The complexity of the Kth largest subset problem and related problems

We show that the Kth largest subset problem and the Kth largestm-tuple problem are in PP and hard for PP under polynomial-time Turing reductions. Several problems from the literature were previously shown NP-hard via reductions from those two problems, and by our main result they become PP-hard as well. We also provide complementary PP-upper bounds for some of them.