# How to compare two different rankings of same set of objects?

I have $N$ objects $A_1,\dots,A_N$. I have two algorithms that assign two different scores to each of this objects. Thus sorting on this scores gives me two different rankings of these same objects. Now how do I measure the similarity (or dissimilarity) of these different rankings in a visually understandable manner. Are their known approaches to this?

• A Spearman correlation would capture the ordinality in the agreement of the rankings. Visualizing that relationship could be as simple as creating deciles for each set of scores and cross-classifying them (i.e., a crosstab). Next, by highlighting with different colors the agreement on the diagonal versus the diagonal plus one or two deciles off and summarizing the percentages of each with a few numbers should communicate what you need. Oct 16, 2015 at 13:20
• What is the purpose of the comparison? Are these rankings according to different criteria, or are they supposed to use the same criterion, but made by different judges? ... Probably these matters. Oct 16, 2015 at 13:20
• These rankings are according to different criterion, but there should be certain natural things I expect in them. For instance, certain objects are really good and I naturally expect to them to score higher. However Algorithm 1's criterion doesn't reflect this whereas Algorithm 2 does. I do have a rigorous explanation of this effect. However, I don't have a nice way of putting the numbers. Oct 16, 2015 at 13:44