I have n measured rankings for k objects, which I want to combine such that the combined ranking maximizes the average correlation with the measured rankings. As correlation measures I need solutions for spearman's rank correlation and for Kendall-Taus.
The intention here is to find the upper limit on the average correlation for the given data to compare to the performance of various models & predictors.
I have searched through this webpage, wikipedia and some forums, but found only references to heuristic methods like averaging or taking medians etc. and many posts describing that you might come to different conclusions if you weigh the different rankings differently.
While this is all true, it does not solve my problem. So to emphasize the points how my question differs: 1) There is no weighting or different interpretation for the different rankings (think: I asked n people to rank these objects, all opinions are equally important) 2) The metric for what is the best ranking is clear: Maximize spearman rank correlation/ Kendall-taus. I am not searching for just any method which sensibly averages rankings.
I would be grateful for any hints to literature on how to do this!
P.S: I guess for spearman simply averaging the ranks should do the trick, but it would still be great to have a source confirming this (or tell me if it should be the median instead for example)