Real world examples of the sleeping beauty paradox

Question

The Sleeping Beauty problem is a thought experiment concerning a participant, Sleeping Beauty, who is woken once or twice based on the flip of coin and is asked her degree of belief on the coin having come up heads. Extensive analysis here. It seems to me that this is a philosophical question about the nature of truth. The objective truth is that $Pr(H) = 1/2$ however Sleeping Beauty is best to operate under the belief that $Pr(H) = 1/3$ to win any kind of betting game. This belief is not just dependent on the nature of a coin but also subjectively depends on the situation in which she finds herself.

Now the Sleeping Beauty problem comes across as a very contrived problem. Are there any real world analogues to this problem? Either one you can devise or one that actually hapened?

Answer 1

My candidate for a real-world analogue: "How likely is it that there is intelligent life elsewhere in the universe?"

To simplify things, assume that God picked the fundamental physical constants at random. Assume that there was a 50% chance of picking values which would result in a universe hostile to life, where intelligence would only evolve on one planet (corresponding to Sleeping Beauty being woken up only once), and a 50% chance of picking values which would result in a universe friendly to life, where intelligence would evolve millions of times (corresponding to Sleeping Beauty being woken up multiple times.)

Then the question of whether the evolution of intelligence on our own planet should increase our probability that values friendly to life were picked corresponds to the question of whether Sleeping Beauty should consider her own waking up to be evidence that she is woken up multiple times.

To make my description of this scenario correspond better to reality, replace the random variable "which of these two hypothetical sets of physical constant values were picked" with the random variable "how probable is the evolution of intelligent life on a random planet given the laws of physics."

One objection to my argument would be: Sleeping Beauty knew going in that she would be woken up, but we didn't know that we would evolve until after we did. My reply: if we modify the Sleeping Beauty problem setup so that she doesn't initially know she's part of the experiment, and the experiment is only explained to her each time she is woken up, I don't think that fundamentally alters the paradox.

You could make the case that the question of how likely it is that we live in a computer simulation similarly corresponds to the Sleeping Beauty question.