I once went to a talk in which Christopher Zeeman modelled this behaviour using catastrophe theory. I'm not sure you need the mathematics for the thesis, which was (roughly) that arguing for your position pushes people towards it in their underlying beliefs, but also pushes people to be more defensive about their initial beliefs (because it's a conflict situation). When they go away afterwards and calm down, they may find that they have moved towards your your position ... without necessarily remembering the argument as having any part in it.

He claimed to have applied this theory successfully to push a committee he was on, by making a big fuss months before the final decision on the topic was needed.