I read this interesting experiment from The Origin of Wealth, a book by Eric B. Beinhocker (paraphrased):

Imagine that a stranger proposes you and me the following deal.  She will give us 5,000$ if we can agree on how to split it.  It works like this: I choose a split and you don't get to negotiate it, you can only accept the deal (in which case each of us gets what I chose) or reject it (in which case neither of us gets anything).

After giving it a short thought, I propose that I get 4,990$ and you get 10$.

Would you accept the deal?

(I'm not asking what you think is the rational thing to do from either a selfish or political standpoint, but what would you actually do.)