How to reach legitimate decisions when the procedure is controversial

Imagine a group that faces a decision problem but does not agree on which decision procedure is appropriate. In that case, can a decision be reached that respects the procedural concerns of the group? There is a sense in which legitimate decisions are possible even if people disagree on which procedure to use. I propose to decide in favour of an option which maximizes the number of persons whose judged-right procedure happens to entail this decision given the profile. This decision rule is based not only on a profile in the standard sense, but in addition on a profile of judged-right procedures. To justify this decision rule, I present a set of simple axioms leading to it as the only solution.