An analysis published in The Atlantic sought to test a hypothesis whether Mitt Romney’s Twitter followers are real or whether they display ‘bot-like’ behaviour. This follows a sudden recent spike in followers to his account. The same analysis was completed for Barack Obama’s account as well. So, are Mitt and Barack’s followers real?

The analysis looked at the number of incoming nodes (followers) a Twitter account has — its indegree. They looked at the indegree distribution of the 150,000 most recent followers of Mitt Romney and Barack Obama, and the twenty accounts closest to them in size, to see if each candidate’s account differed from the typical distribution for accounts their size. The article explains:

Accounts that are likely to be bots will tend to have a small indegree. … As a result, these fake accounts tend to have 0, or at least very few followers. Based on this, we looked at the proportion of new followers with low follower counts as a proxy for determining the proportion of the accounts that were likely to be “followers for hire.” More sophisticated bot networks can use algorithms to follow each other in an attempt to mimic indegree distribution of authentic users. But since our method tests for how distributions differ, it can detect any notable deviation from the expected distribution, not merely the over-presence of accounts with small indegree we would expect from unsophisticated bots.

The results? For Romney:

According to a random sample of 1000 followers from the candidates’ accounts, 26.9% of Romney’s 150,000 newest followers had fewer than 2 followers. For other accounts of similar size, only 9.6% of new followers had less than 2 followers themselves. The median number of followers for Romney’s new followers was 5, whereas the median for the comparison group was 27. … the p-value on this was 0.0000. … In short, the degree distribution of Romney’s new followers is strongly indicative of a concentration of bot or bot-like followers.

Whereas, for Obama:

New followers of Obama tended to have more followers than those of comparison accounts. The median number of followers for Obama’s cohort was 7, while the median number in the comparison accounts was 6. Additionally, we found no statistically significant difference between the distribution of followers among those who had recently followed Obama and those who had recently followed other accounts of the same size.

The article is very clear to point out that they aren’t suggesting the Romney campaign is buying followers. They suggest “perhaps (conspiratorially) someone else was buying them to make Romney look bad”.

Read the article for a fuller explanation and to see graphs of the distributions.

Source: Statistical Probability That Mitt Romney’s New Twitter Followers Are Just Normal Users: 0%.