- #1

Moes

- 72

- 7

- TL;DR Summary
- What is the argument of a third?

Many people debate the sleeping beauty problem, and seemingly there are many who take the thirder view. I don’t see how anyone can argue that the answer is anything but 1/2. Before she goes to sleep the probability of heads or tails is 50/50. The only argument I can think of, to say that anything changes when she is put to sleep and wakes up, is that she could think to herself what were the chances of her being woken up that day? Well if the coin landed heads it was only 50/50, so it would be a slight surprise that she was woken up that day, so shouldn’t she assume it landed tails in which case she was for sure going to be woken up? Well I don’t see this as an argument since the only time she could think to herself about the chances of her being woken up is the one time she is woken up, so it’s no surprise. Even if she was to be woken up just once in the next million days there is no surprise on the day she wakes up. She always knew there was a day she was going to be woken up. Therefore, she doesn’t get any new information when she wakes up, so her credence that the coin landed heads should still be 1/2.

As for the argument against the halfer view that if she is told it is Monday when she wakes up the chances of heads or tails should be 50/50, I think this is obviously wrong. If the coin landed tails it’s slightly surprising that it’s Monday, but if it was heads it was obviously Monday. So the odds should be that the coin probably landed heads. It’s easy to see this through the extreme case where she is woken up for the next million days if the coin lands tails. If she is told when she is woken up that it happens to be the one Monday that she would have been woken up whether the coin landed heads or tails, she should obviously assume the coin landed heads.

So what is the argument for the thirder position?

As for the argument against the halfer view that if she is told it is Monday when she wakes up the chances of heads or tails should be 50/50, I think this is obviously wrong. If the coin landed tails it’s slightly surprising that it’s Monday, but if it was heads it was obviously Monday. So the odds should be that the coin probably landed heads. It’s easy to see this through the extreme case where she is woken up for the next million days if the coin lands tails. If she is told when she is woken up that it happens to be the one Monday that she would have been woken up whether the coin landed heads or tails, she should obviously assume the coin landed heads.

So what is the argument for the thirder position?