This is really the kind of thing where A/B testing is both necessary and straightforward. Decently intuitive arguments can be made for both sides and there isn't really overwhelming strength on either of them.
What, pray tell, is the hypothesis to be tested? Whether "my" or "your" results in more clicks? How do we know they aren't clicks borne of confusion? Whether "my" or "your" users visit the site more often? Over what time frame? A day? A week? A year? A decade?
A/B testing isn't magic fairy dust that settles design questions. You need to have a clear hypothesis to test. It's especially difficult if the design question concerns long-term perceptions and psychology. An A/B test in this situation is anything but straightforward.
I'd be interested to learn about how this design decision was made in the companies that have had to face it.
It seems like this would also change per application, in which case A/B testing could really help you understand how users are thinking about and interacting with your program / tool / application. I think both of the paradigms that Dustin brings up in his article are good and there are applications I use that fall into both camps. Just as an example, SimpleDNS is a tool where I work on my stuff. Facebook is a social network where I got to interact with lots of stuff and the Your feels more appropriate there*
* Interestingly enough, it seems like most of the major platforms have moved away from using either "my" or "your" altogether, eg Facebook and Twitter both just have Friends, Followers, Tweets, Photos, etc.
A/B testing isn't magic fairy dust that settles design questions. You need to have a clear hypothesis to test. It's especially difficult if the design question concerns long-term perceptions and psychology. An A/B test in this situation is anything but straightforward.
I'd be interested to learn about how this design decision was made in the companies that have had to face it.