I think 1/2 argument makes essential use of the fact that the "2 people" are the same person at different times. Ultimately it comes down to a different idea of the way "being right twice" is valued. In the 1/3 position, the model is that each time you answer the question you get something good if you're right. In the 1/2 perspective, the idea is that after the whole experiment is over you either were simply correct or incorrect, and being correct twice doesn't count any extra.