"conquer a woman?"
Beyond my disbelief at that comment, I would say if you ask a question then listen more than lip service to the answer. I think men and women want the same things. To be respected, listened to, receive courtesy and be honest in your feelings and be there in the moment.
I think you have the right idea, in that acting polite and being extra sweet will make a difference. But I think you have the wrong idea, in that women are not some sort of neuro-reflex that will always respond to xyz stimulus with abc results. Youll be very dissappointed in how quickly most women can tell the difference between obvious shallow manipulation (works for about 5 minutes) and failure to understand cooperation and synergy. You are not going to conquer anything in the long run. I cannot, however, deny that you will probably manage to get down some pants in the short term.
Your question made me think about the things men have said to me over the years......and the first one that popped into my head was how my youngest son always says "Hi beautiful" when he texts or calls me. We both know it is a "silly" little thing - but it never fails to put a smile on my face.
How nice of you to want to do this. I assume you have a girlfriend? Don't forget actions: opening doors, carrying items (yes, even her purse), and offering to do car washes, fill the tank (labor, not money). I love it when my bestie says "I want to take you out, so everyone can see you, you're beautiful"...that makes me gush a bit. Or he will refer to me as 'my girl',.. I like all those little niceties. We like to get dressed up and go out to dinner, and music venues. Now, if you're single and in a bar trying to pick up women for a hook up, it probably won't matter what you say. She's there for the same reason and eye contact will do it. But a serious couple should automatically compliment each other, because they want to, and not all compliments need to lead to the bedroom, respect each other more than that. Good luck!
Assuming that we already know each other or are dating, my suggestion is "That's a good idea / I hadn't thought of that / Looked at it that way, etc."
That said, in terms of pick-up lines for the sole sake of conquering or anything of the sort, nothing. It will all seem fake.
I'm with KK Gator--don't lie. Talk about her character. Does she have a kind heart? Is she compassionate? Does she do goot things for others? If so...when you SEE these things happening, tell her! "You know, that's something I REALLY LIKE about you! You're always kind to others." Etc. Of course...there's always this one...."You should see how the light shines on your hair tonight." Then SMILE!
Say something sincere that is real, not based on sex appeal or appearance..notice things about her, compliment her outfit, or something she did herself, etc. For example; I loved that piece you wrote for the country news section. It had some great ideas."
Or compliment her appearance without sexualizing it, such as, "That color brings out the blue in your eyes."
Given you say you are a political scientist and a philosopher I would have thought not coming off like a failed Machiavelli would have been a no brainer. While witty banter is always appreciated, given the example above, thinking before you speak or type would be a good start