When women let you pick the movie, it's not because they don't care what they're about to spend the next two hours watching. And it's generally not because they have exactly the same taste as you and trust you to make a good choice. It's because they love you so much that they want you to watch whatever you want. No compromises necessary.
A woman in love will sit through as many action films as you request. She simply loves cuddling up to you while it's playing. However, if you're in love with her too, she knows you'll sit through all the movies she wants to see, too. This is how the strongest partnerships work. It seems like such a small and insignificant decision, but it's ultimately about figuring out how to make both people happy.