First, let me give you a brief explanation about how politics in the United States of America works. Several candidates vie for the nomination in their party. They compete just for the ability to run for office. Only the members of that party are allowed to vote in the primaries. The extreme Republicans and the extreme Democrats who belong to that party all go out to vote for the person who best exemplifies the most radical ledge of that party's beliefs. Then, the candidate for the Democrats and the candidate for the Republicans go out and campaign for the general election. Now, despite all the rhetoric they used during the primaries about how they will continue to fight for the future of their party, blah, blah, blah, they now say that they are tireless supporters of the people and will only do what is in the best interest of everyone, even those who don't vote for them. Clearly, at some point they are lying. Yet we all still go out and support one candidate over another, not because we like them, just because they're not as crappy as the other guy (or girl, though women are underrepresented).

When you go to vote, you decide who you believe will better represent you, or who you believe didn't lie to you, or who you believe won't steal money from the public coffers. Is this democracy?

I have a better idea (in my opinion).

The people will decide on all matters that involve all the citizens of a society. For instance, the people would decide on all budgetary issues but would not vote on whether women can play in the NFL.
The legislature would still exist but would only deal with exclusive issues, giving Republicans and Democrats something to debate about, because that is what they disagree on the most. i.e. welfare, affirmative action, abortion, etc.
The president's power would be diminished and the cabinet's power would be increased to roughly equal with the president's. All cabinet members would have to be approved by the people in the next election, though they may serve up until that time.