**Greg Gandenberger**

Frequentists appear to be committed to the sufficiency principle (*S*) and the conditionality principle (*C*). However, Birnbaum (1962) proved that (*S*) and (*C*) entail the likelihood principle (*L*), which frequentist methods violate. To respond adequately to Birnbaum’s theorem, frequentists must place restrictions on (*S*) and/or (*C*) that block Birnbaum’s proof and argue that those restrictions are well motivated. Restricting (C) alone will not suffice, because (*S*) by itself implies too much of the content of (*L*) to be compatible with frequentist methods. Specifically, frequentists need to restrict (*S*) so that it does not apply to mixture experiments some of whose components have respective outcomes with the same likelihood function. Berger and Wolpert (1988, p. 46) claim that such a restriction would be artificial, but in fact it has a strong frequentist motivation: reduction to the minimal sufficient statistic in such an experiment throws away information about what sampling distribution is appropriate for frequentist inference. On the other hand, frequentists face difficult challenges in trying to state the restriction they need in a precise and general way.