The paper in question addresses the first criticism (of numbers). "However, the ability to reach large populations online means that even small effects could y

The paper in question addresses the first criticism (of numbers). "However, the ability to reach large populations online means that even small effects could yield behaviour changes for millions of people. Furthermore, as many elections are competitive, these changes could affect electoral outcomes. For example, in the 2000 US presidential election, George Bush beat Al Gore in Florida by 537 votes (less than 0.01% of votes cast in Florida). Had Gore won Florida, he would have won the election" "To put these results in context, it is important to note that turnout has been steadily increasing in recent US midterm elections, from 36.3% of the voting age population in 2002 to 37.2% in 2006, and to 37.8% in 2010. Our results suggest that the Facebook social message increased turnout directly by about 60,000 voters and indirectly through social contagion by another 280,000 voters, for a total of 340,000 additional votes. That represents about 0.14% of the voting age population of about 236 million in 2010. However, this estimate does not include the effect of the treatment on Facebook users who were registered to vote but who we could not match because of nicknames, typographical errors, and so on. It would be complex to estimate the number of users on Facebook who are in the voter record but unmatchable, and it is not clear whether treatment effects would be of the same magnitude for these individuals, so we restrict our estimate to the matched group that we were able to sample and observe. This means it is possible that more of the 0.60% growth in turnout between 2006 and 2010 might have been caused by a single message on Facebook." It's important to note that 0.14% of the population is the small number. It was 0.6% of the mobilized voting population and they got these results messaging 1/6 of the population. Furthermore they only report on effects that they could track and so all numbers are lower bounds.