Women and Empathy: Is there a Difference?

I was struck by President Obama's appointment of Judge Sonia Sotomayor as Supreme Court Justice this morning. In choosing her, he affirmed that he was looking for a woman as well as a person who held a "different sense of justice", by which I understood that he was seeking out someone who would listen to the legal issues of the day with a certain empathy that may be harder to attain in a man. I had dinner with a friend from law school over the weekend, who has been a Superior Court Judge for 12 years. She readily admitted that she believes women bring a heightened sense of empathy to negotiation, and when acting as a mediator. I personally attributed my empathetic leanings to being a mother. Isn't that part of the job description? And yet, Judge Sotomayor is apparently single and without children. So is there a true genetic difference? I have recently taken an advanced training by Dana Curtis (also a woman, and I don't know if she's a mom) on empathy. It was based upon very specific steps which will open both the listener and disputant to a sense of empathy at every level of the negotiation (including the money side after insulting offers and demands were exchanged). As usual, I don't have the answers to these questions, but I'm undertaking an updating of my old "gender and negotiations" talk to study the specific question of "Learning Empathy: Can Men Learn to Listen Like Women and Women Learn to Speak like Men?" Do they/we want to?