Independence Axioms in Social Ranking

TL;DR

This paper analyzes various independence axioms in social ranking solutions, introducing new axioms and characterizing key solutions like lexicographic excellence and plurality through these axioms.

Contribution

It introduces two new independence axioms and provides a novel characterization of social ranking solutions using these axioms.

Findings

Characterization of lexicographic excellence and plurality solutions.

Identification of differences among social ranking solutions based on independence.

Introduction of two new independence axioms.

Abstract

Independence from non-essential changes in input information is a widely recognized axiom in social choice theory. This independence reduces the cost of specifying and/or analyzing non-essential data. This study makes a comprehensive analysis of independence axioms in the context of social ranking solutions (SRSs). We consider seven independence axioms (two of which are new) and provide a novel characterization of the lexicographic excellence solution and plurality by substituting these independence axioms in the existing characterization of the intersection initial segment rule. The characterizations highlight the differences among the three SRSs in terms of independence.