I can't formalize my response, so here's an intuition dump:

It seemed to me that a crucial aspect of the 1/3 solution to the sleeping beauty problem was that for a given credence, any payoffs based on hypothetical decisions involving said credence scaled linearly with the number of instances making the decision. In terms of utility, the "correct" probability for sleeping beauty would be 1/3 if her decisions were rewarded independently, 1/2 if her (presumably deterministic) decisions were rewarded in aggregate.

The 1/2 situation is mirrored here: There are only two potential decisions (ruling out inconsistent responses), each applicable with probability 0.5, each resulting in a single payoff. Since "your" decision is constrained to match the others', "you" are effectively the entire group. Therefore, the fact that "you" are a decider is not informative.

Or from another angle: Updating on the fact that you (the individual) are a decider makes the implicit assumption that your decision process is meaningfully distinct from the others', but this assumption violates the constraints of the problem.

I remain thoroughly confused by updating. It seems to assume some kind of absolute independence of subsequent decisions based on the update in question.