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 so…
People will be more likely to vote in the first place because they can exert greater influence over the outcomes they care about (say, gay marriage). Once in the voting booth, they can use marginal votes against things they oppose but less passionately (say, farm subsidies). Of course, there are complex design issues--just how much should people vote about, and should a representative system be used instead. But on balance QV should motivate people to vote more not less.