Points:
1st: The USA would NOT have won a diplomatic victory after WWII. You had the whole Soviet bloc that wouldn't have voted for them, plus you had all of China that wouldn't have voted for them. I seriously doubt that the Soviet bloc and China would amount to less than 41%, seeing as how china at that time held between 1/4 and 1/3 of the world's population. France likely wouldn't have voted for the USA either, just out of spite. The USA may have gotten the vote for Secretary General (I have no idea), but if it were the Diplomatic Victory vote there would have been quite a few abstainers.
2nd: India would not win a diplomatic victory. Ghandi diplomicized the Brits out of there, but as far as global diplomacy?
3rd: The reason that the USA has -1 or worse relations now with so many nations is that the USA is the only superpower left. The world wants the USA to be dominant, but then complains about her dominance.
"USA - solve African hunger."
"USA - North Korea is up to no good again."
"USA - there was a Tsunami. We'll all chip in, but we expect more from you. That's all you can give? Sure - it's more than anyone else, but that's all?"
"USA - this country has gotten out of hand. We need you to send the most troops in, but they'll be under some other UN country's general. Oh - you don't like that? You think you should be in charge all of the time? We don't care that the general is sending your troops in without armor support in an area that clearly needs it. You're not in charge."
"USA - we know that you are feeding much of the world with your fishing and livestock and they'd go hungry without you, but we condemn your devastation of fishing waters and the treatment of your animals."
"USA - we condemn you invading Iraq for no good reason that most of us actually agreed with you on to begin with. What's that? You're closing your military bases in our country? We'll shut up now."
"USA - your greenhouse gases are killing the entire world. We realize that about half of the cars sold in the USA aren't American made, but we want to keep that money AND complain about your Greenhouse gases.
"USA - you won't get rid of the landmines in S. Korea. Please remove them so that we may then complain about the vast number of troops you had to put on the border to "protect" against an invasion."
"USA - please do something else that we can complain about. We're bored with our own country."
In other words, it's not half the world against the Soviets anymore. Now everybody's sites are on the USA. Most of the world hates the USA. Even half of the USA hates the USA. I swear, I think that the liberals just argue for the sake of arguing sometimes.
Republicans: We want to put forth an initiative to clean up America!
Liberals: Your initiative violates the civil rights of the people living in those areas. You are suggesting that the people in these areas are not as good as the people in "clean" areas.
Republicans: We're just trying to help.
Liberals: Go back to executing murderers you villians while we continue to support abortion, since we then get the women's vote. You can have the murderer's vote. Oh - they can't vote. Ha!
Republicans: But....
Liberals: Oh shut up.
[dramatization - may not have happened]
4th: China would not win a cultural victory. Their policies for thousands of years was one of isolation. Indeed - they even built a wall to further isolate themselves. Yes, they invented many things that are important today: gunpowder, paper, spaghetti. Yet those things were stuck in China until Europeans went there and brought them out.
As for today, being the world's only bastion of Communism that counts (I don't count Cuba, as that borders on a Dictatorship, plus they're insignificant except for their baseball team and their cigars) they still don't have relations good enough with the rest of the world to consider a cultural victory. Heck - they didn't even have great relations with their Soviet Communist brothers.
5th: The reason things worked so well in Japan was that the Emperor was left on the throne. Quite a shrewd move by Truman. Whatever the Emperor said, the people did. As for Germany, the ones in the west were just happy not being in the Red area. The ones in the east who caused trouble would be shot on site. Plus they were tired of the war, and knew that they were beaten.
6th: It is folly to say that the USA's culture is not one of the most dominant in the world. During the cold war, everybody in the Communist countries wanted US goods. People from all over the world come to Disneyland (or World - I get them mixed up).
Whether you agree that coffee and cheeseburgers are "culture", they ARE a way of life that was invented here and that "culture" has spread throughout the world. Ok, I don't buy the coffee thing. People want coffee whether Starbucks is there or not. Starbucks didn't invent the coffeehouse. But MacDonalds is huge, and is an American ideal. If they don't have a MacDonalds, they have their own thing. Plus - NYC is a culture all on it's own. How many great people have risen from there in the last century and a half since it took dominance over from Philadelphia?
Not saying that the USA should win a cultural victory - but let's not discredit her contributions just because we hate America. And that's another thing. We can say USA or America and it typically means the same thing. Doesn't really, but everyone around the world considers America to be the USA.
7th: Rome would NOT have won a domination or cultural victory. They have to control 70 percent of the territory, right? The known world at the time included India, China, all of Africa (not just Egypt), and whatever was in Russia at the time. They had little or no influence in any of those areas. That's not to mention that roughly 1/3 of the world was not yet discovered at the time. The game goes by control of a percentage of the whole world; not just the known world.
Ok, I'll stop now. Oh - and I notice that Astalder beat me to it on the superpower theory.