Consistency, unanimity, and the Borda rule in social ranking

TL;DR

This paper introduces a new Borda-type social ranking solution that evaluates individual competence based on properties like consistency, unanimity, neutrality, and independence of perfunctory participation within social choice theory.

Contribution

It characterizes a novel Borda-based social ranking solution satisfying key properties and extends the framework of social ranking with a new, theoretically grounded method.

Findings

Characterized a Borda-type social ranking solution with key properties.

Proposed a new social ranking method based on Borda rule.

Ensured the solution's neutrality and independence of perfunctory participation.

Abstract

The social ranking is a recently proposed framework for evaluating the power of individuals according to the performance ranking of their coalitions. Although its origin can be traced to the classical power indices in simple games, social ranking approaches carry out this evaluation within the ordinal framework of social choice theory. This article introduces the Borda rule into social ranking. Specifically, we focus on two essential properties of the Borda rule--consistency and closeness to unanimity--and investigate the social ranking solutions (SRSs) satisfying these properties. Among several possible definitions of the Borda rule as an SRS, we characterize one of such solutions by (a weak version of) consistency, closeness to unanimity (under the linear and symmetric domain), neutrality (i.e., names of the individuals do not matter), and independence of perfunctory participation (i.e., adding a perfunctory coalition into the worst class of the coalitional ranking does not affect the social ranking). We therefore propose a new Borda-type SRS for evaluating the competence of individuals in coalitional contexts.