I'm not a big fan of the Nobel committee's decisions, but given the pressures they face and the confusion of their task I don't think they've done a ridiculously inadequate job.

Hypothetically, if Nobel had been a sociopath and instituted a "Nobel War Prize" or "Nobel Deadly Conflict Prize" with an equally poorly defined mission, how inadequately would you judge their work had they given the award to exactly the same recipients as were actually awarded the Peace Prize?

The 2004 prize went to Wangari Maathai "for her contribution to sustainable development, democracy and peace". She was reported by the Kenyan newspaper Standard and Radio Free Europe to have stated that HIV/AIDS was originally developed by Western scientists in order to depopulate Africa.

The 1989 prize was awarded to the 14th Dalai Lama. This wasn't well-accepted by the Chinese government, which cited his separatist tendencies. Additionally, the Nobel Prize Committee cited their intention to put pressure on China.

The 1945 prize was awarded to Cordell Hull as "Former Secretary of State; Prominent participant in the originating of the UN". Hull was Franklin Delano Roosevelt's Secretary of State during the SS St. Louis Crisis. The St. Louis sailed from Hamburg in the summer of 1939 carrying over 950 Jewish refugees, seeking asylum from Nazi persecution. Initially, US President Franklin D. Roosevelt showed some willingness to take in some of those on board, but Hull and Southern Democrats voiced vehement opposition, and some of them threatened to withhold their support of Roosevelt in the 1940 election. On 4 June 1939 Roosevelt denied entry to the ship, which was waiting in the Caribbean Sea between Florida and Cuba. The passengers began negotiations with the Cuban government, but those broke down at the last minute. Forced to return to Europe, over a quarter of its passengers subsequently died in the Holocaust.

You forgot my favorite case!

The 1973 prize went to North Vietnamese leader Le Duc Tho and United States Secretary of State Henry A. Kissinger "for the 1973 Paris Peace Accords intended to bring about a cease-fire in the Vietnam War and a withdrawal of the American forces". Tho later declined the prize. However, North Vietnam invaded South Vietnam in April 1975 and reunified (This is not sufficiently euphemistic. I suggest replacing "reunified" with "happy-fuzzified-togethernessed" -Ed.) the country. Kissinger's history included the secret 1969–1975 campaign of bombing against infiltrating North Vietnamese Army troops in Cambodia, the alleged U.S. involvement in Operation Condor—a mid-1970s campaign of kidnapping and murder coordinated among the intelligence and security services of Argentina, Bolivia, Brazil, Chile (see details), Paraguay, and Uruguay—as well as the death of French nationals under the Chilean junta. He also supported the Turkish Intervention in Cyprus resulting in the de facto partition of the island.[citation needed] According to Irwin Abrams, this prize was the most controversial to date. Two Norwegian Nobel Committee members resigned in protest.[97][98] When the award was announced, hostilities were continuing. (Emphasis added)

Digressing somewhat...

The leader of a very large country [...] 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

I suspect you mean "...a fraction of a percent nicer than the average candidate for that leadership position."

Though perhaps it should be "...a fraction of a percent nicer than whoever would have otherwise held the position."

Or perhaps not? Perhaps the right comparison is actually between the results of what they did do (take the position and act as nicely as they did) and what they could have done (act more nicely, or less nicely, or abdicate in favor of someone better qualified, or whatever).

I'm genuinely uncertain, here. It's difficult, when comparing actualities to counterfactuals, to establish clear criteria for what counterfactuals to use.

Additionally, it seems unclear whether the Peace Prize is primarily meant to reward or to encourage efforts toward global... let's say "altruism", since "peace" seems too narrow. There have been controversial awards falling into both categories (Kissinger's was unambiguously the former), but controversy over the latter seems to make the news more consistently.

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.