Anyone know of empirically driven lobbying efforts?

I was recently in an argument with a friend about the efficacy of WhiteHouse.gov petitions. He was disappointed that atheists hadn’t pushed the Free Alexander Aan petition up to 25,000 signatures and thought this was a bad sign for future projects. I thought it wasn’t a very good ‘ask’ so it was reasonable for otherwise committed activist to ignore it. He ended up pulling Pascal’s Mugging by arguing “nothing tangible may ever happen as a result, but we don’t know that, and it does send a palpable signal either way.”

I was annoyed, but I also noticed I couldn’t think of any GiveWell equivalent for advocacy efforts. I was pretty confident that this WhiteHouse.gov petition was a waste of time, but I wasn’t sure whether I’d prefer for a cause I supported to focus on petitions, voter education, wacky stunts to up coverage, etc etc. I’ve seen plenty of studies on how to get people to sign petitions, but none on whether they work.

The Human Rights Campaign used to run into a lot of criticism for just wining and dining legislators instead of getting pushier or focusing on electing new allies, but, when DADT was killed, the pundits seemed to think the strategy had paid off. It looks like no one is very good at predicting which lobbying techniques will work, just popping in at various timepoints, seeing whether the policy changed, and passing or failing the outreach effort on that basis.

I’m actually a researcher for a consumer protection group that does a fair amount of lobbying, and it can feel a little like a cargo cult over here. It feels a bit like we just try to keep an issue in view (through visits, press coverage, etc) so that when Congress or a regulatory body lumbers into action, they might think of our pet issue.

Government gridlock is out of our hands, so the metrics we track (number of signatures on a petition, press citations of our work, social shares of data infographics) are meant to be proxies for our influence, but I’m not aware of any heuristic we use to check which align best with the regulatory results we’re actually seeking.

Has anyone seen interesting data on this or have heuristics they use when deciding which advocacy efforts to support and promote?