I don’t think that works? Or at least I’m missing something.
I do not see how your “without loss of generality” holds. If B > A, your ‘correct’ response with a monotonically increasing function becomes an incorrect response with a monotonically decreasing function—and with two distinct random reals the probability of this happening is… 50%. (At least in cases where this is probability is even defined...)
It’s not clear to me what you’re trying to say. Do you have a concrete counterexample in mind, e.g. an algorithm for ROB to follow, alongside a monotonically increasing function of your choice, such that the math does not give a strictly >50% accuracy for any agent which replies “yes” with probability determined by the function in question?
I don’t think that works? Or at least I’m missing something.
I do not see how your “without loss of generality” holds. If B > A, your ‘correct’ response with a monotonically increasing function becomes an incorrect response with a monotonically decreasing function—and with two distinct random reals the probability of this happening is… 50%. (At least in cases where this is probability is even defined...)
It’s not clear to me what you’re trying to say. Do you have a concrete counterexample in mind, e.g. an algorithm for ROB to follow, alongside a monotonically increasing function of your choice, such that the math does not give a strictly >50% accuracy for any agent which replies “yes” with probability determined by the function in question?
Long story short, I misinterpreted the question. (I was thinking it was trying to predict if ROB chose A > B or A < B)
Long story short, I misinterpreted the question.