That arose the other day with some aid+confusion provided by Jameson Quinn, is this. V voters each provide a score for each of C candidates (V*C scores in all) from some fixed set of allowed scores, e.g. the integer interval [0,1,2,...,9999]. Now plain "range voting" would be, the candidate with greatest average score, wins. We here instead consider this voting system, which might be called "(N,V) maxprob winner": If N voters were selected as a random subset of the V (0<N<=V) then the candidate with the greatest probability that his sample mean is maximal, wins. Note that if N=1, this is plain plurality voting. If N=V it is plain range voting. If done using pairs of candidates and N=1 then it is "Condorcet voting." So this is an interesting way to "hybridize" several proposed voting systems as one. Anyhow, QUESTION: is there any efficient algorithm to compute the (N,V) maxprob winner, or is this task #P-hard or NP-hard? (I have a pseudopolynomial time algorithm, i.e. if C and the score-set-cardinality are bounded, then it runs in polynomial time.) -- Warren D. Smith http://RangeVoting.org <-- add your endorsement (by clicking "endorse" as 1st step)