Carter has done great work promoting peace, international development and works within the US, even if his politics are still controversial (ie his last books).
Arafat (who won with Rabin), for all his faults, turned the PLO from a terrorist organization to the recognized, moderate authority for Palestine. He was willing to negotiate with Israel (and Rabin was willing to recognize Palestian issues).
Gore was a funny choice, as he was more an environmentalist (particarly after 2000) than a peacemaker, but he did something.
Obama did what exactly so far? The Nobel Peace Prize has officially jumped the shark.