Do not send 7 letters, my guess is no adcom will want to read all 7, might count against you. I'd send 4, actually I did send 4, was fine. I recommend sending
LORs from Econ and Math profs and not PoliSci. I wouldn't base it on how well you get along with them or how often you see them even though it's important that they know your abilities, but I think it should be based on how highly they would rate you. Would they say you are the top 1% in their entire career, top 1-5% of your class or a wonderful student. A lot of
LOR forms ask the profs to rate you with all the other students they've seen, so that's one of the most important element to consider. I remember some other categories are leadership and team work but the main ones are about academic ability.
Also, when you are discussing Ph.D programs with these profs, what programs are they encouraging you to apply to? Is it top ranked programs or second tier? That can also tell you a lot about where they think you rank among your peers. Good luck!