Given that most people are quite resistant to changing their minds, the most skilled debater is the one that gets the most people to change their mind, rather than the one that gets the most people to agree.
I was thinking of debate, more as a persuasive technique than as a way of discovering the truth. Changing my mind is easy -- the powers of advertising, manipulation, coercion, etc., are all highly refined arts. Arriving at the truth is harder, even if "truth" is merely a plausible choice of one alternative over another.
It seems possible that if stubbornness is a acquired trait, it is one because it confers a survival advantage.
A silly distinction - the most skilled debater is the one who makes you think their idea is the best.