Arrow's impossiblity theorem also demonstrates the fallacy of claiming that it is impossible to prove a negative.
Firstly Mike, Arrow's impossiblity theorem is derived from Social Choice theory.
Any social science is in fact pseudoscience in my book. I'm surprised you consider it to be a real science when it depends mainly on questionnaires, surveys and the like.
It has been said whoever makes a claim carries the burden of proof regardless of positive or negative content in the claim. In that spirit, I can show you no proof of god because nobody has ever found any, even the Turin shroud is a fake. That is reasonable proof of a negative unless someone can come up with a positive, right?
More sensibly, rejecting or disproving the null hypothesis is the way to go.