  We consider the problem of finding the $k^{th}$ highest element in a totally
ordered set of $n$ elements (select), and partitioning a totally ordered set
into the top $k$ and bottom $n-k$ elements (partition) using pairwise
comparisons. Motivated by settings like peer grading or crowdsourcing, where
multiple rounds of interaction are costly and queried comparisons may be
inconsistent with the ground truth, we evaluate algorithms based both on their
total runtime and the number of interactive rounds in three comparison models:
noiseless (where the comparisons are correct), erasure (where comparisons are
erased with probability $1-\gamma$), and noisy (where comparisons are correct
with probability $1/2+\gamma/2$ and incorrect otherwise). We provide numerous
matching upper and lower bounds in all three models. Even our results in the
noiseless model, which is quite well-studied in the TCS literature on parallel
algorithms, are novel.
