Of course, there are plenty of frequentists in the world, but I presume they are uninterested in the Sleeping Beauty problem, since to a frequentist, Beauty’s probability for Heads is a meaningless concept, since they don’t think probability can be used to represent degrees of belief.
To make the concept meaningful under Frequentism, Luna has Beauty perform an experiment of asking the higher level experimenters which awakening she is in (H1, T1, or T2). If she undergoes both sets of experiments many times, the frequency of the experimenters responding H1 will tend to 1⁄3, and so the Frequentist probability is similarly 1⁄3.
I say “apparently Frequentist” because Luna doesn’t use the term and I’m not sure of the exact terminology when Luna reasons about the frequency of hypothetical experiments that Beauty has not actually performed.
Tangent: I ran across an apparently Frequentist analysis of Sleeping Beauty here: Sleeping Beauty: Exploring a Neglected Solution, Luna
To make the concept meaningful under Frequentism, Luna has Beauty perform an experiment of asking the higher level experimenters which awakening she is in (H1, T1, or T2). If she undergoes both sets of experiments many times, the frequency of the experimenters responding H1 will tend to 1⁄3, and so the Frequentist probability is similarly 1⁄3.
I say “apparently Frequentist” because Luna doesn’t use the term and I’m not sure of the exact terminology when Luna reasons about the frequency of hypothetical experiments that Beauty has not actually performed.