G+'s problem at it's root is that it's a FB clone. They copied the core functionality and tacked on a few specs that make it, literally, FB+1. The problem is no one is going to move their whole social network for FB+1 or FB+2. Google needed to build a product an order of magnitude better to win social.
There are plenty of colas that are +1 better then Coke but to take away Coke's base you'd need to be Coke+100.
The obvious solution is to stop trying to make a FB clone and do something else to get your ad demographics. I think they should stick with their core advantages and innovate in the vein of their own Adsense product:
(1) Users sign up with Google and volunteer their demographics.
(2) While signed in, Google tailors searches to them.
(3) Google gives the user a tiny percentage of the increased ad revenue. It's peanuts for most people so make it Google Play credit.
(4) If you're not signed in everything is anonymous.
Test run the whole thing on a smaller scale with Android users that already have Google accounts and (for many) credit card info on file.
Nielson families give up a lot of personal data about their viewing habits. This is rewarded with free cable, internet and cell phone service, heck they may even be paid. Even people that just take an hourlong phone survey about tv or radio are rewarded with $50+ checks. The reason market research companies pay this is because the data is extremely valuable to them and their clients. Obviously every web company wants to get that data "for free" like they do now but the giant tracking databases and all the personnel behind that certainly aren't free and create an adversarial relationship that can dilute your brand.