* Emphasize that the goal is fairness. You're not negotiating out of a sense of greed, just a desire that the transaction be fair.
* Focus more on having a good BATNA (best alternative to the negotiated agreement) than on being good at negotiating. In particular, this means try to have multiple offers before you start negotiating any of them. Some of my most stress-free negotiations have been when I essentially just acted as an intermediary middleman between two (or more) parties.
* The outcome of the negotiation is dependent on the least skilled negotiator, not the most skilled. Some of my most stressful negotiations have been against people who cared more about getting the proper respect or not losing face vs getting a good outcome. It's gotten to the point where it's just too stressful negotiating with bad negotiators. It's easier to just say no.
The goal of the negotiation is to find the sweet spot that fits both ranges. There shouldn't be anything personal about it (as in the author's hilarious example).
If your ranges don't converge, then you're in the wrong meeting.