In the past I frequently tried to begin arguments / discussions by carefully going over what I thought of as background assumptions. (To me, this is at least closely related to the proposed step 1, restate your opponent's position clearly.)
My experience suggests that if you do that, the other party will never stop disagreeing with you no matter how far up the chain you go. Many, many, many arguments never happened in my mind, while having happened quite heatedly in the other person's, because of this.
There was another phenomenon which might be related: a person would start telling me about a problem of theirs (I used to think it was weird for people I barely knew to do this, but I've come to suspect that people just like venting about problems they're experiencing), I'd rephrase it to be sure I understood what they were saying, and they would say something along the lines of "thanks, that was really helpful" and go away happy.
>>My experience suggests that if you do that, the other party will never stop disagreeing with you no matter how far up the chain you go.
Absolutely true.
There was a MOOC about argumenting at coursera I think. The proffessor had the same viewpoint. One of the lessons was that you have to start at a common reference point and argument from there. If you and the other person have no common reference points, you will never resolve your difference of opinion ever.
Regarding your last paragraph, people explain their current problems as a coping mechanism . But when people do that, what they're really looking for is someone to understand them. It's an emotional thing, and you provided it.
Moreover, paraphrasing is one of basic tools in psychotherapy. Obviously it's used as a part of a larger process, and depending on therapist' aims it may have various forms, from a clarification or a simple restatement, to a more reflective proposition or interpretation
Global warming debates are well-suited for this: first get the "denier" to agree that the physical mechanism is valid. If you can't agree on physics, then there's no point in continuing. If you can, great, at least he/she can't question the physical mechanism when they're back into a political/economic corner.
My experience suggests that if you do that, the other party will never stop disagreeing with you no matter how far up the chain you go. Many, many, many arguments never happened in my mind, while having happened quite heatedly in the other person's, because of this.
There was another phenomenon which might be related: a person would start telling me about a problem of theirs (I used to think it was weird for people I barely knew to do this, but I've come to suspect that people just like venting about problems they're experiencing), I'd rephrase it to be sure I understood what they were saying, and they would say something along the lines of "thanks, that was really helpful" and go away happy.