Should You Be More or Less Convinced?

Tyler Cowen writes:

“Un-convinceable people are frustrating to talk to. But being around only convinceable people, you just end up at the average belief…I think I gravitate too much to the convinceable, finding the nonconvinceable too annoying except in very small doses.”

1) Is there such a thing as being a convinceable or nonconvinceable person? Or are we more likely to find that people are convincible in some areas while unconvincible in others? I.e., is “convincibility” a universal category?

2) Socrates claimed he was the wisest person because he knew that he knew nothing—and yet he was not all that convincible. Usually, it’s his interlocutors who end up saying, “Yes, Socrates. It is as you say.” Is Socrates “nonconvinceable”? If so, how do you square that with his purported humility?

3) If good relationships are rooted in reciprocity, what’s a better formula for a successful one (all else being equal): two equally stubborn, non-convinceable friends who hold opposite views or two equally open-minded convinceable friends who hold the same ones?