  The rank aggregation problem has received significant recent attention within
the computer science community. Its applications today range far beyond the
original aim of building metasearch engines to problems in machine learning,
recommendation systems and more. Several algorithms have been proposed for
these problems, and in many cases approximation guarantees have been proven for
them. However, it is also known that some Markov chain based algorithms (MC1,
MC2, MC3, MC4) perform extremely well in practice, yet had no known performance
guarantees. We prove supra-constant lower bounds on approximation guarantees
for all of them. We also raise the lower bound for sorting by Copeland score
from 3/2 to 2 and prove an upper bound of 11, before showing that in particular
ways, MC4 can nevertheless be seen as a generalization of Copeland score.
