Your Two Coin Toss version is isomorphic to classical Sleeping Beauty problem with everything this entails.
The problem Elga solved in his paper isn’t actually Sleeping Beauty problem—more on it in my next post.
Likewise, the solution you propose to your Two Coin Toss problem is actually solving a different problem:
Two coins are tossed if the outcome is HH you are not awakened, on every other outcome you are awakened. You are awakened. What is the probability that the first coin came Heads?
Here your reasoning is correct. There are four equiprobable possible outcomes and awakening illiminates one of them. Person who participates in the experiment couldn’t be certain to experience an awakening and that’s why it is evidence in favor of Tails. 1⁄3 is unambiguously correct answer.
But in Two Coin Toss version of Sleeping Beauty this logic doesn’t apply. It would proove too much. And to see why it’s the case, you may investigate my example with balls being put in the box, instead of awakenings and memory erasure.
My problem setup is an exact implementation of the problem Elga asked. Elga’s adds some detail that does not affect the answer, but has created more than two decades of controversy.
Your Two Coin Toss version is isomorphic to classical Sleeping Beauty problem with everything this entails.
The problem Elga solved in his paper isn’t actually Sleeping Beauty problem—more on it in my next post.
Likewise, the solution you propose to your Two Coin Toss problem is actually solving a different problem:
Here your reasoning is correct. There are four equiprobable possible outcomes and awakening illiminates one of them. Person who participates in the experiment couldn’t be certain to experience an awakening and that’s why it is evidence in favor of Tails. 1⁄3 is unambiguously correct answer.
But in Two Coin Toss version of Sleeping Beauty this logic doesn’t apply. It would proove too much. And to see why it’s the case, you may investigate my example with balls being put in the box, instead of awakenings and memory erasure.
My problem setup is an exact implementation of the problem Elga asked. Elga’s adds some detail that does not affect the answer, but has created more than two decades of controversy.
The answer of 1⁄3.