People being represented proportionally by their population is taken as true in many democracies, although it isn't true in other populations obviously. In the US, people are represented proportionally by the House of Representatives according to their population and redrawn and decided upon every 10 years by the national census.
There are not only democrats and republicans in America. There are libertarians, and tea party people, and socialists, and independents, and a lot of other parties that could be represented. We should not have a two party system, but a proportional representation system where more ideas are debated and where coalitions in the government need to be formed.
Proportional representation would be a better reflection of American political ideals because a party would not need a majority of votes in order to win representation within government offices. This would put an end to the bipartisan stalemate that has been increasingly been disrupting and even preventing productive government activity by filling in representation between the two extremes of both parties.
Proportional representation would be a great idea for the United States. The Republicans and Democrats monopolize American politics, even though numerous other parties have large followings. Our system doesn't allow a third or even fourth party to penetrate into politics, so prorportional representation would eliminate such a problem right away.
The direct election of our representatives to Congress and the national election of our president is uniquely American and it should stay that one. Voting in America is about choosing individuals and not a particular party in our legislative bodies. That way, no one party gains power very quickly. If the United States did move to a PR system, the changeover would take decades.