The Byzantine Genitals

You are the emperor of Byzantium (lucky you!) and you have N genitals working for you. You know that more than half of your genitals are loyal, and the rest are traitors. You can ask any genital about the loyalty of any other genital: If the genital you ask is loyal, he will answer correctly, but if he is a traitor he can answer however he likes. Your goal is to find one genital you are absolutely certain is loyal while asking the fewest possible questions.
What is the minimum number of questions (in terms of N) that will guarantee a solution, and what strategy produces it?

Anyway — that’s how I read it.