So, EDI has a body. And Joker's interest is... well he's interested. And, in the couple of discussions I've had with EDI so far, she doesn't seem to be opposed. But I love to play the matchmaker and see new love blossom (and I do really want to see this ridiculousness), so how do I make sure that the two are united in human-robot love? Is there any conversations that I need to make sure I don't miss along the way? Would there be any way, heaven forbid, for me to accidentally CPU-clock-block, as it were?
Eventually, Joker will send an Email to Shepard asking to meet the commander in Purgatory. This is when you can convince him to go for it (or not go for it). There's no beating about the bush, Joker asks for your opinion, and you give it.
Or as my Shep said: "Why not?"