If p0>p1+ε, then in the setting with no malign hypotheses (which you assume to be safe), 0 is definitely the output, since the malign models can only shift the outcome by ε, so we assume it is safe to output 0. And likewise with outputting 1.
I’m pretty sure removing those is mostly just a technical complication
One general worry I have about assuming that the deterministic case extends easily to the stochastic case is that a sequence of probabilities that tends to 0 can still have an infinite sum, which is not true when probabilities must ∈{0,1}, and this sometimes causes trouble. I’m not sure this would raise any issues here—just registering a slightly differing intuition.
This is very nice and short!
And to state what you left implicit:
If p0>p1+ε, then in the setting with no malign hypotheses (which you assume to be safe), 0 is definitely the output, since the malign models can only shift the outcome by ε, so we assume it is safe to output 0. And likewise with outputting 1.
One general worry I have about assuming that the deterministic case extends easily to the stochastic case is that a sequence of probabilities that tends to 0 can still have an infinite sum, which is not true when probabilities must ∈{0,1}, and this sometimes causes trouble. I’m not sure this would raise any issues here—just registering a slightly differing intuition.