Does anyone know how "Improve Relations" works?

I've been experimenting with it (trying various amounts, then reloading the save and trying other amounts). As near as I can tell, a successful use adds 8 sympathy points and a rejected attempt drops sympathy by 1-3 points. The smallest amount anyone has accepted has been 10,000 gold, but that only happened once out of 4-5 attempts. I've yet to see 30,000 gold fail out of at least as many tries.

I'm using the Battle Mod, so I don't know if that changes anything (one of the mod's effects is a reduction in the effectiveness of diplomatic buildings, so it may alter other sympathy bonuses).