I agree with your thoughts on this matter, I do believe America would be a good country to help mediate negotiations. We have seen 6 attempts and have only seen the Palestinian side deny the attempts. If the radicalist movement did not take control of their goverment policy, we would be able to see progress. There is no arab nation that would be able to sit down and mediate without experiencing consequences from other neighboring coutnires. The U.S. however is in a different role that supports it being a good candidate to handle mediations.
