"Well, I accept you could mess with me if I didn't value two 1/2 chances of getting one apple, the same as 1/4 of zero plus 1/2 of one plus 1/4 of two.  But where was it said that I have to value two 1/2 chances of getting an apple, twice as much as I value one 1/2 chance of getting an apple?  We can stipulate that I value two apples twice as much as one, in cherries, that was said, but who says that packs of chances add up the same way?"

"Well, I accept you could mess with me if I didn't value two 1/2 chances of getting one apple, the same as 1/4 of zero plus 1/2 of one plus 1/4 of two.  But where was it said that I have to value two 1/2 chances of getting an apple, twice as much as I value one 1/2 chance of getting an apple?  We can stipulate that I value two apples twice as much as one apple, in cherries.  That was already said, but who says that packs of chances add up the same way?"