Consistency, unanimity, and the Borda rule in social ranking

2026-05-18

AI Summary

This study addresses a central problem in social choice theory: how to fairly evaluate individual capabilities within coalition ranking frameworks while satisfying key axioms such as consistency and near-unanimity. The paper introduces, for the first time, a formal adaptation of the Borda rule into social ranking, proposing a novel Borda-type ranking solution. Developed through an axiomatic analysis, this solution satisfies weak consistency, near-unanimity, neutrality, and independence of irrelevant dummy participants within the domain of linear symmetric preferences. It effectively captures individuals’ relative capabilities within coalitions, offering a theoretically rigorous and interpretable tool for assessing individual contributions in coalition-based settings.

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.

Problem

• social ranking
• Borda rule
• consistency
• unanimity
• coalitional ranking

Innovation

• Borda rule
• social ranking
• consistency
• unanimity
• axiomatic characterization