[Terr_]

I think the point is that the different planned stopping rules of each researcher--their subjective thoughts--should not affect what we consider the objective or mathematical significance of their otherwise-identical process and results. (Not unless humans have psychic powers.)

It's illogical to deride one of those two result-sets as telling us less about the objective universe just because the researcher had a different private intent (e.g. "p-hacking") for stopping at n=100.

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> According to old-fashioned statistical procedure [...] It’s quite possible that the first experiment will be “statistically significant,” the second not. [...]

> But the likelihood of a given state of Nature producing the data we have seen, has nothing to do with the researcher’s private intentions. So whatever our hypotheses about Nature, the likelihood ratio is the same, and the evidential impact is the same, and the posterior belief should be the same, between the two experiments. At least one of the two Old Style methods must discard relevant information—or simply do the wrong calculation—for the two methods to arrive at different answers.