The leader of a very large country, like the United States or the Soviet Union, can have a greater positive influence on the world just by being a fraction of a percent nicer than the average person, than the leader of a small country, or a private individual, can have by being an amazing saint (Obama).
On the other hand Robin Hanson will vote against Obama even in a simple election because he, in Hanson's judgement, started a war unjustifiably.
Some dictator or lunatic who mellows out and murders less than usual probably has a very large beneficial effect on the world, compared to his usual murder rate (Arafat and the Israelis).
The "slightly less of a warmonger than you used to be" prize? I don't think the mission is quite that poorly defined! That said, he shared that year's prize with some Israeli folks so it was more a bipartisan honor for a specific act than in honor of the person. That is perhaps justifiable.
A reminder for everyone: on this day in 1983, Stanislav Petrov saved the world.
It occurs to me this time around that there's an interesting relationship here - 9/26 is forgotten, while 9/11 is remembered. Do something charitable, and not patriotic, sometime today.