I read an article somewhere (CFC maybe) about favorite and shunned governments. I think it has to do with the AI's attitude toward you.
Example: I don't know each civ's favorite and shunned governments, so I'm just going to make some up. Say you're playing as the Russians. Their favorite government, I believe, is Communism. One of your neighbors is the Americans, whose favorite government is Democracy and shunned government is Communism. If you (Russia) becomes a Communism, America will lower its attitude toward you.
On the other hand, you might play as India, whose favorite government is Democracy. If you and America both become Democracies (sp?), America's opinion of you will sky-rocket (or just increase by a little).
I don't know the exact math, but I think the article about it is in the War Academy at CFC.
I hope this helped.
Here it is.
CFC: AI Attitude Exposed