Cyrus Shepard reports on the Moz Blog that this year, for the first time, the Moz Data Science Team measured the correlation between Google +1s and higher rankings.
They discovered that after Page Authority, a URL's number of Google +1s is more highly correlated with search rankings than any other factor. In fact, “the correlation of Google +1s beat out other well known metrics including linking root domains, Facebook shares, and even keyword usage.”
In addition, Searchmetrics, another firm, used a slightly different methodology and found Google +1s to be the highest-correlated factor they studied.
They also make some recommendations about how to use Google+ to optimize SEO. Included in these are to follow great people, comment on posts, and share great content, making longer Google+ posts, as well as adding the rel="author" meta tag to your website or blog.
Another important factor is to post public. Posts shared privately don't pass the same juice as publicly shared post. Shepard concludes by saying that the point is not to go out and accumulate a bunch of +1s, but that earning a link on Google+ is like earning any other type of editorial link, and these links have actual value with real benefits.