^No, we're going to need it all. I'll settle for nothing less than a full Dyson Shell, none of this pansy Dyson Ring or Dyson Cloud bullshit. I know! The petition will be worded so that there's enough asteroids in the solar system to complete the project, and also to change some laws of physics that would make such a project problematic.
Although, the main reason I want a Dyson Sphere, aside from it being awesome, is that the aliens won't be able to just abduct and probe people whenever they want. They'd have to make an appointment and wait for us to open the hatch. Maybe it would be easier to start a petition that would prevent he aliens from abducting people? Or, at the very least, when they abduct people, to not have such cold hands.