  We study the optimization problem of selecting numerical quantities to clean
in order to fact-check claims based on such data. Oftentimes, such claims are
technically correct, but they can still mislead for two reasons. First, data
may contain uncertainty and errors. Second, data can be "fished" to advance
particular positions. In practice, fact-checkers cannot afford to clean all
data and must choose to clean what "matters the most" to checking a claim. We
explore alternative definitions of what "matters the most": one is to ascertain
claim qualities (by minimizing uncertainty in these measures), while an
alternative is just to counter the claim (by maximizing the probability of
finding a counterargument). We show whether the two objectives align with each
other, with important implications on when fact-checkers should exercise care
in selective data cleaning, to avoid potential bias introduced by their desire
to counter claims. We develop efficient algorithms for solving the various
variants of the optimization problem, showing significant improvements over
naive solutions. The problem is particularly challenging because the objectives
in the fact-checking context are complex, non-linear functions over data. We
obtain results that generalize to a large class of functions, with potential
applications beyond fact-checking.
