Too clever by halfing

We offer three arguments against the halfing response to the sleeping beauty problem. First, we outline an epistemological version of the sure-thing principle. Roughly: if it's certain that the probability of E should be r, whichever of some distinct (predetermined) options obtains, then the probability should be r simpliciter. We show that double-halfers violate this principle. Second, we outline a principle of framing-invariance. Roughly: probability assignments should not depend upon mere artefacts of how we frame a scenario. We show that single-halfers violate this principle. Third, we show that any halfer who respects the framing-invariance principle must either give up their intuitions about “irrelevant” evidence or violate basic statistical reasoning.