Think about it!
Of course this'd be hard to pull off, and may only be done on the Xbox 360/720 and the PS3/PS4, but it's not impossible.
EDIT: you guys seem to think that it has to be directly via the LIVE / PS network but what I was trying to say is that they could send the data from the game to a central server located at Bungie or Activision and work it that way. Software and hardware don't matter as they could send the same packets of player / enemy / etc positions to every console and have the game's engine translate it. Think outside the (x)box.
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I expect separate realms segregated by platform. This will also sort out some of the exclusive content everyone's been raging about. Most likely is that a user may have combined stats here on bungie.net Think about it, one can login using either network.