  We study the complexity of reductions for weighted reachability in parametric
Markov decision processes. That is, we say a state p is never worse than q if
for all valuations of the polynomial indeterminates it is the case that the
maximal expected weight that can be reached from p is greater than the same
value from q. In terms of computational complexity, we establish that
determining whether p is never worse than q is coETR-complete. On the positive
side, we give a polynomial-time algorithm to compute the equivalence classes of
the order we study for Markov chains. Additionally, we describe and implement
two inference rules to under-approximate the never-worse relation and
empirically show that it can be used as an efficient preprocessing step for the
analysis of large Markov decision processes.
