RedBlue bills itself as an "an exciting yet safe way to engage directly with someone on “the other side” of the political spectrum."
The idea is to pair participants with their ideological counterparts, then provide an opportunity for constructive dialogue by having each read a fictional scenario and then for them to engage each other in a computer-facilitated discussion. Apparently, the "moderator" is designed to help participants avoid dead-ends, to help them find common ground.
RebBlue is now accepting beta-testers (embedded request at bottom).
Sounds like an interesting experiment, though I imagine participants would have a selection bias towards moderates. I wonder whether such techniques would have much effect at all on the more ideologically extreme.