I fail to see how this variation is going to settle the debate. Thirders will agree with your solution but halfers would disagree with it the same way as in the original sleeping beauty problem.
Halfers will ask why should beauty regard the four outcomes (HH, HT, TH, TT) equal probable? Yes they are equal probables if this is a simple tossing of two coins. Yet the experiment is far from that simple: my awakenings depend on it, the dime is being manipulated half way, my memory is erased after the first awakening....Halfers will say HH is never in the sample space to begin with, and there is no good reason to believe HT, TH and TT are equal probables. Beauty should just examine the information she has once waken up. She knew that she would definitely find herself awake in the experiment since the dime is manipulated, so right now being awake gives no new information about the Quarter, the probability ought to remain at 1⁄2. The same old dispute as in the original sleeping beauty.
Without trying to figure out the correct way to interpret today or this awakening the debate is not going to be settled. Some halfers (SSA) think this awakening shall be interpreted as a random awakening. Some thirders (SIA) think this awakening should be regarded as a random sample from all potential awakenings (thus being actually awake gives new information as the case of your argument). There are others (FNC) who think we should ignore indexicals such as today or this awakening all together but consider all objective information available. And I’m suggesting treating indexicals like fundamentals: they are primitively understood from the first-person perspective and irreducible. These are all attempts to solve the anthropic mystery. I don’t think this debate can magically go away just by using a different experiment setup.
I fail to see how this variation is going to settle the debate. Thirders will agree with your solution but halfers would disagree with it the same way as in the original sleeping beauty problem.
Halfers will ask why should beauty regard the four outcomes (HH, HT, TH, TT) equal probable? Yes they are equal probables if this is a simple tossing of two coins. Yet the experiment is far from that simple: my awakenings depend on it, the dime is being manipulated half way, my memory is erased after the first awakening....Halfers will say HH is never in the sample space to begin with, and there is no good reason to believe HT, TH and TT are equal probables. Beauty should just examine the information she has once waken up. She knew that she would definitely find herself awake in the experiment since the dime is manipulated, so right now being awake gives no new information about the Quarter, the probability ought to remain at 1⁄2. The same old dispute as in the original sleeping beauty.
Without trying to figure out the correct way to interpret today or this awakening the debate is not going to be settled. Some halfers (SSA) think this awakening shall be interpreted as a random awakening. Some thirders (SIA) think this awakening should be regarded as a random sample from all potential awakenings (thus being actually awake gives new information as the case of your argument). There are others (FNC) who think we should ignore indexicals such as today or this awakening all together but consider all objective information available. And I’m suggesting treating indexicals like fundamentals: they are primitively understood from the first-person perspective and irreducible. These are all attempts to solve the anthropic mystery. I don’t think this debate can magically go away just by using a different experiment setup.