Hi Shahab, you mention two different things: (1) comparison of rankings, (2) choosing the best ranking. I have some experience in the field of identification of hazardous road locationswith.
For the first task there are various consistency tests, see for example here - https://www.researchgate.net/publication/41450878_A_comparative_analysis_of_hotspot_identification_methods
But the second task is a little bit tricky - in order to find the best comparison, you need to have some "ground truth" to compare with. I am not sure if you have this possibility in your field. If yes, epidemiological criteria may be used to find the ranking which is the closest to the "ground truth". An example: https://www.researchgate.net/publication/245562564_Comparative_Analysis_of_Techniques_for_Identifying_Locations_of_Hazardous_Roads
Article A comparative analysis of hotspot identification methods
Article Comparative Analysis of Techniques for Identifying Locations...
It depends on what data that you have on these two ranking methods, and how you want to define what makes a ranking system good, for example do you have some outcome data or do you just have data from the two rankings. If you just have the later, you can use some for of cross-validation. Depending on the specifics of what you are looking at, you might look at the netflix challenge literature (http://www.netflixprize.com/).
If correlation then Spearman's rank correlation is widely used (spearman's rho)
There are other tests depending on whether data is raw, initially not ranked or tests that will compare distributions, these could be Mann-Whitney Test, Wilcoxon Signed-Ranks Test, Kruskal-Wallis Test or Friedman Test
Really an extensive and supportive answer dear Jiří Ambros, but the link you suggested had only abstract, I request if you could provide full paper, please!!
Dear Daniel Wright, I Thanks for your reply, but I could not get the literature at netflixprize.com, for which you are recommending me to go through!!
If you can precisely tell me the methods?
i have books name as final output and the output came after the several steps of calculation and tricks, which is summarized in an algorithm, and two different techniques were suggested....?