It seems important to distinguish between actually voting, where everyone votes or has a chance to vote (at near-zero cost), and lobbying for individual legislation, where only the very highly-motivated "vote", at high cost.

In the latter case (lobbying), most people seem to believe that small groups exert too much power over the process. But that's entirely because the majority have essentially zero influence. If some small industry has an intense preference for a special tax break, they would easily be defeated if everyone else expressed their mild disapproval. The problem is not that the rich get too many votes, but that the first vote is too costly.

In ordinary voting, the opposite situation is more likely. A small group of people are very passionate about some issue (gay marriage, drug liberalization, environmental protection), while the majority doesn't know or care very much, but is slightly negative on average. In that case, the weak preferences of the majority win out, giving an inefficient outcome. This is where Quadratic Voting could help.