I really enjoyed this Slate article about the duty of representatives to their constituents. The basic takeaway: it's not just the job of representatives to echo their constituents' preferences in congressional votes; it's their job to work with other representatives to forge solutions that are best for the country as a whole.

I didn't realize this, but this exact question was considered by the founders. They considered a "right to instruct" amendment to the constitution that would let citizens meet and vote on a binding position for their representative to take on a particular vote. This idea was eventually rejected, and the Slate article outlines the reasons why. It's pretty interesting.