This paper reviews the recent literature on the “social ranking problem”, that is, the problem of converting group rankings into individual rankings. We introduce and categorize existing social ranking methods and we briefly explain their attributes. Three main categories of social ranking methods are identified: lexicographic social rankings, methods based on voting mechanisms, and those inspired by the theory of coalitional games. An open-source R package called socialranking for computing the majority of the existing social rankings is also presented and discussed.

We present an axiomatic study of various solutions to the social ranking problem, where a solution links any ranking of coalitions of players to a binary relation between individual players. We focus on solutions that align with the desirability relation, asserting that player i is more desirable than player j if any coalition including i but not j ranks higher than the corresponding coalition formed by replacing i with j . Unlike previous characterizations, our study highlights the central role of the desirability property as a foundational axiom in the characterization of five solutions from the related literature: Ceteris Paribus majority, lexicographic excellence and its dual, $$L^{(1)}$$ L ( 1 ) solution and its dual. Our main results reveal additional similarities among these five solutions and emphasize the essential features that should be considered when selecting the most appropriate solution for a given scenario. A practical application involving a bicameral legislature is also presented.