I have a ranking of 10 items from best to worst. Let's assume that the best is ranked 1 and the worst is ranked 10. Each item is ranked according to some rules that we cannot know so all we get is the ranking from 1 to 10.
We also have a factor that ranges from .5 to 1.5 that corresponds to some beneficial property one of the items could have (so 1.5 would be better).
We want to adjust the ranking according to the factor.
Is it fair to adjust the rankings by multiplying the rank of an item by 1/(factor) and then re-order them from best to worst? Or is this just going to make a large impact for the worst items and little to no impact for the best items?
Or is this something that is not even possible to implement given the circumstances?
If so would things change if we know that the ranking is determined based on the value of a linear function with larger being better?
Example for clarity: Ten rooms are filled with a random number of objects. Someone ranked them from 1 to 10 by the number of objects in each room. Room rank 1 having the most. We are only given the rank. Now we want to rank them based on the number of blue objects in each room to the best of our ability. We can assume that the best room divided by the worst room is no greater than 100.
We are given the proportion of blue objects for each room which ranges between .5 and 1.5 (and some rooms may have the same proportion). I know that 1.5 isn't a real proportion of blue objects but lets just say that somehow we find that the original counter missed that there were actually another .5 worth of blue items in the room.
What is the best method for re-ranking the rooms based on number of blue objects?