Inspired by a comment on this question.
Assume that I have an algorithm which uses ordinally scaled data. The algorithm in the original question was the solution of the Secretary Problem. It uses the ordinal data to maximize something.
Is there a heuristic which tells me how likely it is that the feeding the algorithm with the same data in reverse will deliver a result which minimizes something? Which criteria are a sign that this won't work?
Also, is the answer different for interval or ratio scaled data?
I will also accept an answer which says "there are too many possible criteria to find a meaningful heuristic", if this is the case.