Tourism influence

So I know you need this to win a culture victory, but do the various levels actually do anything? I think it would be neat if the higher your influence over a civ was the better relations you had or more prosperous trade routes or something.

I'm not sure if it's tied to the levels (unknown, exotic, familiar, popular etc) but they do create ideological pressure if the two civilizations follow different ideologies. The party being dominated culturally will receive a nasty amount of unhappiness and may experience city flipping.