Social Ranking Problems at the Interplay between Social Choice Theory and Coalitional Games

Abstract

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.

Keywords

• social ranking
• coalitions
• power indices
• lexicographic relations