  We investigate issues related to two hard problems related to voting, the
optimal weighted lobbying problem and the winner problem for Dodgson elections.
Regarding the former, Christian et al. [CFRS06] showed that optimal lobbying is
intractable in the sense of parameterized complexity. We provide an efficient
greedy algorithm that achieves a logarithmic approximation ratio for this
problem and even for a more general variant--optimal weighted lobbying. We
prove that essentially no better approximation ratio than ours can be proven
for this greedy algorithm.
  The problem of determining Dodgson winners is known to be complete for
parallel access to NP [HHR97]. Homan and Hemaspaandra [HH06] proposed an
efficient greedy heuristic for finding Dodgson winners with a guaranteed
frequency of success, and their heuristic is a ``frequently self-knowingly
correct algorithm.'' We prove that every distributional problem solvable in
polynomial time on the average with respect to the uniform distribution has a
frequently self-knowingly correct polynomial-time algorithm. Furthermore, we
study some features of probability weight of correctness with respect to
Procaccia and Rosenschein's junta distributions [PR07].
