Either you accept the democratic principle or you don't. I would like you to reexamine your evidence, however. What exactly is it?
People voted this man into office:
I rest my case. 
George Bush is the perfect example. He might have beaten a marionette like Al Gore (though thanks to the supreme court we'll never know the truth of the matter), as well as John Kerry, who was basically the Democratic Party's Mitt Romney. The contest was over who was the lesser of two evils, a contest which is predicated upon the dominance of a pair of incredibly well-funded bureaucracies whose sole duty is to get people into office. These financial giants can not only outspend any third party challenger, but they also work together to create rules making it nearly impossible for third parties to break in, or even to hold whatever ground they gain. In addition, they each reserve the right to draw district maps that guarantee their incumbents a certain level of job security. Bush is still, after five years, widely regarded as the worst president in United States history, yet his policies remain in place, held there by a man whose only campaign promise was to change them. Do you really think that if his policies were truly subjected to a referendum, as the Democrats claimed they were, that any of them would still be law? Seventy percent of Americans now think that the Patriot Act was a bad idea. But it's still not going anywhere. The near-impossibility of third parties gaining and keeping name-recognition they can bank on ensures that American representatives suffer almost no accountability.
Make no mistake, George Bush made a handful of people very very rich, and Obama is doing the precise same thing. If these two have made a lot of other people very very poor, it wasn't because of those people's stupidity, but for the lack of a competitive, genuine alternative. The election rules in this country are so arcane, that for most third parties, managing to get on the ballot at all is seen as a major victory. It eats up most of their funds, and there is nothing left over for airtime. If representative democracy seems to have failed in America, it isn't because the democratic principle doesn't work.
I love it how you get all defensive.
But I actually had a serious point to make here, which had nothing to do with your country or its indirectly elected leaders. The point is this:
People, in general, are uneducated morons lacking even the basics necessary to make educated decisions about anything. I could just as well have illustrated my earlier post with our prime minister, or just about anyone, but it's safe to say that Bush is better known. He is also a prime example of an idiot having been elected into office.
A number of years ago there was a public referendum in Sweden about whether or not to keep the nuclear power plants in the country, I think 12 at the time. It was a hugely populistic vote in just about every way, happening as a direct result of the Harrisburg incident in the US, but for some reason the powers that be carried it through every step of the way.
Lobbyists pulled the public opinion back and forth and the people were polarised into roughly two camps, not three, debating about nuclear power based on fear and fiction, but eventually the vote was carried through and the country is still recovering from it.
The notion of the people making an informed decision about a specialised technical matter is almost as bizarre as the idea of politicians making it. But this is what democracy is; people making decisions about matters that are far beyond their education or reasoning capabilities.
Or electing equally ill-informed politicians who then base their decisions not on any factual merits but on how they affect their jobs.
phobia.