  STV and ranked pairs (RP) are two well-studied voting rules for group
decision-making. They proceed in multiple rounds, and are affected by how ties
are broken in each round. However, the literature is surprisingly vague about
how ties should be broken. We propose the first algorithms for computing the
set of alternatives that are winners under some tiebreaking mechanism under STV
and RP, which is also known as parallel-universes tiebreaking (PUT).
Unfortunately, PUT-winners are NP-complete to compute under STV and RP, and
standard search algorithms from AI do not apply. We propose multiple DFS-based
algorithms along with pruning strategies, heuristics, sampling and machine
learning to prioritize search direction to significantly improve the
performance. We also propose novel ILP formulations for PUT-winners under STV
and RP, respectively. Experiments on synthetic and real-world data show that
our algorithms are overall faster than ILP.
