“What you are proposing is equivalent to adding an extra binary variable d to the model, and replacing the observation R(y, Monday) or R(y, Tuesday) with R(y, d). That in turn is the same as randomly choosing ONE day on which to wake Beauty (in the Tails case) instead of waking her both times”—Yes, that is equivalent to what I’m proposing by saying that only one day “counts”. I’ll explain why this formalism is useful in my next post.
“What you are proposing is equivalent to adding an extra binary variable d to the model, and replacing the observation R(y, Monday) or R(y, Tuesday) with R(y, d). That in turn is the same as randomly choosing ONE day on which to wake Beauty (in the Tails case) instead of waking her both times”—Yes, that is equivalent to what I’m proposing by saying that only one day “counts”. I’ll explain why this formalism is useful in my next post.
But randomly awakening Beauty on only one day is a different scenario than waking her both days. A priori you can’t just replace one with the other.