See 3.1 in my old tech report: https://www.fhi.ox.ac.uk/wp-content/uploads/Anthropic_Decision_Theory_Tech_Report.pdf
I have an idea about non-fiction example of sleeping beauty—do you think it will be a correct implementation:
A person is in a room with many people. He flips a coin, and if it is heads he asks one random person to guess is it head or tails. If it is tails, he asked two random people the same question. Other people can’t observer how many peoples were asked.
You’re rediscovering some classics ^_^
That problem addresses some of the issues in anthropic reasoning—but not all.