Send these petitions through a filter; so that offensive, ungrounded, and underdeveloped petitions may not be voted for.

You're looking for petitions you might support and what do you see? Petitions made by people who have not done any research, don't understand what they're saying, or are just trying to be downright offensive. As just a few examples, at the present there is a petition that asks to "order" an extremely expensive reenactment of the events on 9/11, as if anyone that lost family members on 9/11 would love to see it all happen again; or that this would be a financially responsible act. Another example is a petition asking to, please, arrest the entire GOP. Apparently unrealized is the fact that this would turn the government into a totalitarian state; by eliminating the only major party in opposition to the Democratic Party. Simply appoint someone to look through the rare petitions that appear.