Paul_Gowder comments on Beautiful Probability - Less Wrong
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Uh, strike the "how would the math change?" question -- I just read the relevant portion of Jaynes's paper, which gives a plausible answer to that. Still, I deny that an actual practicing frequentist would follow his logic and treat n as the random variable.
(ALSO: another dose of unreality in the scenario: what experimenter who decided to play it like that would ever reveal the quirky methodology?)