From New York Times:
“I asked Sasha Koren, the deputy editor of interactive news, whose bailiwick this is, about this. She and Bassey Etim, the community manager, responded:
Verified commenters are selected algorithmically based on the breadth and quality of the comments they have submitted over time. First, we require a certain number of total submissions over the course of their entire commenting history for the Times, and we also require a certain number of submissions over the past few months. Then, in both of those categories, we require a very high percentage rate of comments approved by our moderators versus those rejected.
There is no human intervention in the selection process besides the setting the parameters outlined above. However, verified status can be revoked from users for either a flagrant violation of our commenting rules or a series of violations that follow a warning from the Community team.”