Do the principles of capitalism and democracy contradict each other?

Think about it, the US is both a democratic and a capitalistic society, yet the corporations which form the foundations of its economy function more like autocracies. A company that takes every vote into consideration probably wouldn't last long in the fast paced, highly competitive world that is the capitalistic market place. Democracy is based more on communal/social concerns whilst capitalism is very much the opposite - it's more like survival of the fittest, with the weakest of the group getting wiped out and the strongest earning far more than their expected shares in a corresponding socialist government. My point is that these two models - capitalism and democracy - seem innately opposed to each other, and that a society couldn't at heart be both. This could explain a lot of the corporate bribing and electoral fraud that goes on in the US and other purported democracies; the drive for supremacy that capitalism creates would effectively undermine any true efforts at democracy.