So how do we reconcile these studies?
Google does itself no favors
The Burst study seems to substantiate similar findings from GlobalWebIndex and Nielsen seems to substantiate ComScore data. There isn't even a clear consensus among studies. And while I'm prone to believe that Nielsen probably has a better understanding of representative sampling than the other studies (and data that isn't self-reported), it's difficult to buy into any of them because they're so dissimilar. If you've ever zeroed a rifle by triangulating your shot groups, you realize that the further removed each individual shot is from the others the less confident you can be about your aim. And that's an apt analogy for these disparate numbers around G+.
The fact that Google Plus is a subdomain of Google (plus.google.com) probably doesn't do them any favors, nor does the fact that their internal numbers are more extraordinary than the most bullish data that comes out. The truth is, if you want to know what's truly going on with G+, you'll probably be left wanting.
But I don't think that network size the point of or the best argument for Google Plus.....
17th century philosopher Blaise Pascal developed an argument (called "Pascal's Wager) for believing in God. The good contributors to Wikipedia explain his argument like this:
"Given the possibility that God actually does exist and assuming the infinite gain or loss associated with belief in God or with unbelief, a rational person should live as though God exists and seek to believe in God. If God does not actually exist, such a person will have only a finite loss"
The pragmatic case for Google Plus has a lot of similarities to Pascal's Wager.
Like rooting for your favorite sport team, you can argue that Google Plus is bigger or smaller than anything else. But our understanding of the methodology of any study is slight and our experience and biases are a poor bellwether for the state of social media. Much like Pascal's wager, faith in Google Plus is irrelevant to its ability to influence search and drive business. You have to believe that there is far more to lose by ignoring G+ than by participating on it, and that there is a possibility for bigger rewards (engagement, attribution, search discovery) by participating.
I'm curious to know what you make of this data or of G+ in general? Have any insider information about any of these being more accurate than the others?