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I went through Harvard SSP last summer and just wanted to share experiences with others who went for future applicants.
First and foremost, yes, it is exclusive to a certain degree (my Harvard advisor said there was less than a 20% acceptance rate), but your essays/application play a huge role. I only had a 3.4 GPA with no PSAT scores, but my essays were the best single-page peice of work I have ever written. I discussed politics, economics, and the correlation between the two using linear regression analysis and the extrapolation of past economic trends. It took me a week to write.
I studied linguistics and got a B+, but I worked my a** off -- the classes are curved and you're in a room of kids ranked in the top 5% of their classes. I highly suggest supplementing your primary interest with an easy class like Gender Works so you can walk away with a higher GPA to show off when it comes to undergraduate application time. Everybody there is bright and motivated and I didn't meet a single person who "slipped through" the admissions process.
The actual experience was AMAZING--I met so many bright people from all over the US who I visit and talk to all the time to this day. My roommate became my best friend who lives in New Jersey -- I live in New York but we visit each other once every two months at least and talk on the phone a couple of times per week. I might be going back this summer if I don't get accepted to other summer programs.
If you have any questions, feel free to ask. Others please feel free to share your experiences to help future applicants.
And apply early! Your dorms are first come first serve.