I have an idea. Every petition should have, as well as a place for showing your support, a place for showing your opposition. This will lead to a more balanced and fair outcome.
For example; suppose you want to persuade whoever is persuaded by petitions (probably no-one, but maybe I'm wrong) that every petition should have a place to sign if you agreee, and a place to sign if you disagree. And suppose that only one person in a hundred agrees with you, and the other 99 are anti. By reaching 100 million people (for example, by using Facebook, or this blog) you would amass your million signatures. But the person receiving your petition would rightly ask "But how many people are against this ingenious idea?"
By using this idea, you would be able to say "only one, and he's a bit of a scroat anyway". Without this idea, the 99 million against the idea are, effectively, disenfranchised, unless someone goes to the trouble and expense of organising a counter-petition.
You can show your support, or otherwise, in the comments.