I jump on these regularly, and always fill out my info. Would be really nice to cache that, so that I can just sign one and continue on.
How about it?
It would go something like this:
You are logged in and decide to participate in a petition. At that time, you can ask for your signature info to be cached so that future ones would auto populate.
There is a secondary option where a person can ask not to be asked again.
Then, you either use it or not. If you ask for the info to be cached, future petitions auto-populate, leaving you to just add value for that one, editing the bits you need to.