- 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 criterion
  • The 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