- Kendall tau distance: equal to the total number of steps to migrate from the first to the second ranking by reversing adjacent pairs of objects
- Kemeny (Kendall + ties): counts the number of interchanges of couples of elements that are required to transform one (partial) ranking into another
- Spearman
- Multinomial Logit
Algorithm - rank aggregation with ties
- Ailon 3/2
- BioConsert (top all-rounder. Alternatives are mostly for extreme situations)
- BnB
- BordaCount (great when short run-time matters when few ties are involved)
The Borda count satisfies the monotonicity criterion, the consistency criterion, the participation criterion, the resolvability criterion, the plurality criterion (trivially), reversal symmetry, and the Condorcet loser criterionThe Borda count does not satisfy the Condorcet criterion, the independence of irrelevant alternatives criterion, the independence of clones criterion, the later-no-harm criterion, or the majority criterion.- Chanas
- ChanasBoth
- CopelandMethod
- FaginDyn
- ILP
- KwikSort (best quality results for extremely large datasets (also being positively influenced by similarity of datasets)
- MC4
- MEDRank (excellent candidate when short run-time matters and many ties are involved)
- Pick-a-Perm
- RepeatChoice
Algorithms - Top K
- Spectral MLE
- PageRank
- Rank Centrality