Testing for differential ranking between lists relative to a reference list I am interested in comparing ranked lists in order to find elements that are differently ranked. Suppose we have 10 lists, each ranked (and for simplicity assuming the elements overlap and only the ranking was different). What method could I apply to find elements with high ranks in list1 that consistently have low(er) ranks in all the other lists?
The background here is that each of these lists represent outputs from differential testings from experiments that cannot be directly compared to each other as confounders exist between them that are nested with the effect we want to compare. Hence, I would like to at least prioritize elements that in the given reference list ranked highly (and therefore were very significant or "important" in experiment1), but have low(er) ranks in all other experiments, suggesting that this element was "unique" to experiment 1, meriting downstream experiments with these elements.
For elements consistently ranked highly I would use RobustRankAggregation or the Rank Product calculation, but what about actually finding differences in ranked lists? Obviously one could simply take the topX elements from list 1 and calculate something like the variance for their ranks across the other lists, but I am hoping for a method that is more sophisticated. If possible links to respective implementations/packages in R would be appreciated.

My suggestion is to first confirm that there is indeed a difference in the ranking between two lists.  This could be accomplished using something like Cohen's kappa-coefficient (though I would suggest a weighted kappa).  This is essentially asking to build a contingency table with the items and their paired rankings.  Then, this contingency table is assessed for something like an inter-rater reliability.
If you confirm that the rankings are substantively different, then you can asked which items are truly being ranked differently simply by looking at how far the items are from the diagonal of the contingency table.
Next, if you wish to do a pairwise comparison for each of your 10 rankings or so (this is probably reasonable for a relatively small number like this), you can build a list of how often and how far away from the diagonal any one item is for each of the possible pairings...but I would only use those that indicated reasonable differences for the rankings.
For packages to help with this, the psych package in R has a function for kappa calculations.
Happy to clarify as needed.
