According to the moz.com editor Cyrus Shepard, the number +1's received by a page greately influences that page's position in Google.
Dr. Matt Peters and the Moz Data Science Team measured the correlation between Google +1s and higher rankings.
The results were surprising.
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.