Different evaluators typically disagree how to rank different candidates since they care more or less for the various qualities of the candidates. It is assumed that all evaluators submit vector bids assigning a monetary bid for each possible rank order. The rules must specify for all possible vectors of such vector bids the collectively binding rank order of candidates and the “payments” for this bid vector and its implied rank order. Three axioms uniquely define the “procedurally fair” ranking rules. We finally discuss how our approach can be adjusted to situations where one wants to rank only acceptable candidates.