Ryan, thanks for responding, but I may have not been clear in my question. Your answer is about domain authority for the ultimate destination of the link; let's say http://bit.ly/xyz redirects to http://www.seomoz.org/q/are-url-shorteners-building-domain-authority-everytime-someone-uses-a-link-from-their-service

And let's say 20 people on tweet the http://bit.ly/xyz link, and the text of several of those tweets is reproduced (link included) on eight websites. Does http://bit.ly 's domain authority increase as a result of those 20 tweets and eight website links?

My understanding of domain authority is that the more links pointing to any page / resource on a domain, the greater the overall domain authority (and weight passed from outbound links on the domain) is.

Because URL shorteners create links on their own domain that redirect to an off-domain page but link "to" an on-domain URL, are they gaining domain authority each time someone publishes a shortened link from their service? Or does Google penalize these sites specifically, or links that redirect in general? Or am I missing something else?

Ryan, thanks for responding, but I may have not been clear in my question. Your answer is about domain authority for the ultimate destination of the link; let's say http://bit.ly/xyz redirects to http://www.seomoz.org/q/are-url-shorteners-building-domain-authority-everytime-someone-uses-a-link-from-their-service

And let's say 20 people on tweet the http://bit.ly/xyz link, and the text of several of those tweets is reproduced (link included) on eight websites. Does http://bit.ly 's domain authority increase as a result of those 20 tweets and eight website links?