Arkansas Crush is having an attraction, usually a mild to moderate intimate infatuation for a First or Second cousin. An Arkansas Crush doesn't mean that the individual wants to pursue the cousin sexually, however, the idea may cross one's mind.
Bo really has the Hots for his gorgeous cousin Daisy! He really has an Arkansas Crush on her!
When you have a crush on someone but there is one or more reasons why you can't date them, don't think it is worth trying to date them or not worth trying to get them to like you back. Usually occurs when you like someone you can't have.
In which case, most people would say, "I would like him/her if _____."
Jon: "So you hooking up with anyone?"
James: "Well, Emily is hot and I would hook up with her if she didn't have a boyfriend already."
Jon: "Sounds like you have a conditional crush."