1. Maybe I'd be more interested if I knew or in some way could identify with the people sharing quotes. So what about names being visible. Or:
2. Maybe I'd be more interested still if there was a way to filter by group. Christians might be interested in random quotes from other self-styled Christians. Atheists might be interested in god-debunking soundbites. Technophiles might be interested in "android v. apple" slugfests. And so on.
3. Maybe I'd also be interested if event-specific or news-specific quote voting were possible. E.g., I'm at a baseball game and I can follow people from all over the park sharing observations about players and hotdogs. Or there's an earthquake, and I can follow stuff about that. In this respect, you'd be doing something that makes Twitter interesting rather than just the thing that makes it boring, and the voting would be a real addition.
Caveat: complete novice here, in awe of people who can so readily conceive and execute an idea like this.