With most governments, there is just way too much going on to have anything but a representative democracy and it be fair(by that I mean the people having any sort of power). There are too many people to have a direct democracy and it ACTUALLY work, imagine having to get an entire country together to vote on a law pertaining to something like speed limit! That'd be crazy!
And what are the other choices of government we have? Monarchy, theocracy, dictatorship, etc. There are a lot, but in short representative democracy looks pretty stinking good compared to all of them. With representative democracy we, as the people, may not have a direct say so, but we have as close to one as we will ever get and it is not half bad.
If I go to elections and people vote for me, I can become president and govern all the entire state. Of course I'll like that, why not? Imagine you are my minister of something and you rule the state together with me. It is so so cool. Representative democracy is what we need it, with me president.
Democracy has one of the most prolific pitfalls when it comes to representation: No one is directly represented. The very bent of the representative appears in every issue; the bias is destructive to the process and the value of the propositions are weakened; it is a microcosmic dictatorship which is inevitable.