Pardon for my English, I also agree that the measurement on the game is really impractical and I have been wanting to ask this to Firaxis. However as of now, I think that might be the only way the game able to present the quantitative measurement on how a culture embraced by other countries. I mean, how would you measure how people embrace a culture other than being a fan of something and do some touristy visits to the country ? IRL, would it be like the Grand Tour or England in Victorian era where people all over the world came to study and do businesses ? I don't know but is there any other measurements that could measure a culture victory than this? Language ? What do you think ?
I think, we'd better let people studying the field of culture or arthropology to answer your wonder.
I cant call myself well informed in this field but I will still try to contribute my opinions.
I supposed, cultural influence can be shown by similarities in the people's activities. It could be of a wide range. From worshipping the same religion, listening to songs from the same composers, down to the usage of common vocabularies, etc.
My emphasis is the "similarities" because there are always "differences", even if you are already under heavy influence by another culture.
Take the example of the roman languages. They all originated form the same latin root, but they have their local influence that eventually all themsevles to develop into numerous european languages.
Therefore I would propose cultural influence is the similarities towards foreign culture vs differences rised from local culture. Thats why I think the tourism against local culture theory is a measure on the right track. Just there are staffs better than tourism that can reflect this.
For example, vocabulary composition of a language: like English vocabularies contain 50% latin derivatives, Spanish vocabularies contain 90% derivatives, etc.
But it is not possible to do so in the game, as the whole culture is just a simplified measure. You cannot look at the language, people's dressing style, art, separately.
They do take in measure of the religion, policy and ideological differences. The deeper part of the culture is too hard to be made. Thus I suppose the simple tourism mechanism is good enough.
Or you have to revolutionize the game entirely.