Two steemians have set up a new metric to work out Authority on Steemit. See the following post:
The idea is that UA should by harder to game than reputation (reputation is simply based on the rshares of the people who have upvoted you and is easy to purchase).
You can check your UA on the following site:
https://steem-ua.com/ (you will need to log in via steemconnect).
According to the site my ua is 2.660 and I have a ua rank of 13646.
I shall be trying to improve this in the next few weeks, not least because they are going to start giving upvotes to those with high user authority.
It does look like UA is based partly on the authority of those who follow you and upvote you - someone described it a bit like Google Page rank in that pages rank based on how many important pages are linking to it. So in theory the more followers you get, and the more upvotes, the greater your authority.