I'm sorry for, pointing out how popular isn't the best choice of word?

But no matter how you slice it, popular isn't a great descriptor. Whether you choose the prescriptivist "the dictionary says x thus the word means x no matter what" or the descriptivist "most people use the word to mean y thus the word means y no matter what", in this case they both agree.

Both groups agree that when I say "Jim is popular" it makes you think that people generally like Jim. It evokes some level of communal approval. The dictionary literally defines the word to mean likeable, and the general usage still seems to denote general approval.

So either way, it doesn't represent the Empress situation. A situation where the majority of the community at best doesn't care and at worst openly dislikes her as a person because of her behavior, but still comes back for the games. She has a monopoly, but that doesn't make her inherently popular. Most people who know seem to dislike, and most who don't will also have no bearing on her popularity.