and take few if any classes, depending on your program. Having said that, it will not necessarily be less stressful. I would suggest you talk about your feelings with your director of graduate studies or/and with any faculty member who you feel comfortable talking to. But also do try and consult a mental health professional; possibly your university will have a place where you can go and talk to specialists. Depression is common these days but it should be taken seriously. Your health is most important!!!
I personally found it beneficial to also talk to other people in my cohort - the chance is, they are going through a similar struggle. Also, remember, in grad school, there is always more work than there is time to complete it. This means you will have to prioritize and draw a line - you need to set aside time for yourself, even if the work is pilling up. Physical exercise is a great way to relieve stress and combat mild depression, and it helps with the consequences of all the sitting. A tip: buy/construct a standing table, don't just sit all day long.
Regarding job prospects with an MA degree for international students, well, that depends on what country you are in, what's your citizenship and visa status, do you speak the local language, and a bunch of other things. I don't think anybody here will be able to advise you on that without having much more information. The short answer is: it depends.

GRE scores are not a good predictor of math or whatever other skills but they are highly indicative of one thing: your resilience. Basically, with enough time spent, almost everybody can get a high score. The question is - how hard will you try/how easily will you give up?
The way I see it, a good score will not really help your application, but a bad score can hurt because it can mean one of two things - you are just bad at math/language skills or you just did not work on it hard enough, which begs the question of whether you'll be willing to work hard once in the program.
What is a safe score? There is not a one number because it depends on things such as your subfield, exposure to math and whether you are a native speaker.

I think the ranking stuff is pretty fascinating, 
Top 10 positive changes in rank vs score
University 2013 Score 2013 Rank 2017 Score 2017 Rank Score Differential Rank Differential University of Pennsylvania  3.3 28 3.8 19 0.5 9 University of Houston  2.3 68 2.7 51 0.4 17 University of Oklahoma  2.1 83 2.5 61 0.4 22 Vanderbilt University  3.1 36 3.5 24 0.4 12 University of California—Davis  3.5 23 3.9 17 0.4 6 University of California—Riverside  2.5 54 2.9 48 0.4 6 American University  2.3 68 2.6 56 0.3 12 University of Massachusetts—Amherst  2.3 68 2.6 56 0.3 12 Georgetown University  3 40 3.3 33 0.3 7 Duke University  4.2 10 4.5 7 0.3 3 -----
University 2013 Score 2013 Rank 2017 Score 2017 Rank Score Differential Rank Differential University of Oklahoma  2.1 83 2.5 61 0.4 22 University of Houston  2.3 68 2.7 51 0.4 17 Vanderbilt University  3.1 36 3.5 24 0.4 12 American University  2.3 68 2.6 56 0.3 12 University of Massachusetts—Amherst  2.3 68 2.6 56 0.3 12 Temple University  2.2 76 2.4 65 0.2 11 University at Buffalo—SUNY  2.2 76 2.4 65 0.2 11 University of Connecticut  2.2 76 2.4 65 0.2 11 Georgia State University  2.1 83 2.3 72 0.2 11 University of Pennsylvania  3.3 28 3.8 19 0.5 9  

 
If anyone is interested, you're more than welcome to the data set.
USNews_rankings_dataset.xlsx

I'm not a super chatty person and I was also a little worried, but actually pretty much all my meetings went very well, in a nice atmosphere. The faculty may have a bunch of questions too, and set the tone of the talk. Feel free to ask questions, also about the students they have been advising. When it comes to some matters like tenure or advising, you may prefer to talk about that with current grad students, or DGS, if this is of concern to you. You can talk about what research you have been doing so far (likely not much at this point, but still). Ask professors about it too, you can't always tell by their publications what are they really working on these days. Ask general questions about the department, etc. Get to know them, get a sense of whether these are the kind of people you would enjoy working with in the future. And remember, people may come and go, but there is this more general things as a department atmosphere too, try to sense it, see if you fit in. And totally feel free to be honest about what other schools you are considering and what your concerns are, what are the questions marks with regard to that particular school. But don't waste people's time if you are not seriously considering that school.

Fully funded PhD offer at an R1 vs. a non-funded MA, isn't it obvious?

Keep one thing in mind: the number of applicants is growing every year and it is harder and harder to get admission. At my department, just over the past 2 years we've had a 50% increase in the number of applicants. Admission is not just about how good you are. It is also about how good are the other candidates.

Keep one thing in mind: the number of applicants is growing every year and it is harder and harder to get admission. At my department, just over the past 2 years we've had a 50% increase in the number of applicants. Admission is not just about how good you are. It is also about how good are the other candidates.

Fully funded PhD offer at an R1 vs. a non-funded MA, isn't it obvious?

Agree with @Comparativist. The best we can do is take the USNews rankings and possibly divide them into tiers so that minuscule ranking differences are gone. 

So you would rather trust prospective grad students opinions about something they haven't even experienced before rather than systematic surveys distributed to professors throughout the field?
Well all know there are flaws with ranking systems but nonetheless they have been shown to correlate fairly well with placement. 

I was in this boat last year actually (deciding between Princeton, UPenn, GWU and WashU). I think my perspective was a little different since I was less concerned with the overall ranking of the department/program, and far more concerned with the individual people I would be working with. My closest mentors said the decision was crystal clear, an absolute no contest but for me it wasn't immediately evident because GWU had amazing people I could work with, and their placement record in recent years has been fantastic. I also go along extremely well with everyone I met, as well as the graduate students. I also really loved DC. 
I was torn, because I wanted to go somewhere where I could write the best dissertation, and that stemmed first and foremost from mentorship. I asked every professor I met with, no matter the institution, very blunt questions. Who was leaving. What was funding like for fieldwork, or research on top of the stipend. What was their hiring strategy. What was their long run plan as a department in terms of goals. What was it like for women in the department there. What was the teaching load like. What were courses like. What research opportunities were there out of coursework, as an RA, or as a co-author with faculty. I asked the same of current graduate students and I was told very honest, unbiased information about the state of affairs, and some other surprising details about hiring strategies (or lack thereof...). Four months in, everything they said is true (for better or worse). 
Faculty genuinely don't want to "fool" you into picking their program because you're all the more likely to be miserable, less productive and reflect poorly on them if you find yourself in a situation you didn't expect. I did openly ask programs why I should pick them over a top 3 and they gave strong answers. Everyone was also open about why I shouldn't pick them (another good question to ask, albeit a blunt one).
I didn't decline offers until I was sure of where I wanted to go, which was admittedly quite close to the April 15th deadline but evident to me as soon as I was in the airport heading back after my last visit. Don't feel compelled to turn someone down. Consider your options carefully. Happy to talk more over PM as well. 
 

GRE scores are not a good predictor of math or whatever other skills but they are highly indicative of one thing: your resilience. Basically, with enough time spent, almost everybody can get a high score. The question is - how hard will you try/how easily will you give up?
The way I see it, a good score will not really help your application, but a bad score can hurt because it can mean one of two things - you are just bad at math/language skills or you just did not work on it hard enough, which begs the question of whether you'll be willing to work hard once in the program.
What is a safe score? There is not a one number because it depends on things such as your subfield, exposure to math and whether you are a native speaker.