logic problem (fixed wording cuz i suck)

[d10]

The cancellation principle is an axiom of Subjective Expected Utility theory, which states that if A>=B, then A+C>=B+C. I believe that OP and possibly his girlfriend is a bit confused about the application of this principle in this problem. It is actually an example of when the cancellation principle doesn't hold to be true. According to Ellsburg's paper, where this ball problem originally appeared, people were much more inclined to choose option a given the first pair (bet on red as opposed to black, or R>B), and option b given the second pair (bet on black and yellow as opposed to red and yellow, or B+Y>R+Y). According to the Cancellation principle, if B+Y>R+Y, then B>R, but this was shown to be not true.