Yeah, there is an ongoing debate on the meaning of "representation", of course. After all, most electoral systems are based on geographical locations, but actual politicians usually belong to specific parties "representing" different political philosophies, so there's a friction even at a theoretical level. Add to that the vagaries of actual electoral rules (first-past-the-post etc etc) and an inevitable dose of human nature (corruption, ambition etc), and you have a recipe for the clusterfuck that is modern representative democracy.

Unfortunately, the few alternative models emerging in the last century (usually just variations on one-party rule, really) backfired quite spectacularly, so we're nowhere near finding better solutions to the problem.