A Ceteris Paribus Borda Solution to the Social Ranking Problem

Rachel Ruellé, Stefano Moretti, Ozturk Meltem

Keywords: Social Ranking, Coalitional Ranking, Borda, Axiomatic Approach, CP Majority

TL;DR: We introduce and axiomatically characterize a solution to the social ranking problem over individuals based on a Borda score computed using CP comparisons of coalitions.

Abstract: In our society, individuals are often rewarded based on their merits when they work in cooperation. Therefore, we need to design solutions that can fairly rank individuals based on their contribution to the success achieved by alternative groups or coalitions. In this paper, we focus on a novel social ranking solution where individuals are ranked based on the pairwise comparison of coalitions that differ for one single element (denoted in the related literature as Ceteris Paribus (CP-)comparison). We first introduce a set of axioms inspired by voting theory and social ranking to establish properties that a solution should satisfy when only a limited number of coalition is considered. Then, we show that our set of axioms uniquely characterizes a new solution that mimics a Borda rule computed over a coalitional preorder. These axioms include the one of desirability, a very well-established property in the setting of coalitional games but never used before in connection with a Borda rule. The other axioms, specifically neutrality, separability, and cancellation, are standard properties reflecting eponymous axioms in voting theory. Although a Borda score-based solution shows a cardinal feature, our axioms, which we also prove to be logically independent, are strongly rooted in an ordinal coalitional setting defined over a variable domain of possible coalitions. Connections with another solution from the literature on social ranking (CP-majority) reflecting a majority principle over the same type of CP-comparisons, are also illustrated.

Area: Game Theory and Economic Paradigms (GTEP)

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Submission Number: 453