Over the course of the game, I repeatedly encouraged both Jeff and EDI to pursue a relationship. However, at many junctures, I had options that seemed to discourage the two of them from getting together. I could either try to make Jeff be more cautious (and avoid injury) or stomp out EDI's blossoming emotions/humanity.
Not to spoil anything major, but judging from late game cutscenes, it seems kind of "hard coded" that they're going to get together. If I'd been overly negative towards the both of them, could I have changed anything between them? Or is this just the way the game plays out, regardless of my input?
Best Answer
If you had discouraged them from getting together they would have remained friends but not developed a romantic relationship.
The pivotal sequence for the Joker-EDI romance relationship occurs after Priority:Citadel 2. When you encounter Joker in the bar you have a final chance to discourage the relationship.
If you do then they will not then if Joker survives the crash of the Normandy in the final sequences (eg if you have a high enough EMS) then EDI will not accompany him.
I had read this a few days ago while looking for other information and it's mostly confirmed by the Mass Effect Wiki.