Most democracies in the world today have healthy multiparty systems, but older ones (such as America and the UK) don't. The reason is simple: the idea of proportional representation hadn't been conceived when the older democracies were formed.
It wasn't until the 1840s that John Stuart Mill first wrote about it, which is why most democracies formed after 1850 have healthy multiparty systems that represent a broad range of political opinions. Older democracies are usually two-party states.
Knowing that there was a deficiency in the American system, James Madison wrote long letters and articles begging America's politicians not to form political parties, but it was all for naught. By the late 1790s, the Democratic Republicans had split off from the Federalists and we've had a two-party system in the United States ever since.
The problem is that we have winner-take-all elections. If more than two candidates run, it's possible for a candidate to take the seat with fewer than a majority of the votes--and, as Madison noted, then the people are represented by a candidate whose opinions reflect only a minority of Americans. (A good example was the presidential election of 2000, in which Bush got three million fewer votes than his opposition, Gore and Nader.)
There are two solutions to this problem...
Read more of this extract from "What Would Jefferson Do".