If a Koch brother really wants to use up $40 billion on voting, he could put 200,000 votes on a single issue. If everyone opposes his position, he could be easily outvoted by a small town of low-income people casting a couple votes each for a few dollars. They would also get nearly all his money.
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.