Something along the lines of: if x is your number say yes (1-1/x) % of the time? Anything that makes your likelihood of saying yes increase as x gets bigger. Given two numbers, you thus would have been more likely to say yes to the larger number.
Flips a fair coin (under the same “this is a quick way to say ‘the ROB has a private random oracle’ assumptions as the arbiter has and game-theory in general requires”). If heads: A=0.25/B=0.75, otherwise A=0.75/B=0.25.
Something along the lines of: if x is your number say yes (1-1/x) % of the time? Anything that makes your likelihood of saying yes increase as x gets bigger. Given two numbers, you thus would have been more likely to say yes to the larger number.
Consider a ROB that does the following:
Flips a fair coin (under the same “this is a quick way to say ‘the ROB has a private random oracle’ assumptions as the arbiter has and game-theory in general requires”). If heads: A=0.25/B=0.75, otherwise A=0.75/B=0.25.
This is indistinguishable from a ROB that always returns those two numbers in a consistent order.