Each ballot rates each candidate Top, Bottom, or Other (the abstention default). For each candidate X let TopX) be the number of ballots on which X is rated Top, and Bot(X) the number on which X is rated Bottom. Let RBTP(X) and RBBP(X) be the respective Random Ballot Top and Bottom Probabilities for X, where each ballot B contributes to the respective probabilities an amount 1/(nk) or 1/(nj), respectively, where k and j are the respective numbers of candidates rated Top and Bottom on B with X ... and without X the contributions are zero. Naturally Top ratings are counted as approvals. Additionally ballot B approves candidate X rated neither Top nor Bottom on B if TopLightness(B)/BottomHeaviness(B) is less than Top(X)/Bot(X), where TopLightness(B) is the sum of the values RBTP(Y) for Y rated Top on B, and BottomHeaviness(B) is the sum of the values RBBP(Z) for Z rated Bottom on B. So now Approval(X) is the number of ballots on which X is rated Top plus the number of ballots on which X has been promoted to approval status from the other category. Let W=argmax Approval(X). If W is uncovered, elect it ... otherwise elect from among those X's that cover W, the one with the greatest approval .... unless this X is also covered ... etc. There it is! -Forest