On my blog powered by WordPress, I see a "g +1" button with a counter next to it. Is there a way to find all the public posts that shared my article?
No. While it is possible on WordPress powered blogs to see certain information about your posts that were shared using other services e.g. Reddit, Digg, it is not possible with Google Plus posts.
Google has a very clear policy (finally!) about this. While you can get certain information from Webmaster in aggregate, Google won't reveal information on individuals who mark the Google+ button for a URL on your site:
Publishers may not attempt to discover the identity of a Google+ button user unless the user consents to share his or her identity with the Publisher via a Google-approved authorization procedure. This prohibition includes identifying users by correlating Google+ button reporting data from Google with Publisher data.
That seemed to be your question, but the title was slightly different...
Did you want to know who shared your WordPress posts, by URL, on the Google Plus platform?
The answer to that is still no, you can't get that information, not in a comprehensive way. This is why: Your post(s)
- could have been marked +1 by someone and only shared with others by email, which may done directly from a website, or
- could have been marked +1 without sharing it in a post.
Even if the post were shared on the Google+ platform, if it is shared in any way other than publicly, it isn't discoverable.
If it is shared publicly in a post on Google+, there may be a way to find it using Google's own user interface with Sparks or even through a developer API. I have found that it is easier, on an ad hoc basis, to check Topsy. Topsy allows searches for public Twitter content and Google Plus content, no other services than those two. Topsy is free for manual queries. Topsy also offers searching in other languages, not just in English. I have been able to locate public shares of URLs from my WordPress blog, and other blogs, that were +1 button'ed and shared by using the Topsy basic service.
For example, if I wanted to search for occurrences of this website URL on Google Plus:
I could append
/link to the end, or several other choices. If I wanted to do the same search for that URL on Twitter:
/link or several other options, see left sidebar of Topsy.