How to know the list of people who gave a Google Plus One (+1) to the website. The Facebook likes people list are displayed when clicking the like count button, but +1 doesn't displays any user IDs that gave a plus? Any ideas?
I don't think it is possible to determine the identities of the people who gave a Google +1 to a website or URL, whether on your own website or one that you don't control. This wasn't announced until 27 Jun 2012 by Google, a long time after you asked your question! Now Google policy seems quite explicit (emphasis mine):
I don't know what Google-approved authorization procedure is referred to in the first sentence.
I'm not sure how this will be accomplished, other than by web crawlers, but Google sounds like they are serious about it:
Google Analytics and Google Webmaster Tools
Yes, it is true that you can get aggregated Google +1 activity data on your own websites from Google Analytics. The same is true for Google Webmaster Tools, for your own site or others:
However, Google Webmaster Tools also aggregates reports on +1 activity related to your content, so no further detail can be determined.
Blogger and other social sharing
As @mvark mentioned, on a Blogger blog, if one is the owner, the admin panel displays how many +1's were given to each post (URL). Sometimes the person's identity is disclosed. That seems to be dependent on a variety of factors that include
Here is a very recent page, from 29 October 2012, Google Developers, about Social Tracking. It has new information about Google+ tracking as well as Twitter and Facebook likes and un-likes. There is also a new Google+ private beta program, that might allow you to do what you requested, but I'm not sure who is eligible to participate in it.
There is no way you can get that,Google+ will give you the count but not the list of people with link to there Google+ Profiles.
You can find out with Google Analytics "Network Referrals". It includes "Social User Handle " and "User Profile URL".