So, if you find yourself thinking this person you are arguing with is an idiot, you are likely to get more out of the argument by trying to understand where the person is coming from and what their motivations are.

Having spent some time on the 'net I can boast of considerable experience of arguing with idiots.

My experience tells me that it's highly useful to determine whether one you're arguing with is an idiot or not as soon as possible. One reason is that it makes it clear whether the conversation will evolve into an interesting direction or into the kicks-and-giggles direction. It is quite rare for me to take an interest in where a 'net idiot is coming from or what his motivations are -- because there are so many of them.

Oh, and the criteria for idiotism are not what one believes and whether his beliefs match mine. The criteria revolve around ability (or inability) to use basic logic, tendency to hysterics, competency in reading comprehension, and other things like that.